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Layered Basket Option Hedging

Currency risk management for multinational corporations

- Sandvik AB -

Master Thesis in Corporate Finance

Authors: Gustav Carlsson & Robin Ericsson

Tutors: Andreas Stephan & Louise Nordström

Jönköping May 2012

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Acknowledgement

This thesis would not have been possible without the guidance and help of several

individuals who in one way or another contributed and extended their valuable assistance

in the preparation and completion of this study.

First and foremost, we wish to express our gratitude to the personnel at Sandvik Financial

Services, and above all, to Thomas Hamberg for taking an interest in us and making this

study possible.

We would also like to thank our tutors Andreas Stephan and Louise Nordström, for giving

us support and guidelines throughout this thesis.

Last but not least, we want to offer our sincerest gratitude to our fellow students for all the

feedback received during this study.

Gustav Carlsson Robin Ericsson

Jönköping International Business School 2012

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Abstract

Master Thesis within Business Administration

Title: Layered Basket Option Hedging Authors: Gustav Carlsson & Robin Ericsson Tutors: Andreas Stephan & Louise Nordström Date: Jönköping May 2012 Key words: Currency risk, Hedging, Options, Basket, Forwards, Diversification

Background: In an increasingly globalized environment, corporations perform

transactions across borders on a day-to-day basis. As multinational corporations expand

their businesses the number of currencies in their operations increases. The consequence of

operating with several currencies is the risk associated with currency fluctuations. Sandvik

AB is a worldwide corporation where activities are conducted through representation in

more than 130 countries. Currency exposures are controlled through risk management

where financial derivatives are applied to protect the corporation from potential losses

caused by fluctuations. Sandvik AB recently implemented a hedging strategy entitled

Layered Basket Option hedging. The strategy is a combination of a layered- and a basket option

approach to maximize the effect of the hedge. There is a limited amount of previous

research regarding Layered Basket Option hedging and Sandvik AB is the first corporation

to actively practice this strategy.

Purpose: The purpose is to investigate and provide information about how currency risk most effectively is

hedged for the multinational corporation Sandvik AB. Furthermore, we want to evaluate if Sandvik’s

recently implemented hedging strategy, Layered Basket Option hedging, is the best-suited strategy for them

and if there are any improvements to be made. This thesis will further investigate the importance of currency

hedging for multinational corporations, which are dependent on reporting to their stakeholders. Hopefully,

this thesis will also facilitate the communication of Sandvik’s currency strategies throughout the organization

and make it more comprehensible.

Method: Exchange rates on daily basis for the period 2002-2012 were collected from Bank

of Canada and Reuters database. The collected data was thereafter used as a basis to

perform calculations to determine if Layered Basket Option hedging is the optimal solution

for Sandvik AB.

Conclusion: The results of this study highlight the benefits from applying a Layered

Basket Option hedging strategy and the strategy succeeds to reduce the volatility caused by

currency fluctuation. The results indicate that the combination of a layered- and a basket

option approach successfully creates a suitable strategy for Sandvik AB.

Furthermore, this thesis has recognized that there exists room for improvement by actively

allocating currencies according to their weights and correlations to fully exploit the effects

from the strategy.

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Definitions

Correlations A statistical measure determining how assets or currencies move together. Currency peg Refers to a fixed relationship between currencies

Derivatives Financial instruments used to hedge risks. Options and forwards are examples of derivatives.

Exotic option An option that differs from vanilla option in the form of underlying assets or payoff. A basket option is a form of exotic option.

Exposure Refers to the risks associated of operating with different currencies.

Layered hedging Hedges with the same expiry date are entered at regular intervals.

Risk free rate The rate of return with zero risk, where government bonds are an indication of the risk free rate.

Rolling hedging To continuously create hedges between regular intervals with different execution dates.

Spot rate The current price of an asset or currency

Strike price The price at which an instrument can be exercised.

Time to maturity The time until a financial contract expires.

Value at Risk (VaR) The magnitude of adverse outcomes that occur with a specified probability in a specific time interval.

Vanilla option Is a call or put option with standardized terms and no unusual features.

Weight The amount of a single currency in a basket proportionally to other currencies. The weight can both be positive and negative.

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Table of Contents

1 Introduction ................................................................................. 1

1.1 Background............................................................................................... 1

1.2 Sandvik AB ............................................................................................... 2

1.3 Problem discussion .................................................................................... 3

1.4 Purpose .................................................................................................... 4

1.5 Research questions ..................................................................................... 4

1.6 Delimitations ............................................................................................. 4

2 Theoretical Framework................................................................. 5

2.1 Hedging currency risk ................................................................................. 5

2.2 Options .................................................................................................... 5

2.3 Black-Scholes ............................................................................................ 6

2.4 Basket options ........................................................................................... 7

2.5 Minimum variance portfolio (MVP) .............................................................. 8

2.6 Systematic & non-systematic risk .................................................................. 8

2.7 Layered hedging ......................................................................................... 9

2.7.1 Layered vs. Rolling ................................................................................... 10

2.8 Layered Basket Option Hedging ................................................................. 10

2.9 Forward contracts .................................................................................... 11

2.10 Alternative methods ................................................................................. 11

2.10.1 Value at Risk (VaR) .................................................................................. 12

2.10.2 Futures contracts ..................................................................................... 13

2.10.3 Currency swaps ....................................................................................... 13

3 Method ...................................................................................... 14

3.1 Research approach ................................................................................... 14

3.2 Research design ....................................................................................... 15

3.3 Secondary data ........................................................................................ 15

3.4 Primary data ............................................................................................ 16

3.5 Materials used in the financial analysis ......................................................... 17

3.6 Method for developing a financial analysis ................................................... 17

3.6.1 Correlation .............................................................................................. 18

3.6.2 Standard deviation ................................................................................... 18

3.6.3 Risk free rate ........................................................................................... 18

3.6.4 Weights .................................................................................................. 18

3.6.5 Minimum variance Portfolio ...................................................................... 19

3.6.6 Black-Scholes .......................................................................................... 20

3.7 Assumptions ........................................................................................... 20

3.8 The layered hedging approach .................................................................... 21

3.9 The effects of applying a basket ................................................................. 21

3.10 Alternative hedging strategies ..................................................................... 22

3.11 Improved baskets..................................................................................... 22

3.12 Manipulation of variables to realize the actual effect of changes ...................... 22

3.13 Criticism of theories and models ................................................................ 23

3.14 Reliability and validity ............................................................................... 24

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4 Empirical Findings .................................................................... 25

4.1 Sandvik’s hedging purposes ....................................................................... 25

4.2 Standard deviation ................................................................................... 25

4.3 The MVP approach .................................................................................. 26

4.4 The premium using Black-Scholes .............................................................. 26

4.5 The total result of the hedging strategies ...................................................... 27

4.6 The results of the Layered Basket Option .................................................... 29

4.7 The results of the Layered Forward ............................................................ 30

4.8 Manipulated baskets ................................................................................. 30

4.9 The effects of applying a basket ................................................................. 31

4.10 Improved baskets – Divided Layered Basket .................................................... 31

5 Analysis ..................................................................................... 34

5.1 Incentives to hedge .................................................................................. 34

5.2 The Layered approach .............................................................................. 34

5.3 The Basket approach ................................................................................ 35

5.4 The Layered Forward approach ................................................................. 36

5.5 The Layered Basket Option approach ......................................................... 37

5.6 Improvements ......................................................................................... 39

6 Concluding Remarks .................................................................. 41

6.1 Conclusions ............................................................................................ 41

6.2 Discussion and further studies ................................................................... 42

7 List of References ....................................................................... 43

8 Appendices ................................................................................ 47

8.1 Appendix 1-10 Basket Variance, Weights and Premiums 2003-2012 ................ 47

8.2 Appendix 11-20 – Correlation 2003-2012 .................................................... 57

8.3 Appendix 21-22 – Improvements, 2011 Q4 ................................................. 67

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List of figures

Figure 1, Black-Scholes Diagram .................................................................................................... 7 Figure 2, Layered hedging .............................................................................................................. 10 Figure 3, Rolling hedging ................................................................................................................ 10 Figure 4, Standard Deviation ......................................................................................................... 25 Figure 5, Basket Standard Deviation ............................................................................................ 26 Figure 6, Premium ........................................................................................................................... 27 Figure 7, Result from hedging strategies ...................................................................................... 29 Figure 8, Layered Basket Option vs. Spot Rate .......................................................................... 29 Figure 9, Layered Forward vs. Spot Rate ..................................................................................... 30 Figure 10, Layered Forward ........................................................................................................... 37 Figure 11, Layered Forward vs. Layered Basket ......................................................................... 38

List of tables

Table 1, Johnson & Lidbark, Diversification effect ..................................................................... 8 Table 2, Basket of currencies ......................................................................................................... 17 Table 3, Result from hedging strategies ....................................................................................... 28 Table 4, Manipulated Baskets ........................................................................................................ 30 Table 5, Diversification improvements ........................................................................................ 31 Table 6, Improved baskets ............................................................................................................. 32 Table 7, Improved baskets ............................................................................................................. 33 Table 8, Outcome of strategies ...................................................................................................... 34 Table 9, Diversification 2003 Q3 & 2011 Q3 ............................................................................. 35 Table 10, Spot vs. Layered Basket Option ................................................................................... 38 Table 11, Premium reduction ........................................................................................................ 40 Table 12, Reduction in diversification effect ............................................................................... 40 .

Chapter 1 G.Carlsson & R.Ericsson Introduction

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1 Introduction

This first chapter will introduce the concept to risk management in a global market. It will further be

narrowed down to the problem that the Swedish multinational enterprise, Sandvik AB, is facing and the

model developed to solve this.

The world has accelerated towards a more globalized environment during recent decades.

Cities have transformed from success to failure, where corporations move production from

its origin to areas with cheaper labour and production (Schifferes, 2007). Simultaneously,

restrictions are shifting in more beneficial directions for global businesses. Tolls, quotas

and transportation costs are being reduced, making it cheaper to import and export (Reiter

& Jönsson, 2002). However, the financial volatility is increasing around the world, where

countries such as Greece, Portugal and Ireland are all jeopardous markets for businesses to

enter (Barth, Li, & Prabgavivadhana, 2011). The financial volatility is resulting in fluctuating

currencies, which make transactions between countries a vital phase (IMF, 2011). The risk

of being a multinational corporation is growing and hedging becomes increasingly

fundamental for border-crossing organizations (Lind, Polak, & Robertson, 2011).

Foreign currency management is a crucial procedure for corporations that act on the global

market. An organization needs to discover and analyze their foreign exchange exposure.

Exposure means, that some segment of the organization is affected by exchange rate

fluctuations. The risk connected to exchange rate exposure depends on the potential degree

of fluctuations in the currencies. Therefore, currency risks increase proportionally with the

volatility in the foreign exchange rates. Due to the massive volume of currency constantly

changing hands over a single global market the volatility has increased dramatically the

recent years. Unpredictable rate changes may have an unfavorable effect on multinational

corporations return and can be seen as the “cost of going offshore”. The cost of going

offshore is a cost that a multinational corporation, such as Sandvik should minimize in

order to be a competitive player on the global market. To hedge risk and decrease the

volatility in the currency exchange rates is a strategy that should be considered by financial

managers. Sandvik’s currency exposure is created because of the absence of predictability in

the foreign exchange market (Shoup, 1998).

1.1 Background

The introduction of the Bretton-Woods system was the beginning for structured

relationships between currencies. The world economy needed structure after World War II,

and the Bretton-Woods agreement included guidelines and restrictions to help recompose

the economy. The fundamental idea was to implement a fixed exchange-rate system, which

was an important step for the currency market. After the Bretton-Woods was depleted in

1973, some minor phases passed before a floating system was introduced in the early 1990s

(Reiter & Jönsson, 2002).

A floating exchange-rate system naturally leads to new risks for corporations. Multinational

corporations face the risk of potential losses caused by currency fluctuations. There are


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several incentives in why organizations such as Sandvik AB need to implement a hedging

strategy. The fundamental reason is to avoid additional losses because of currency

fluctuations. In the last 20 years, financial derivatives have become an everyday routine

(Brown & Toft, 2002). There is a wide range of hedging instruments, where each

instrument has its own functions but similar purposes (Mahul, 2001).

The reason why Sandvik AB would apply hedging instruments is not only to avoid losses

caused by unanticipated fluctuations, but also to satisfy their shareholders. An aggressive

hedging strategy that is implemented solely to generate profits is more risky in comparison

to other strategies. If large exposures are hedged completely through options, it will

automatically result in large premiums. A hedging strategy is applied to eliminate the effects

of currency fluctuations. That is, to neither make a profit or loss, but to aim at a precise

and foreseeable result. Sandvik’s goal is to satisfy all stakeholders, where a strategy that

meets the corporate’s and the shareholders’ expectations should be implemented (T,

Hamberg, personal communication, 2012-01-12).

1.2 Sandvik AB

Sandvik was founded in Sandviken, Sweden, when Göran Göransson was the first in

history to use a Bessemer process in steel production (Sandvik AB, 2012). A Bessemer

process is an inexpensive process for mass-production of steel from molten pig iron (Wolf,

2001). Sandvik is active in 130 countries and have a total of 50.000 employees with a

turnover of approximately 100 billion SEK. They are a high-technology engineering group

divided into five different business areas, Sandvik Mining, Sandvik Machining Solutions,

Sandvik Materials Technology, Sandvik Construction and Sandvik Venture (Sandvik AB,

2011).

Sandvik possess an exclusive potential of knowledge within materials technology and

provide their customers with expertise about work processes. They always strive to become

market leaders within the areas they operate in. The world is their market and transactions

across borders occur constantly (Sandvik AB, 2011). Customers are given the option to pay

in their own currency and that leads to currency exposures. Sandvik is exposed in several

currencies, where their exposure depends on the distribution between production and sales.

In present time, Sandvik AB has 10-15 billion SEK exposed to currency risks and they only

hedge a part of this outstanding exposure. Their goal is not solely to make a profit, but to

reduce the volatility. The goal is to aim at an accurate result, with no unexpected outcomes.

The CEO should not have to explain to the shareholders why a result suddenly differs

from the predicted (T, Hamberg, personal communication, 2012-01-12).

Layered Basket Options is a hedging strategy developed by the CitiFX Corporate Solutions

Group (CSG), a bank with a global perspective where Sandvik AB is the optimal customer

to implement this strategy. Because of Sandvik’s diversified foreign exchange portfolio they

demand a hedging strategy that reduces the volatility in their currency exposure but at the

same time is flexible enough to take advantage of potential positive movements in their

exposed currencies. The Layered Basket Option hedging model is according to CSG said to


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be the best solution to meet these requirements. The Layered Basket Option hedging

strategy is a combination of a layered and a basket option approach. The layered approach

divides larger hedges into several smaller hedges with different expiration dates to

smoothen the fluctuations. Instead of applying a static hedge where there is only one

expiration date, the multiple expiration dates allows for peaks and downs to cancel out each

other to further reduce the volatility. The basket option approach takes advantage of the

imperfect correlations. By hedging all currencies through a basket option a diversification

effect is created. These two approaches combined create the Layered Basket Option

hedging (Johnson & Lidbark, 2009).

1.3 Problem discussion

Sandvik AB is exposed to currency risks and risk management strategies are applied to

control the risks. The currency exposure increases as the corporation continues to grow

and the risks associated with currency exposures have a larger impact on the result.

According to Thomas Hamberg, Head of Corporate Finance, the intention of applying a

hedging strategy is not only to avoid losses and maximize the profit. Sandvik AB relies on

their investors and it is of importance to satisfy the shareholders demands. Therefore, to

find and implement a hedging strategy that eliminates the effects from currency

fluctuations is desired. Sandvik AB aims to apply hedging instruments to reach a

foreseeable result, where currency movements do not generate unexpected outcomes.

There is a limited amount of previous research regarding Layered Basket Option hedging.

The strategy was recently developed and Sandvik AB was the first corporation to fully

implement the strategy. This results in obscurities in how Layered Basket Option hedging

stands in relation to other hedging instruments and how effective the strategy is. We strive

to clarify the concept and make it more comprehensible to Sandvik AB and the reader. The

model involves complexity, both in a mathematical and a practical way. The combination

of a layered- and basket option approach needs to be explained in a pedagogical and

detailed procedure to demonstrate why Layered Basket Option hedging is a suitable

strategy for Sandvik AB. The lack of previous studies makes it difficult to determine the

prime approach in how to perform the premium calculations. Therefore, the chosen

mathematical approach needs to be carefully studied to attain an accurate result.

The rising demand for suitable hedging strategies will lead to an investigation to conclude if

a Layered Basket Option hedging strategy is an interesting and suitable approach for

multination corporations and Sandvik AB.


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1.4 Purpose

The purpose is to investigate and provide information about how currency risk most

effectively is hedged for the multinational corporation Sandvik AB. Furthermore, we want

to evaluate if Sandvik’s recently implemented hedging strategy, Layered Basket Option

hedging, is the best-suited strategy for them and if there are any improvements to be made.

This thesis will further investigate the importance of currency hedging for multinational

corporations, which are dependent on reporting to their stakeholders. Hopefully, this thesis

will also facilitate the communication of Sandvik’s currency strategies throughout the

organization and make it more comprehensible.

1.5 Research questions

The problem with currency risk exposure has been recognized in Sandvik AB and has

provided us with three relevant questions to be investigated in this thesis.

- Is Layered Basket Option Hedging the optimal hedging strategy for Sandvik AB?

- How will other hedging strategies affect Sandvik’s currency risk management?

- Is there a superior strategy for hedging currency risk exposure?

1.6 Delimitations

A comprehensive understanding about currency risk management for multinational

corporations is essential to present a relevant result about the investigated hedging model.

There exist many hedging strategies within the currency risk management framework. We

have decided to investigate and focus on the most common strategies and also those

strategies that are relevant according to the goals and ambitions for the Sandvik

Corporation. Furthermore, the Layered Basket Option hedging model had to be broken

down into two parts, the layered approach and the basket option strategy, and investigated

separately to later be merged in our calculations. The effectiveness of the hedge will be

evaluated and compared with other strategies to obtain conclusions regarding if there are

improvements to be made for Sandvik’s present currency risk management.

When evaluating the investigated hedging strategy several approaches may be conducted.

Approaches such as a Monte Carlo simulation had to be discarded due to its complexity

and others strategies was rejected early due to the fact that Sandvik is exposed to negative

weights. We choose to evaluate the strategies through a portfolio theory since several

underlying currencies are investigated and transparency is fundamental for the

communication within the organization.

Chapter 2 G.Carlsson & R.Ericsson Theoretical Framework

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2 Theoretical Framework

This chapter will present and explain the necessary theories and models to answer the different problems

associated with currency risk management. Further this chapter will provide the reader with sufficient

material to understand the concepts and how the problems at hand may be solved.

2.1 Hedging currency risk

Techniques for hedging currency risk involve the use of different financial derivatives,

which protect corporations from the fluctuations in the foreign exchange rates. Some of

the most widely used derivatives or techniques if organizations do not want to trade at a

spot rate, is forward contracts, futures contracts, options and currency swaps (Jorion,

2005).

2.2 Options

Options are securities that give the holder right to exchange an asset against a decided

premium. An option is a right to either buy (call option) or sell an asset (put option). It is

also subject to several conditions, which span over a specified period of time. The

underlying asset of an option is often common stocks but could be any kind of assets such

as currencies or commodities (Black & Scholes, 1973). There are several subcategories

linked to the concept of options. Firstly the financial instrument is divided into vanilla

options (or standard options) and exotic options. Vanilla options are the most common type of

options. The holder of a vanilla option owns the right to buy or sell an underlying asset for

a certain price called exercise- or strike price. The exercise of this right must occur within a

pre-determined time called time to maturity or time to expiration. The conditions connected to

this expiration time would further divide vanilla options into different kinds of options. A

European option allows the holder to only exercise the right at the maturity date. Contrary

to the European, the American option implies that the holder owns the right to exercise

this security at any moment within the time to maturity (Zhang, 1995).

According to Zhang (1995), exotic options are a direct or indirect extension of vanilla

options. If vanilla options are categorized as the first generation of options, exotic options

could be seen as the second generation. An exotic option is a non-standard option that

differs in some aspect from the vanilla option. There are different kinds of exotic options

but if it differs in at least one aspect from the rules of a vanilla option, it should be

categorized as an exotic option. One example of an exotic option that will be further

investigated is the basket option. Options may further be categorized in terms of

“moneyness”. An option could, depending on its strike and spot price, either be “at the

money” (ATM), “out of the money” (OTM) or “in the money” (ITM). When a put option

is ITM it refers to the spot price being below the strike price and the option in this case has

an intrinsic or time value. Contrary, the put option is OTM when the spot price is above

the strike price and the value of the option is subsequently equal to nothing. A put option

that is ATM has only a time value and no intrinsic value, since the strike price is equal to

the spot price (Bakshi, Cao, & Chen, 1997).


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Hedging currency risk through put options is commenced when the risk encountered is a

downward trend in the investigated currency. An example would be if a corporation wants

to secure a certain currency from a downward trend but at the same time earn money if the

currency increases in value. The corporation wants to secure an amount of USD to the

SEK, it may then buy the right to sell the USD for a certain amount in SEK depending on

the current exchange rate. This would be equal to buy an ATM-put option where the

corporation hedge the risk from a weakening in the USD in comparison to the SEK but it

will still benefit from a strengthening in the USD. This advantageous opportunity however,

does come at cost; a premium has to be paid which is the risk a buyer of the put option has

to consider (Wong, 2003).

2.3 Black-Scholes

There are several methods for valuating options, where one of the most widely used is the

model developed by Fischer Black and Myron Scholes.

There are many factors that influence the price of an option, where the value of the

underlying asset is an important factor that determines the price. If the price of the asset

were much lower than the exercise price of a call option, the value of that option would be

close to nothing. However, if the price of the underlying asset were much higher than the

exercise price the value of that call option would automatically be high. The time to

maturity of the option is a crucial determinant for the value of the option, since the

forecasting and probability that the desired strike price would be fulfilled changes as the

maturity date approaches. Normally the value of the option declines as the maturity date

approaches. Fluctuations and volatility influence the risk that the different parties take on

and therefore also affect the valuation of the option (Black & Scholes, 1973).

A diagram illustrated by Black and Scholes (1973) (see figure 1) shows the properties

between the call option’s value and the underlying asset price (i.e. stock price). Line A

represents the maximum value of the option with an exercise price of $20, this because the

value of an option cannot exceed the stock price. Line B represents the minimum value

since the option value cannot be negative or smaller than the stock price minus the exercise

price. The remaining lines, T1, T2 and T3 symbolize the value of the option for successively

shorter time to maturity. Notice that the value of the option is more volatile than the stock

price since it is concave upward sloping. This proves that the closer to the maturity date,

the percentage change in the option value is larger than the change in the stock price (Black

& Scholes, 1973).


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Figure 1, Black-Scholes Diagram

The mathematical approach of this formula, where the necessary variables are included will

be presented in the next chapter together with the methodological approach.

2.4 Basket options

The value of a basket option depends on the average value of the underlying assets over a

specific period (Turnball and Wakemann, 1991). The basket consists of different weights

of each currency depending on the distribution of exposure between the currencies

(Johnson & Lidbark, 2009). The overall cost is normally lower if currencies are hedged

through a basket option compared to individual vanilla options. The reduction is explained

by imperfect correlation between currencies (Hakala and Wystrup, 2008). It implies that

currencies react differently given external circumstances (Madan, 2009). An example is if

oil-prices are rising, currencies can respond differently, where some currencies increase and

others decrease in value. By including currencies that behave differently, it is possible to

reduce the risks and thereafter the premium.

As illustrated by Johnson and Lidbark (2009), the diversification effect reduces the volatility

for the basket in comparison to the individually hedged vanilla options (see table 1). The

exposed amounts are shown in the second column, while the third column illustrates the

amount exposed to risks in relation to regular market movements. The last column displays

the individual volatility for each currency. When the basket’s total value-at-risk is compared

to the total value-at-risk of the individually hedged currencies there is an improvement by

37%. It is explained by the reduction in volatility, where the average volatility between the

currencies equals 14% and the basket’s volatility equals 9%.

Stock Price

Option Price


8

Currency Pair (EUR) VaR, 95% Volatility

USD 10 000 000 2 024 154 14%

GBP 10 000 000 1 878 531 13%

CHF 10 000 000 962 102 6%

JPY 10 000 000 2 550 430 18%

SEK 10 000 000 1 709 819 11%

CAD 10 000 000 1 947 290 13%

ZAR 10 000 000 2 755 853 19%

INR 10 000 000 4 211 665 17%

BRL 10 000 000 2 663 688 19%

CNY 10 000 000 2 136 119 15%

Total Basket 100 000 000 13 299 226 9%

Tot. Individual 21 039 652

Difference 7 740 426

Diversification 37%

Table 1, Johnson & Lidbark, Diversification effect

One of the ideas behind constructing a basket is to exploit the diversification effect.

Diversification effect means to reduce the total risk by adding several assets to a portfolio

or basket. Since different assets tend to move differently given external circumstances, the

risk will be reduced when a new asset is added. The explanation is the underlying

correlation between assets. When the correlation between currencies equals 1 the

diversification effect is lost, hence it is the non-similarities between assets that lead to a

reduction in risk. Therefore, it is of importance to ensure that the assets do not move

identical given uncontrollable circumstances if the diversification effect will be captured

(Chen, 2012).

2.5 Minimum variance portfolio (MVP)

Basket options make use of portfolio theory since the currencies are not perfectly

correlated. If a basket of currencies is seen as a portfolio of assets, portfolio theory models

can be applied to determine the volatility of a basket (Penza & Bansal, 2001).

A basket consists of several assets, where the assets contribute with different weights. The

assets have different standard deviations and the correlation between the assets is widely

spread. Harry Markowitz introduced a concept allowing investors to find the portfolio

variance by combining all the underlying factors for all currencies (Markowitz, 1959). The

correlation between the different assets can contribute to a risk reduction. If the correlation

between the underlying assets is imperfect, the standard deviation will be reduced. The

Minimum Variance Portfolio theory calculates the variance of a portfolio, based on the

correlations, weights and standard deviations of the underlying assets (Schuck & Brown,

1997).

2.6 Systematic & non-systematic risk

Systematic and non-systematic risks, also known as non-diversifiable and diversifiable risks

are common terms in portfolio management. Systematic risk cannot be diversified away

while the non-systematic risk will nearly be eliminated with a larger portfolio due to the

diversification power (Elton et al., 2009). Systematic risk is connected to the market and


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examples that correspond to this type of risks could be wars, inflations and other

uncontrollable fluctuations in the market (Balvers, 2001).

A mathematical explanation of systematic and non-systematic risk may be derived if we

look at the formula representing the risk of a portfolio presented by Elton et al. (2009)

where N represent the number of underlying assets in the portfolio:

(∑

) (1)

The non-diversifiable systematic risk is denoted by

which entails that it is not related

to the number of assets N and will not change since is constant. According to the

formula above, it is shown that the non-systematic risk ( ) will approach to zero as N

goes to infinity (Elton et al., 2009).

2.7 Layered hedging

According to Hirigoyen (2003) a key concern for multinational corporations, which depend

on reporting stable currency results, is to manage their foreign exchange risks. Extending

and layering the hedge horizon to reduce the problem of forecasting accuracy several years

ahead should solve the problem.

Companies’ goal is to reduce their year-on-year currency impact on their result due to the

volatility in the exchange rates. This goal is not best reached with static hedging programs

since a static hedge one year, is totally isolated from the following year. The most

important aspect to achieve this goal is to discover the link between the aim of the

corporation’s risk management and the layout of the hedging strategy. When the link has

been detected, the best strategy to reduce the year-on-year volatility in exchange rate is, as

mentioned before, to create longer hedging tenors. Forecasting errors and opportunity

costs should be taken into consideration when extending the tenors since these kinds of

negative outcomes tend to increase with a longer time horizon (Lidbark, 2006). A good

strategy to implement when dealing with forecasting accuracy in a long tenor is to layer the

hedge with several intervals to make room for adjustments along the period (Hirigoyen,

2003).

With a layered hedging program, hedges with the same expiry date are entered at regular

intervals. In the model below (see figure 2), 25% of the exposure of the four upcoming

quarters is hedged every quarter. With this strategy the hedging rate becomes an average of

the previous tenors. In the example given, a moving average of hedging rates becomes

available for four previous quarters. The year-on-year changes in the hedging rates are

connected to the created moving average. Due to this connection the layered strategy

creates smaller year-on-year changes compared to the volatility created by a spot strategy.

Hedging with a layered program is rather used as an averaging tool than a delaying one,

which is the result of several other hedging programs and strategies (Johnson & Lidbark,

2009).


10

Figure 2, Layered hedging

2.7.1 Layered vs. Rolling

In a rolling hedging program the hedges are entered at regular intervals but with different

execution dates (see figure 3). This would generate the hedging rate of year-on-year

changes to be driven by the spot rate. The rolling hedging strategy would delay the

outcome of the hedge and push either the positive or negative effect further in the future

(Johnson & Lidbark, 2009).

Figure 3, Rolling hedging

According to Johnson and Lidbark (2009) the layered hedging program is far more

attractive than the rolling program if options are used as the hedging tool. This comes from

the perspective of premium spending, since the average tenor for a regular 12-month

rolling hedging program is 12 months, whereas the average tenor for a 12-month quarterly

layered program is ((3+6+9+12)/4) 7.5 months. As mentioned before, the value of the

options will decline as the maturity date approaches. When the value declines the price of

the option must decline as well and the shorter average tenor will result in a lower premium

(Black & Scholes, 1973).

2.8 Layered Basket Option Hedging

Sandvik and Citibank have developed a hedging model called Layered Basket Option hedging.

The model is built on the concept of regularly buying options, which gives the right to sell

a basket of currencies that reflects the corporate group’s currency exposure. The strategy

implies that they combine two independent hedging models, the layered hedging procedure

and the basket option approach, that both reduce the volatility and decrease the premium

payments. The layered program possesses much more desirable risk characteristics as they

reduce the year-on-year changes in effective hedging rates by spreading out execution over


11

time and creating an averaging process. The volatility may be further reduced due to basket

hedging. Instead of hedging each individual currency, a basket of several currencies is

applied. This creates diversification power, due to correlations between currencies

(Johnson & Lidbark, 2009).

Sandvik AB computes the exposure in foreign currency that they have realized in the past

12 months. The total sum of the different foreign currency exposures from the underlying

companies all over the world is put together in one single basket. This basket contains of

18 different currencies with diverse amounts depending on the operations undertaken in

that certain country. Sandvik is, either in a short or long position in a local currency, which

implies that the basket will contain negative exposures in some currencies. The subsequent

valuation process will result in a price for an ATM-basket put option of the underlying

currencies with respectively three, six, nine and twelve months to maturity. This gives

Sandvik an opportunity of negotiation and will make a closure with the bank that offers the

lowest premiums (T, Hamberg, personal communication, 2012-01-12).

2.9 Forward contracts

A forward contract is a simple and efficient financial derivative applied to protect a

corporation from currency fluctuations. A forward is an agreement between two parts, that

is to either sell or buy an asset at a specific date in the future for a predetermined price. The

two parties in the contract are presented by either two financial institutes or between a

client and a financial institute. The parties take either a long or short position, which

implies that the party that is going long agrees to buy the underlying asset for a certain

price in the future. The other party will take a short position and is obligated to sell the

underlying asset for the predetermined price on the agreed date in the future. This indicates

that the two parts have different beliefs in the market they operate in or that at least one

party is eager to hedge the risk of fluctuations in the underlying asset price. Since the

forward contract is binding and there is no premium involved, the possible payout

defaulted or received will represent the value or cost of this contract. This also implies that

there is always one winner and one loser in this binding commitment (Hull, 2012).

According to Hull (2012) forward contracts can be used to hedge foreign currency risk.

Assume that a corporation that is active on the global market wants to report its result in

their domestic currency and wants to convert a basket of foreign currency to the domestic.

The corporation may then take a short position in a forward contract and be safe from

exchange fluctuations and sell the basket at a predetermined price for a sum in its domestic

currency. This hedge is effective in terms of protecting a corporation from drops in foreign

exchange rates but it will lose the opportunities from a strengthening in the foreign

currency.

2.10 Alternative methods

Derivatives that may be used as a hedging tool but does not correspond to Sandvik’s

hedging strategies will still enlighten the overall understanding of currency risk

management. Furthermore, alternative valuation processes should be taken into


12

consideration when valuating derivatives and performing an active currency risk

management within a corporation.

2.10.1 Value at Risk (VaR)

Value at risk is a version of the safety-first rules, where focus is concentrated on the size of

adverse outcomes that occur with a specified probability in a specific time interval (Elton,

Gruber, Brown, & Goetzmann, 2009). VaR measures the loss caused by regular market

movements and losses beyond the “value at risk” only occur with a particular probability.

Compared to other statistical risk-measuring concepts, the model generates a transparent

result and increasing the general understanding and communication within organizations. It

is an appropriate measurement for larger business, allowing members of the board to

understand and realize the organizations risk exposures. Assume there is an asset with a

VaR of 1000 SEK at a 95% confidence level. It implies that there is a 95% probability that

the possible losses will not exceed 1000 SEK. Then there is only a 5% chance that the asset

will drop more than 1000 SEK. The 95% confidence represents the normal movements in

the market and the remaining 5% represents abnormal movements (Hopper, 1996). Value

at risk is basically the value or price of a derivative, for example the value of a basket

option.

There are three different approaches to Value at Risk, the Historical, Variance-Covariance and

the Monte Carlo approach. The historical approach is based on historical changes in market-

rates and prices. The data is then used to predict future outcomes to anticipate the value at

risk as the loss exceeds a certain percentage (1, 5 or 10%) (Linsmeier & Pearson, 1996).

The Variance-Covariance approach assumes that returns are normally distributed around a

mean return of zero. There are only two factors applied when calculating Variance-

Covariance method, the estimated standard deviation and the cut-off factor in the left tail

of the distribution. These factors are then used to predict future outcomes based on today’s

data (Hopper, 1996).

The Monte Carlo approach is a parametric method, which generates random changes in

risk factors from estimated parametric distribution. The process is divided into two

different steps. The first step involves a parametric stochastic process for all risk factors. It

means that factors such as standard deviation can be derived from historical data. The

second step is based on the first step, where random price paths are simulated from the

different risk factors (Jorion, 2007). The simulated processes are realized using a

pseudorandom generator, which is an instrument, built on an algorithm that generates

possible outcomes. The Monte Carlo process is relatively similar to the historical process,

but does not base future outcomes on sampled historical data (Linsmeier & Pearson, 1996).

Since a basket option can involve many variables, a Monte Carlo simulation gives the most

accurate result because of the number of possible outcomes generated from the process

(Hakala & Wystrup, 2002). The disadvantage is that a Monte Carlo simulation is time-

consuming (Hull, 2012). Assume there are ten different currencies in a basket. Then there

are different risk factors connected to each individual currency and some currencies are

affected by changes in one another A Monte Carlo approach randomly creates different


13

price paths, allowing a business to realize the value-at-risk. The Monte Carlo approach is

superior to other methods because of its flexibility and the ability to take a wide range of

risks into account (Jorion, 2007).

2.10.2 Futures contracts

Similar to the forward contract, a futures contract is an arrangement between two parties to

sell or buy an asset at a certain price at a predetermined time in the future. Any of the two

parties does not necessarily have to be represented by a financial institute and unlike

forward contracts the futures contracts are normally traded on an open exchange market.

The underlying asset of a future includes a wide range of commodities and financial assets,

where the financial asset includes Treasury bonds, stock indices and currencies. The price

of a futures contract is determined by the laws of supply and demand and the exchange

market provides mechanisms which ensure that the contract will be honored (Hull, 2003).

2.10.3 Currency swaps

Currency swaps are agreements between two parties to exchange one currency for another

at a specific date. For the swap to be justified, a price is paid that corresponds to the

difference in interest rates between the two currencies. The main purpose with currency

swaps is to minimize currency exposures. Assume there is an exporting business that needs

10 million USD to make a payment today and they do not have any USD in their account.

At the same time, they are expecting a payment of 10 million USD in three months. The

business needs USD today, but they want to avoid exchanging money at two different

occasions. The business then makes a currency swap, where they buy USD at the current

rate and at the same time sells USD to be delivered in three months. This is done to avoid

exchanging twice and to minimize the risk exposure (Shoup, 1998).

Chapter 3 G.Carlsson & R.Ericsson Method

14

3 Method

The following chapter will explain and examine the different methods applied in this thesis. We will further

discuss and motivate the applied methods and provide the reader with insight into the research, as well as a

credibility assessment.

3.1 Research approach

The purpose of this thesis is to evaluate a new hedging model for currency risk

management in the multinational corporation Sandvik AB. Theories and models developed

solely for this purpose had to be investigated. A key factor was to discover a relationship

between the reality, which is the possible outcome of the hedge, and the existing theories

for valuing the undertaken hedging methods. The reason to hedge currency risk is to

protect the exposure in the foreign currency from negative fluctuations. By collecting daily

historical data from several currencies, the hedging results may be investigated from

different hedging models and theories. Personal contact with personnel at Sandvik

Financial services was necessary to conduct reliable and relevant research within this

specific subject.

Patel and Davidson (2003) states that the most central problem for a scientific research is

to identify and connect theory to reality. Three key concepts when dealing with this

problem are deduction, induction and abduction. The deductive approach allows a researcher to

draw conclusions and obtain results through already proven existing theories. An inductive

approach implies that the researcher formulates a theory based on the data collected and

the analysis received from it. A combination of these two approaches would be the

abduction approach. Two other expressions within business research are quantitative and

qualitative and are used to distinguish different data analysis processes and data collection

techniques. A qualitative approach implies that the techniques and analysis of the data and

procedure is based on, or generates non-numerical data. A quantitative approach could be

used as a synonym for data collection techniques and analysis that generates and is based

on numerical data. The quantitative data analysis procedure predominately involve

analyzing statistics and graphs, while in the qualitative manner the collection is mostly

focused on interviews and the analysis of the data are achieved through conceptualization

(Saunders, Lewis, & Thornhill, 2009).

According to Saunders, et al. (2009) the deductive approach involves testing theories rather

than building them. A hypothesis about the relationship between several variables must be

deduced. The hypothesis would due to the large amount of different currencies, involve the

relationship between the correlation and the volatility of currencies. Furthermore, because

of the framing of the investigated model, the relationship between the volatility and the

hedging tenor should be of significant importance.

A collection of quantitative data, which is a characteristic of a deductive approach, was

necessary to test this hypothesis between hedge tenors, correlation and volatility. The


15

quantitative data collection contains daily historical exchange rates from 18 different

currencies with the SEK as the base currency, nearly ten years back in time. The large

numerical sample size would be sufficient to fulfill the deductive characteristic, called

generalization. That is, a sufficient numerical sample size is necessary for generalizing a

statistical behavior (Saunders, et al., 2009).

The procedure of evaluating the Layered Basket Option hedging clearly shows that we have

undertaken mainly a deductive and quantitative approach. Statistical data has been central

to conduct the subsequent calculations based on the theories of currency risk management.

The personal contact with representatives from the Sandvik group has been a crucial part

for us to succeed with our research and a qualitative approach should not be totally

detracted.

3.2 Research design

There are three main research perspectives; exploratory, descriptive and explanatory

(Saunders et al, 2009). We have applied a combination of an exploratory and an explanatory

approach. Exploratory research means to achieve improved knowledge within a subject

and to clarify dimensions that have not been fully explained. An exploratory study refers to

exploring the unknown, and concludes if a study is worth pursuing. In an exploratory study

the researcher must be willing to change direction if new findings are found (Saunders et al,

2009). Layered Basket Option hedging is a recently developed model. Due to this novelty,

there is a lack of information within the subject. Information was gathered through articles

provided from Citibank and interactions with our contact person at Sandvik Financial

services, Thomas Hamberg. Explanatory research explains the relationships between

variables to clarify a situation or a problem (Saunders et al., 2009). Layered Basket Option

hedging differs from other strategies in the sense of the number of variables taken into

consideration. For example, the imperfect correlation between assets helps explain why the

basket volatility is being reduced in comparison to the average volatility between

individually hedged currencies. In order to conduct this research we were dependent on

secondary data, where daily exchange rates were the foundation of our collection.

3.3 Secondary data

Secondary data is a form of data that has been gathered through former studies (Saunders

et al., 2009). The purpose of the previous studies is not necessarily the same as ours. It is

important to realize the procedure of data gathering, to comprehend if the data was

conducted in a biased or unbiased way (Befring & Andersson, 1994). The majority of the

information was gathered through secondary data. Information in how multinational

organizations manage their hedging strategies and how the model, Layered Basket Option

hedging, stands in relation to other strategies were collected. There was a necessity to

understand other hedging strategies to realize the unique aspects of the model. Deeper

studies were derived from secondary data in the form of textbooks, academic articles,

relevant newspaper articles and organizational articles.


16

In order to complete our numerical section, other types of secondary data needed to be

collected. Firstly, information regarding theories and models were gathered through

textbooks and academic articles to get knowledge about theories such as Black Scholes,

Value at Risk and portfolio theories. After we determined the best-suited approach,

exchange rates on daily basis needed to be gathered. The data was collected through Bank

of Canada and from Reuters' database.

3.4 Primary data

When the secondary data could no longer fully answer our research questions, we had to

collect further relevant data for our research. This kind of data is equivalent to primary data

and should be collected accordingly to our research questions (Ghauri & Grønhaug, 2005).

According to Churchill (1999, p. 215), “Begin with secondary data, and only when the secondary

data are exhausted or show diminishing returns, proceed to primary data.”

The procedure stated above has been conducted through our research. Our primary data

involved communication with personnel within the Sandvik group. The communication

consisted of personal contact and mail conversations. We have been in contact with the

Head of Corporate Finance and the CEO of Sandvik Treasury AB. The personal

communication have been somewhat informal since we all strove for the same goal, which

was to improve and evaluate the hedging strategy for Sandvik AB. Communication in form

of mail conversations with personnel within the CitiFX Corporate Solutions Group, the

developer of the model, was added to the primary data collected.


17

3.5 Materials used in the financial analysis

Sandvik’s current situation regarding exposed currencies is reflected in their basket. We

have chosen to work with a fixed basket to enable a comparison between periods. The

exposed sums will be fixed in foreign currencies, while the SEK will vary since the spot

rates fluctuate on a day-to-day basis. For example, a USD may be worth 7,00 SEK one day

and 7,10 the day after. This implies, if our foreign currencies stand as fixed, the SEK will

still vary because of currency fluctuations.

Currency Spot Exposure SEK Weight

USD 8,6957 497 200 000 4 323 478 261 36%

AUD 4,8924 269 200 000 1 317 025 440 11%

CAD 5,5036 26 800 000 147 495 872 1%

CHF 6,2854 -373 200 000 -2 345 694 532 -19%

CZK 0,2889 691 600 000 199 792 004 2%

EUR 9,1158 22 800 000 207 839 562 2%

GBP 13,9860 55 600 000 777 622 378 6%

ZAR 1,0138 1 986 400 000 2 013 787 510 17%

SGD 5,0125 -138 000 000 -691 729 323 -6%

PLN 2,2701 180 400 000 409 534 620 3%

NOK 1,2531 -306 000 000 -383 458 647 -3%

KRW 0,0073 95 184 000 000 697 771 538 6%

JPY 0,0732 7 868 800 000 576 063 721 5%

CNY 1,0501 3 144 400 000 3 301 900 662 27%

CPL 0,0121 67 610 800 000 816 018 078 7%

INR 0,1813 -3 287 200 000 -595 929 363 -5%

BRL 2,4558 133 200 000 327 111 984 3%

RUB 0,2721 3 422 800 000 931 333 602 8%

Total 12 029 963 366 100%

Table 2, Basket of currencies

The table above (see table 2) illustrates how a basket is structured according to Sandvik’s

exposure. The “spot” column refers to the spot prices between a foreign currency and the

SEK. The “Exposure” column represents the fixed amounts in foreign currencies that

Sandvik is exposed in and the SEK column is the exposed sum represented in SEK. Some

of the exposures are negative since Sandvik has a larger proportion of production than

sales in some countries and need to make payments in foreign currencies. The last column

demonstrates the basket’s distribution of currencies. The weights will vary between periods

because of exchange rates fluctuations. The weights are calculated by dividing the exposed

sum of a foreign currency represented in SEK, by the total exposed sum in SEK.

3.6 Method for developing a financial analysis

The instruments chosen in our investigation were a combination of the Minimum Variance

Portfolio Theory and the Black-Scholes formula. The models will be used to calculate the

volatility of the baskets and eventually the value of the basket options. The period

investigated will be set to 10 years to achieve sufficient and realistic outcomes. The results

will be compared to the outcomes of other hedging instruments to conclude if the Layered

Basket Option hedging strategy is the appropriate alternative according to Sandviks

strategies.


18

3.6.1 Correlation

Correlation refers to the relationship between two individual assets. Correlation is

measured between +1 and -1, where a positive relationship indicates that assets move in

the same direction given external circumstances, while a negative refers to the opposite

(Aczel & Sounderpandian, 2009). We needed to calculate the pairwise correlation between

all currencies in the baskets, which was a requirement to manage the latter calculations. The

correlation has been based on historical spot rates and was calculated using an add-in

function in Excel. Another alternative is to base the correlation on daily returns. After

further research we concluded that an estimation based on spot rates would be preferred.

The function created a table that illustrated the correlation between the basket’s currencies

(see appendix 11-20). The procedure was repeated every third month, to continuously

generate correlations based on historical data for the last year. In total, 37 different

correlation tables were compiled.

3.6.2 Standard deviation

Standard deviation is a statistical measurement and explains how much a data set varies

from its mean. A high standard deviation refers to a dataset widely spread around the

mean. It is a measure of risk, where a high standard deviation is an indication of a risky

asset and a low standard deviation the opposite (Ramos, Staking, Calle, Beato, O'Shea, &

Carrasco, 2000).

The minimum variance portfolio calculations required a standard deviation for each

currency involved. The standard deviations of the currencies were calculated and based on

daily returns on our collected dataset. The minimum variance portfolio requires annual

standard deviation, which was solved by multiplying the daily standard deviation by √ .

The square root sign is necessary because standard deviation is the square root of the

variance. As mentioned in the correlation section, the same procedure needed to be done

for standard deviation, where each standard deviation was calculated 37 times.

3.6.3 Risk free rate

The Black-Scholes formula requires a risk free rate, which in our case was based on

historical data. The data was based on the period 2002-2012 and was collected from The

Central Bureau of Statistics. We approximated the risk free rate to 4,5%, which was used

throughout our calculations (The Central Bureau of Statistics, 2012). The risk free rate was

also approximated based on several countries risk free rates, since the basket consists of

eighteen different currencies. The risk free rate was set as constant to increase the

transparency for Sandvik AB. This indicates that changes in the basket variance can be

located in a more effective way.

3.6.4 Weights

The currencies are represented in both negative and positive weights, and it is important to

ensure that the currencies in total correspond to 100% of the basket. A consistently on-

going problem throughout this thesis has been to manage the negative weights. If one


19

currency equals -20%, the remaining currencies should represent 120%. The reason why

there are negatively weighted currencies is because of Sandvik’s currency exposure. To

clarify this, if each currency were to be hedged individually, there would be both put- and

call options. Therefore, the basket will contain both positive and negative weights, but still

be classified as a basket put option.

3.6.5 Minimum variance Portfolio

The Minimum Variance Portfolio is an approach to calculate the basket variance based on

several variables.

∑

∑ ∑

(2)

The formula above illustrates how to calculate the variance of a basket. The X’s represents

the weights of the different assets, denotes the standard deviation of an individual asset

and is the correlation between two currencies (Elton, Gruber, Brown and Goetzmann,

2009).

An example that illustrates the concept is provided:

Asset 1 Assets 2

Weight: 50% Weight: 50% Correlation: 0,3

Standard Deviation: 30% Standard Deviation: 20% Avg. Std. = 25%

Basket Variance

√

The basket standard deviation was calculated to approximately 20% which demonstrates

the effect of diversifying risks by including more assets to a portfolio since the average

standard deviation between the two assets equal 25%. A larger amount of assets will most

likely reduce the basket variance in relation to the average variance between each asset

from an individual perspective (Yunker & Melkumian, 2013). The individual risks approach

to zero as the number of currencies goes to infinity, which refers to a non-systematic risk.

(Elton et al, 2009).

Sandvik’s basket consists of 18 currencies and it is necessary to use a matrix to compute the

variance. If the calculations were performed manually it would be too complex and time-

consuming.

[ ] [

] [

] (3)

(Chiang & Wainwright, 2005)


20

The matrix calculates the basket variance and is a conversion of the numerical version of

the portfolio variance formula (see formula 2).

3.6.6 Black-Scholes

The most widely used formula or method when calculating the value of an option is the

Black-Scholes formula. The theory developed by Black and Scholes (1973), where the value

of an option depends on the time to maturity, the volatility and the underlying asset price

of an option can be derived from a mathematical formula. The valuation formula for a

European call option is as follows:

(4)

Where w(x,t) stands for the value of the option, the x is the price of the underlying asset

and c is indicating the exercise price. The letter r stands for the interest rate, which is also

known as the “risk free rate”, and (t*- t) denotes the time to maturity. The N(d1) and N(d2)

represent the areas under a standard normal distribution table, which is calculated as

follows:

⁄ (

)

√ (5)

⁄ (

)

√ (6)

The standard deviation denotes the letter v in the formula above. This is equivalent to the

volatility and implies the risk of the option. The value of a European put option can be

derived from the associated call option since they both must be exercised solely at the

exercise date. Subsequently the value of the put option is computed from the formula:

(7)

Where u(x,t) denotes the value of the European put option (Black & Scholes, 1973).

The underlying asset price in this formula is denoted by the exposed sum in foreign

currencies that Sandvik is realizing. Sandvik’s currency risk management program involves

buying basket put options. The formula developed by Black-Scholes will compose the

foundation of our calculated premium when evaluating the Layered Basket Option hedging

model.

3.7 Assumptions

There are several assumptions to take into consideration regarding modern portfolio

theory. Assumptions appear to be unrealistic since models and formulas used in finance are

providing a researcher with expected values. However, a few assumptions have a greater

impact on this subject than others (Elton et al, 2009). The correlation between assets is

assumed to be fixed. In reality, the correlation between assets is constantly changing

(Kritzman and Thomas, 2004). Since the correlation between our currencies is one of the


21

key variables when determining the basket variance, this assumption is fundamental for this

thesis.

Another assumption that had to be considered was transaction costs. A transaction cost is

referred to as a cost incurred in making a transaction or an exchange (McDowell, Thom,

Frank, & Bernanke, 2006). An example is when a person is selling or buying stocks and has

to pay a fee to a broker. In our case only the premium is taken into consideration and other

transaction costs has been ignored. The last assumption we had to consider was to ensure

that the collected data was normally distributed. Normal distribution means that most of

your data is gathered around a mean and the distribution follows a bell-shaped curve (Aczel

& Sounderpandian, 2009).

3.8 The layered hedging approach

A layered approach is conducted when performing the hedging strategy and the time to

maturity (t*- t) is therefore three, six, nine and twelve months respectively. This obliges us

to further divide the basket into four options with equal exposure and calculate the value

respectively with the different hedge tenors. These different values, where the option with

three months has the lowest value and the one with twelve has the highest and are

summarized to attain a total value of an ATM-basket put options. The summarized value

obtained by using the Black-Scholes formula is the premium of the basket option (see

formulas 4-7).

3.9 The effects of applying a basket

A basket of 18 currencies have been used throughout our examined period. When the

currencies are placed in a basket, a diversification effect is created. If the currencies were

hedged individually, the effect would disappear. There is a possibility that the basket’s

variance eventuates higher than the average variance between the individual currencies.

Currencies with large weights in combination with high correlations and standard

deviations can result in a higher basket variance. We have calculated the effects of

diversification throughout our investigated time-period. The reason why this is performed

is to conclude whether a basket is consistently the best alternative.

∑ (8)

The X represents the amount in one currency and denotes for that currency’s standard

deviation. The symbolizes the confidence interval and is set to 95% (Linsmeier and

Pearson, 1996).


22

3.10 Alternative hedging strategies

Besides calculating the outcomes when a Layered Basket Option hedging strategy has been

used, the results from other strategies have been calculated as a comparison.

Spot Rates – The spot rate indicates that no hedging strategy is applied, and the

corporation instead relies on the spot rates.

3-month Forwards – We have computed the outcome if forward contracts with an expiry

date in three months were used as Sandvik’s hedging strategy.

Layered Forwards – A combination between two strategies, where forward contracts with

different expiration dates were used. This strategy is similar to the Layered Basket Option

hedging but the options have been swapped for forward contracts.

3-month Basket Options – This strategy demonstrates the outcome if the layered

approach was excluded from the Layered Basket Option hedging strategy. Basket options

with an expiration date in three month have been tested as Sandvik’s hedging strategy.

3.11 Improved baskets

Instead of having a basket consisting of 18 different currencies we have tried to reduce the

basket’s variance by dividing the large basket into several smaller baskets. The correlation

has been the benchmark when the new baskets have been constructed. Baskets with

optimal structure have been searched for, where the correlation and weights have been

strategically examined and assembled to reach a lower total variance. We have examined

certain quarters in order to establish an improved currency distribution between baskets.

3.12 Manipulation of variables to realize the actual effect of changes

We have performed a simulation where the underlying variables in the Minimum Variance

Portfolio formula have been manipulated. The correlation has varied between different

periods, and it has been difficult to grasp the actual outcomes caused by changes in the

correlation. The correlation was reduced by 10 percent. This implies that if two currencies

have a correlation of 0,4 it will be changed to 0,36, while if the correlation between to

currencies equals -0,6 it will be shifted to -0,66. The currencies standard deviation has been

relatively consistent throughout the examined time-period. Each currencies standard

deviation was reduced by 10 percent to understand the relationship between the basket

variance and the underlying currencies standard deviation. That is, to realize with what

percent the variance will change after a 10 percent change in the standard deviation.

The purpose is to simplify the searches for improved baskets. If we understand why

baskets behave in different ways, it will simplify our restructuring of a basket to reach a

more desired outcome.


23

3.13 Criticism of theories and models

Decision-makers often use financial models to determine future investments. Even if the

models provide a relatively accurate result there are some limitations to keep in mind.

There are assumptions linked to each financial model, which are unrealistic. Both the

Black-Scholes- and the Minimum Variance Portfolio formula are connected to some

assumptions (Elton et al, 2009).

Black-Scholes

- A possibility to borrow and lend at a constant risk-free interest rate

- No transaction costs

- A constant Volatility

Minimum Variance Portfolio

- Correlation between assets are fixed

- No taxes or transaction costs

The Black-Scholes formula determines the premiums for the basket options. The calculated

value will probably be lower than the actual payment because of transaction costs. Sandvik

usually supply banks with a basket of currencies and the bank will respond with an offer

(Berk & DeMarzo, 2011). In the minimum variance portfolio formula, the correlation is

one of the key variables and the correlation assumes to be fixed. It is not idealistic since

that aspect does not reflect the reality. The dilemma was adjusted by shifting the calculated

correlation every third month. The calculated correlation was based on the last 12-monts

and updated every third month. If we calculated the volatility in April 2010, a correlation

based on the period 1 April 2009 – 31 March 2010 was used. This procedure was

performed to achieve a more realistic result (Kritzman and Thomas, 2004). In the Black-

Scholes formula, the volatility is assumed to be constant, which is misleading since the

volatility is based on the correlation (Berk & DeMarzo, 2011).

An interesting notion is the effect of diversification. When currencies are added to a basket,

the non-systematic risk can be reduced. What studies often fail to mention is when a new

asset is added to a basket or portfolio, the systematic risk will increase (Armstrong &

Vashishtha, 2012). A country has its own problems, where country-specific aspects affect

the domestic currency. This eventually leads to the question whether or not a large amount

of currencies in a basket is the best solution or if a basket should be divided into several

smaller baskets to strategically place the risks.

Another problem with financial models concerns the actual outcome. The outcome can

never be completely accurate. The models do only provide a researcher with an expected

value and not the actual outcome. A model will only take a certain number of variables into

account and these variables rely on certain assumptions. In reality, almost an infinite

number of variables need to be included. Financial models fail to include parts such as

domestic or national circumstances as well as the human factor (Berk & DeMarzo, 2011).


24

This dilemma is impossible to get around. Financial models are the closest to reality a

researcher can accomplish, and this issue is therefore something we had to accept when

writing this thesis.

3.14 Reliability and validity

“Reliability refers to the extent to which your data collection techniques or analysis procedures will yield

consistent findings.”(Saunders et al., 2009, p. 156)

A credible result for a researcher should be of biggest concern and therefore, reliability in

the data collection and analysis must exist. According to Easterby-Smith, Thorpe, Jackson

& Lowe (2008) reliable research should be conducted through three questions. Firstly, will

the same results be yielded from the measures at different occasions? Second, will similar

observations be made from different researchers? Finally, is there a transparency in the

results drawn from the raw data? The data collected for this research was essential to

achieve reliable results. Data in the form of daily, instead of monthly exchange rates from

the currencies that Sandvik is exposed to seemed as an obvious approach to acquire reliable

findings. Daily data in a time span of ten years was collected to further ensure reliable

outcomes. Our results are based on historical values. Transparency from the raw data is

proven since we have not excluded any statistics and all steps are easily followed in our

calculations. Due to the substantial numerical sample size and the large number of different

currencies the three questions stated by Easterby-Smith et al. (2008) are exhibited and

reliability is proven.

The validity of research depends upon the extent the research findings are about what they

claim to be (Saunders et al., 2009). Furthermore, the material collected must be relevant to

the stated purpose and research questions of the thesis (Eriksson & Wiedersheim-Paul,

2011). The problem this thesis is investigating states that we want to evaluate a hedging

model implemented by Sandvik. To achieve this, it is essential to obtain valid data and

material that is related to our purpose. To find such comprehensive data as daily exchange

rates was a central matter for us, and the validity had to be proven. By searching through

respected databases such as Reuters and Bank of Canada, we eventually found this

numerical data from two different sources. This allowed us to confirm their validity after

comparison. Additional secondary data was found solely from respected journals and

publications from the organization that has developed the model. Hence, the theories

applied were clearly relevant to our purpose. The primary data was gathered directly from

persons with important positions within the Sandvik group.

Chapter 4 G.Carlsson & R.Ericsson Empirical Findings

25

4 Empirical Findings

This chapter will present a summary of the hedging purposes within the Sandvik group and their strategies

regarding currency risk management. The financial results of the calculations undertaken will also be

presented in this section. These results will further be used as underlying material for the analysis of the

Layered Basket Option hedging model and other strategies related to currency risk management.

4.1 Sandvik’s hedging purposes

According to Thomas Hamberg, head of Corporate Finance, the main goal is to reduce the

effects of currency fluctuations. The essential purpose is not to make a profit from the

hedging strategy, but to reduce the swings caused by currency fluctuations. Instead of using

a hedging program, large organizations could rely on the spot rates, which could make the

result differ on a year-to-year basis. Seen from a long-term perspective, peaks and downs

caused by the spot rates may cancel out each other. The reason why a hedging strategy is

implied is often to satisfy the shareholders. As a shareholder, a consistent and reliable stock

is generally preferred when investing in this industry. Sandvik wants to ensure their

shareholders that only a small amount of their cash flow is at risk. The unexpected profits

or losses caused by currency fluctuations shall be reduced. Sandvik is searching for

consistency, where only a certain cash flow is at risk each year (T, Hamberg, personal

communication, 2012-04-16).

4.2 Standard deviation

The graph below illustrates the currencies’ standard deviations between the years 2003-

2012 (see figure 4).

Figure 4, Standard Deviation

As seen in the graph above the standard deviation fluctuates heavily during certain periods.

The fluctuations in 2002-2003 and in 2008-2009 can be effects from financial crisis. The

volatility has a substantial effect on the premium, which will be presented later in the


26

empirical findings. It is reflected that some currencies respond stronger to crisis than

others. Certain currencies have a volatility of approximately 40% during 2008-2009, while

others only have a volatility of 10% (see appendix 1-10). When corporations operate with

multiple currencies it is important to understand the behavior of each currency to

successfully handle the risk management processes. The graph implies that currencies

respond relatively similar in directions but different in proportion given external

circumstances.

4.3 The MVP approach

Through the MVP-approach the basket’s standard deviation have been calculated and are

illustrated in the graph below (see figure 5). The standard deviation is a fundamental part

when the premium is calculated and is derived from the portfolio variance.

Figure 5, Basket Standard Deviation

As seen in the graph above, the basket’s standard deviation is reflected in the currencies’

individual standard deviation, which in particular is seen during 2008-2009. The

diversification effect result in a lower standard deviation of the basket compared to the

individual currencies (see figure 4).

4.4 The premium using Black-Scholes

The Black–Scholes formula has some assumptions that have to be considered in the form

of normality and transaction costs among others. These assumptions lead to that the value

derived from the formula does not fully represent the premium. From the value derived, a

qualified hint of the premium may be retrieved.

The standard deviations of the baskets options retrieved from the MVP approach have

been used in the Black-Scholes formula, which is denoted by the letter v and the chosen

risk free rate r (see formulas 4-7). Further, the time to maturity (t*- t) has provided four

different values that have been summarized to one total value of an ATM-basket put

option. The values derived from the Black-Scholes formula have been set as premiums

over the investigated time period and are presented in the following graph (see figure 6).


27

The graph illustrates the premium as a percentage of the exposed amount, which will give a

more applicable picture of the scenario.

Figure 6, Premium

According to the graph above the premium is indeed connected to the standard deviation.

It follows the same pattern and between the years 2008-2009 the premium is noticeably

high due to the high standard deviation presented in figure 4 and 5.

4.5 The total result of the hedging strategies

Sandvik AB is presently using three different strategies when conducting their currency risk

management. These strategies involve the use of forward contracts and the recently

implemented model Layered Basket Option hedging. The third strategy is to not actively

conduct any risk management and currencies are exchanged according to the spot rates. A

comparison of these strategies is necessary to obtain material for an analysis relevant to the

investigated problem.


28

Date Spot Rate 3-Months Basket Option

3-Months Forwards

Layered forward

Layered Basket Option

2003-12-31 2 752 966 634 2 858 072 406 2 887 871 990 2 951 664 573 2 898 728 238

2004-03-31 2 939 608 901 2 884 916 681 2 752 966 634 2 888 033 521 2 906 414 582

2004-06-30 2 887 038 400 2 897 028 261 2 939 608 901 2 877 573 161 2 866 974 148

2004-09-30 2 800 737 387 2 834 772 042 2 887 038 400 2 866 871 481 2 830 216 854

2004-12-31 2 692 557 652 2 760 873 342 2 800 737 387 2 845 087 831 2 786 570 345

2005-03-31 2 798 745 475 2 757 499 588 2 692 557 652 2 829 985 585 2 794 533 023

2005-06-30 3 064 324 650 3 019 164 849 2 798 745 475 2 794 769 729 3 006 346 421

2005-09-30 3 118 595 204 3 060 533 159 3 064 324 650 2 839 091 291 3 060 517 220

2005-12-31 3 200 001 606 3 140 247 129 3 118 595 204 2 918 555 745 3 142 052 523

2006-03-31 3 153 032 524 3 141 298 407 3 200 001 606 3 045 416 734 3 100 486 731

2006-06-30 2 853 690 732 3 099 902 474 3 153 032 524 3 133 988 496 3 063 795 740

2006-09-29 2 881 630 999 2 827 980 756 2 853 690 732 3 081 330 017 3 015 778 791

2006-12-29 2 769 289 448 2 830 072 333 2 881 630 999 3 022 088 965 2 949 564 266

2007-03-30 2 823 777 555 2 782 285 962 2 769 289 448 2 914 410 926 2 860 179 057

2007-06-30 2 833 049 701 2 802 178 485 2 823 777 555 2 832 097 184 2 788 271 974

2007-09-28 2 723 895 484 2 803 521 466 2 833 049 701 2 826 936 926 2 771 992 178

2007-12-31 2 732 145 591 2 702 490 052 2 723 895 484 2 787 503 047 2 744 930 570

2008-03-30 2 473 384 035 2 695 802 557 2 732 145 591 2 778 217 083 2 741 142 970

2008-06-30 2 545 833 743 2 508 253 058 2 473 384 035 2 690 618 703 2 672 685 050

2008-09-30 2 789 031 583 2 737 140 895 2 545 833 743 2 618 814 713 2 747 589 770

2008-12-31 2 897 798 012 2 843 846 772 2 789 031 583 2 635 098 738 2 850 482 148

2009-03-31 3 018 911 324 2 927 413 755 2 897 798 012 2 676 511 843 2 962 646 623

2009-06-30 3 050 018 284 2 957 409 401 3 018 911 324 2 812 893 666 3 009 984 422

2009-09-30 2 808 626 041 2 964 894 069 3 050 018 284 2 938 939 801 2 851 337 355

2009-12-31 2 904 463 130 2 850 227 321 2 808 626 041 2 943 838 415 2 863 715 128

2010-03-31 2 932 294 806 2 877 539 289 2 904 463 130 2 945 504 695 2 876 246 826

2010-06-30 3 070 082 228 3 001 016 089 2 932 294 806 2 923 850 565 2 972 828 126

2010-09-30 2 793 851 164 2 996 334 305 3 070 082 228 2 928 866 551 2 839 458 887

2010-12-31 2 825 091 267 2 761 286 898 2 793 851 164 2 925 172 832 2 847 013 000

2011-03-31 2 655 539 009 2 765 350 905 2 825 091 267 2 905 329 866 2 817 817 697

2011-06-30 2 641 921 514 2 585 801 499 2 655 539 009 2 836 140 917 2 744 802 789

2011-09-30 2 710 583 942 2 638 884 217 2 641 921 514 2 729 100 739 2 671 546 634

2011-12-31 2 790 610 812 2 738 533 433 2 710 583 942 2 708 283 933 2 711 405 902

Average 2 846 458 450 2 850 077 935 2 849 405 758 2 862 199 645 2 871 759 272

St. Deviation 5,03% 4,10% 5,07% 2,26% 2,67%

Table 3, Result from hedging strategies

Table 3 illustrates the outcome for each investigated strategy between the periods 2003-

2012. The sums represent the amount in SEK Sandvik acquired accordingly to each

strategy, and at the bottom of the table the average outcome for the total period is

presented. The standard deviation is based on the outcomes and indicates to what degree

the strategies’ outcome fluctuates between periods.

As seen in table 3, the Layered Forward and the Layered Basket Option hedging strategy are

generating the highest outcomes and the lowest volatility between periods. The 3-month

basket option lowers the volatility from 5,03% to 4,10% while the layered basket option

approach reduces the volatility from 5,03% to 2,67% in relation to the spot rate. The

layered forward reduces the volatility from 5,03% to 2,26%.


29

Figure 7, Result from hedging strategies

A comparison between the hedging strategies applied by Sandvik is illustrated in the graph

above (see figure 7). The 3-month forward contract only delays the outcome of the spot

rate and actually has a higher volatility during the investigated period. The 3-month basket

option slightly improves the outcome and volatility compared to the spot rate, but this

hedging strategy fails to capture the smoothening effect given by the layered approach. The

layered basket option and layered forward approach clearly show improvements of the

volatility and the total outcome in the currency exposure.

4.6 The results of the Layered Basket Option

The outcome of the Layered Basket Option, after testing it between the years 2003-2012,

compared to the spot rate is shown in the graph below. As mentioned earlier the average

volatility decreased from 5,03% to 2,67% when using this hedging strategy. It is illustrated

in the following graph that the hedging strategy prevent losses caused by downward

fluctuations in the spot rates but at the same time allow profits to be made when there is an

upward trend. The effectiveness of the hedge is clearly shown in the graph around June

2006, March 2008 and March 2011 (see figure 8).

Figure 8, Layered Basket Option vs. Spot Rate


30

4.7 The results of the Layered Forward

A comparison of the spot rate and the layered forward approach between the years 2003-

2012 is illustrated in the following graph. The volatility was decreased from 5,03% to

2,26% and the effectiveness of the hedge is shown around the same dates as the layered

basket option. During June 2006, March 2008 and March 2011 the hedging strategy of

forward contracts has a significant impact on the downward fluctuations of the spot rates

(see figure 9).

Figure 9, Layered Forward vs. Spot Rate

4.8 Manipulated baskets

In the table below it is shown that the currencies’ standard deviations have a larger effect

on the basket’s variance compared to a proportionally equally large change in correlation. A

reduction of the individual currencies standard deviation by 10 percent decreased the

variance by 19%, while a 10% reduction in the pairwise correlation decreased the basket

variance by 10% (see table 4).

2012 Q1 Change Effect on the Basket's Variance

Standard Deviation Reduction by 10% -19%

Correlation Reduction by 10% -10% Table 4, Manipulated Baskets

Since a similar procedure has been made on each quarter, it became clear that the standard

deviation consistently had a larger impact on the basket variance compared to the

correlation.


31

4.9 The effects of applying a basket

The table below illustrates the effects of applying a basket option instead of hedging the

currencies as individual vanilla options (see table 5). The percentage indicates how much

the volatility is reduced if a basket option is applied in comparison to the average volatility

if each currency were hedged separately through vanilla options.

Date Diversification improvements

Date

Diversification improvements

2003 Q1 17% 2007 Q3 44%

2003 Q2 37% 2007 Q4 52%

2003 Q3 109% 2008 Q1 50%

2003 Q4 103% 2008 Q2 34%

2004 Q1 82% 2008 Q3 24%

2004 Q2 62% 2008 Q4 47%

2004 Q3 68% 2009 Q1 124%

2004 Q4 49% 2009 Q2 74%

2005 Q1 53% 2009 Q3 66%

2005 Q2 57% 2009 Q4 83%

2005 Q3 48% 2010 Q1 91%

2005 Q4 18% 2010 Q2 55%

2006 Q1 9% 2010 Q3 16%

2006 Q2 12% 2010 Q4 11%

2006 Q3 17% 2011 Q1 15%

2006 Q4 11% 2011 Q2 -3%

2007 Q1 9% 2011 Q3 -9%

2007 Q2 22% 2011 Q4 -10%

Table 5, Diversification improvements

The effects of diversification differ between periods. During unstable periods the effects of

diversification are strong. In late 2003 and early 2009 the effects are perceptually large

compared to other periods. According to the table, applying a basket approach is preferable

in contrast to using vanilla options except in 2011 (see table 5).

4.10 Improved baskets – Divided Layered Basket

When working on the supposition that correlations of the currencies affect the total

volatility of the basket give us an opportunity to improve Sandvik’s current hedging

strategy. Matching currencies that are highly negatively correlated will decrease the total

volatility of the basket. When one currency has an upward trend the other will have a

downward trend. This will smoothen the fluctuations of the exposed currencies and further

hedge the risk. This leads to a reduced volatility and subsequently lower premiums of the

options. Furthermore, the weights of the currencies in the basket play a significant role in

matching the currencies to improve the basket options. Currencies with a large weight have

a great impact on the basket regardless of the correlation with the other currencies.

The problem is to find the ideal allocation of currencies in the baskets and create divided

layered basket options with currencies that have optimal correlations and weights according to

this hedging strategy.


32

An example that supports our findings to actively allocate the currencies into smaller

basket can be seen in the fourth quarter of 2011. The premium becomes substantially lower

when strategically dividing the basket option into two smaller baskets with currencies that

are mainly negatively correlated. Further, the weights (positive and negative) have played an

important role when allocating the baskets according to this strategy. The newly developed

baskets are presented below and a comparison between them and the original layered

basket option shows that the premium is reduced (see table 6 and appendix 9).

Basket 1 Weight SEK 2011 Q4 Basket 2 Weight SEK

CAD 3,91% 44 002 699 USD 53,49% 847 920 925

CHF -62,48% -703 142 870 AUD 28,23% 447 500 612

CZK 5,71% 64 259 696 GBP 9,35% 148 215 753

EUR 4,65% 52 330 575 SGD -11,41% -180 870 775

ZAR 37,52% 422 245 846 NOK -5,64% -89 405 011

PLN 8,32% 93 632 341 CPL 14,01% 222 085 851

KRW 12,22% 137 522 501 INR -7,21% -114 292 576

JPY 15,48% 174 210 173 BRL 7,75% 122 852 630

CNY 74,67% 840 327 754 RUB 11,43% 181 187 814

100% 1 125 388 716 100% 1 585 195 224

Premium 3 months 7 442 129 Premium 3 months 7 400 193

6 months 9 316 777 6 months 10 076 577

9 months 11 210 756 9 months 11 299 096

12 months 12 038 323 12 months 11 130 701

TOTAL 40 007 985 TOTAL 39 906 567

Table 6, Improved baskets

The premium paid in the fourth quarter 2011 was 91.339.419 SEK for the layered basket

option, compared to the divided layered basket option, which is (40007985 + 39906567)

79.914.552 SEK. This gives us a reduction of 12,5% of the premium paid.

A more simple approach is to remove the currency with the largest weight and highest

correlation. By removing the USD exposure from the basket in the third quarter of 2011

and hedging it separately as a vanilla option will further lower the premium of the layered

basket. In the following example the divided layered baskets option decrease the premium to

the amount of (53803779 + 26382435) 80.186.214 SEK, which gives us an improvement of

9,89% of the premium paid (see table 7 and appendix 9).


33

Basket 1 Weight SEK 2011 Q3 Basket 2 Weight SEK

AUD 24,48% 455 037 187

CAD 2,36% 43 790 850

CHF -37,60% -698 876 404

CZK 3,50% 65 046 462

EUR 2,81% 52 197 802

GBP 7,58% 140 830 800

ZAR 24,92% 463 159 858

SGD -9,53% -177 104 723

PLN 5,58% 103 702 000

NOK -4,83% -89 704 503

KRW 7,56% 140 598 578

JPY 8,27% 153 776 402

CNY 41,24% 766 552 901

CPL 12,25% 227 689 336

INR -6,25% -116 125 933

BRL 7,24% 134 545 455

RUB 10,41% 193 566 630 USD 100% 783 238 815

100% 1 858 682 698 100% 783 238 815

Premium 3 months 10 494 535 Premium 3 months 5 168 693

6 months 13 644 673 6 months 6 501 204

9 months 13 255 470 9 months 7 069 818

12 months 16 409 101 12 months 7 642 719

TOTAL 53 803 779 TOTAL 26 382 435

Table 7, Improved baskets

These examples prove that by actively constructing favorable baskets the premium may be

considerably decreased. The correlations and weights change over time so by constantly

evaluating the variables connected to the basket of currencies will result in an improved

currency risk management.

Chapter 5 G.Carlsson & R.Ericsson Analysis

34

5 Analysis

In this chapter an analysis of the different hedging methods is presented. The following discussions are built

on our empirical findings and why there exists incentives for multinational corporations to hedge currency

risk. Further, the analysis is based on how Sandvik AB perform during a fluctuating exchange market

and which hedging approach that suits the goals and strategies of the organization.

5.1 Incentives to hedge

This thesis has consistently argued the different reasons in why multinational corporations

should invest in a hedging strategy. Sandvik AB is a multinational corporation where the

general concern is to satisfy the shareholders. Therefore, the organization’s main priority is

not to implement an aggressive strategy with the intention to make substantial profits.

Instead, they emphasize the importance of reducing the effects caused by currency

fluctuations. The fundamental objective is consequently to exploit derivatives to attain a

predictable result. A hedging strategy should not jeopardize the accuracy of a desired result.

Hence, this thesis has proven that Sandvik’s purpose is to use a hedging strategy to achieve

a result that is easy to forecast, and it should protect the organization from fluctuations that

might affect the result.

5.2 The Layered approach

This thesis has proven that the layered approach has significant impacts on the results of

the different hedging strategies. By layering the hedge quarterly over a year generates

notable effects on the results compared to a spot strategy. The layered approach creates a

smoothening effect, which is difficult to achieve with any other approach. The

effectiveness of the layered approach is shown when implementing this strategy combined

with forward contracts. When entering static forward contracts every third month with the

same period the outcome is delayed by three months. This leads to no reduction in the

volatility, which is argued to be a goal for multinational corporations. However, a layered

forward strategy leads to a reduction of the volatility with approximately 55 % compared to

the spot strategy. The effectiveness of the layered approach is further proven when

comparing statically hedged basket options with quarterly intervals and basket options that

are hedged with a layered strategy. The three months static basket option has an overall

volatility of a total of 4,10%, compared to a layered approach combined with basket

options that gives an overall volatility of 2,67% (see table 8).

Strategy Spot Rate 3-Months Basket Option

3-Months Forwards

Layered forward

Layered Basket Option

Average 2 846 458 450 2 850 077 935 2 849 405 758 2 862 199 645 2 871 759 272

St. Deviation 5,03% 4,10% 5,07% 2,26% 2,67%

Table 8, Outcome of strategies

Dividing the hedging exposure and later hedge them with different time intervals

automatically spread the risk since the peaks and downs of the currency rates cancel out

each other. By increasing the number of different expiration dates may further decrease the


35

volatility since the hedges become more precise. Layering the hedge monthly over a year

would lead to twelve expiration dates for twelve parts of the exposure, but the complexity

of creating such an extensive layering strategy would probably cost more than the positive

outcome of the hedge.

The layered strategy cannot be used alone but has to be combined with another hedging

strategy for it to be useful. The two derivatives that have been combined with the layered

approach in this thesis are the basket option and the forward contracts. Both strategies

have different strengths and weaknesses, but it is proven that the two derivatives in

combination with the layered strategy generate favorable results.

5.3 The Basket approach

The positive effect from applying a basket is a reduction in the non-systematic risk. The

risk reduction is a result from the imperfect correlation between the underlying currencies,

where a correlation less than one will decrease the basket’s volatility and eventually also the

premium. By using formula 9 as a benchmark, it is easier to realize the effects. If the

correlation between two currencies is negative, the second part of the formula will turn

negative, which will reduce the basket’s variance. It will generate a lower variance if a large

proportion of the correlations are negative.

1st part 2nd part

∑

∑ ∑

(9)

Each currency will contribute with a non-diversifiable risk. If the correlation between two

currencies is 1, the diversification effect will be eliminated. Instead, their participation will

result in an increase in the basket’s variance because of the non-diversifiable risk. However,

the effects from adding additional currencies to a basket have a positive effect as long as

the correlation is less than one (see formula 9). Seen from a multinational corporation’s

perspective, premium costs can be reduced by using the concept of a basket approach.

Therefore, the correlation between the different currencies needs to be examined carefully

before creating a basket.

The effects of applying a basket is illustrated in table 9 where the average variance between

the individual currencies is compared to the basket’s variance. The result from applying a

basket varies between different time periods. By examining two periods where the

diversification effect differs, it is possible to localize why the effect differs. In 2003 Q3, the

diversification effect was 109%, compared to -9% in 2011 Q3. This implies that applying a

basket in 2011 Q3 results in a worse scenario in comparison to regular vanilla options. First

of all, the average correlation in 2003 Q3 was 0,52, compared to 0,66 in 2011 Q3 (see

appendix 11 and 19). This has an effect, where a lower correlation results in a lower

variance.

Diversification Improvement

Diversification Improvement 2003 Q3 109% 2011 Q3 -9%

Table 9, Diversification 2003 Q3 & 2011 Q3


36

Although, a generalization of the outcome based on the average correlation is not

sufficient. The average correlation shows the average between all currencies, but each

currency is represented by different weights, making the generalization unfair. A high

correlation between currencies that represent larger weights will have a larger effect.

Therefore, a high correlation between currencies that represent a larger weight will have a

larger impact on the basket variance.

The same logic is applicable for the standard deviation, where a high standard deviation

combined with a large weight will lead to a larger effect on the basket variance. These

notions need to be considered when a basket is created, since a weak structure of the

basket will eliminate the diversification effect, resulting in a high basket variance.

The conclusions drawn above are not applicable for all currencies in the basket. Some

currencies are represented by negative weights (see appendix 1-10). For currencies that

represent a negative weight, a positive correlation is required if the diversification effect will

be seized. By applying formula 9 as a benchmark, the second part turn negative if the weight

is negative. A negative correlation in combination with a negative weight will increase the

variance. For currencies with negative weights, a high positive correlation is therefore

desired, resulting in a decrease in the basket’s variance.

Overall, this thesis has proven that a basket approach has a substantial effect if used in a

carefully prepared manner. The underlying factors need to be examined and evaluated. If

the proportion and structure between the weights and correlation is carefully planned,

applying a basket approach can seize significant advantages. Although, a basket that is not

carefully planned can result in a basket variance that is higher compared to the average

variance between individual currencies.

At last, we believe that a perfectly built basket is a benefit for every organization that is

exposed to currency risks in several currencies.

5.4 The Layered Forward approach

When combining the derivative of forward contracts and the strategy of layered hedging an

effective tool for risk management has been developed. We have earlier discussed the

benefits when conducting the layered approach together with forward contracts. The

results of the outcome from our test period state that the layered forward approach has the

lowest volatility among our investigated strategies. There is especially one great benefit in

using the layered forward approach when undertaking currency risk management within a

multinational corporation. This benefit is that a forward contract does not have any

premium costs to consider. The different parties only enter a binding contract to exchange

an amount of currencies at a specific date in the future. The absence of premiums paid is a

great advantage for the forward contract, but as mentioned earlier there is always one

winner and loser in a binding contract where no premiums exist.

The party that oblige itself to receive a predetermined amount of SEK in the future, in our

case Sandvik, bet on a weakening of the foreign currencies and is safe from drops in the


37

exchange rates. If this scenario occurs, Sandvik becomes the winner in this contract. The

financial institute that has agreed to buy the currencies will become the winner when the

currency market is strong and Sandvik will miss out of realized exchange profits. Sandvik is

obligated to prosecute the contract and sell the foreign currency at the specific date. Their

exposure becomes fixed and the cash flow is negatively affected. There is no limit of how

much profit a company that hedge with forward contracts can miss out on. An unforeseen

strength in the foreign currency exposure will have a negative effect in the corporation’s

economic reports if they do not follow the upward trend that their competitors are

realizing. Some negative effects may be illustrated in our results during the years of 2005

and 2008-2009 where the layered forward strategy miss out of the upward trends in the

spot rate (see figure 10).

Figure 10, Layered Forward

The foreign exchange market is a very volatile market where an infinite amount of variables

affects the movements of different currencies. Our results show that the volatility is

decreased by actively hedge with layered forwards and that the organization is safe from

drops in the exchange rates. The shareholders play an important role in the management’s

decision-making process. From a shareholder’s perspective, it is sometimes unacceptable

when the market outperforms the corporate strategy. A strategy where the corporate is safe

from drops in the exchange rates but at the same time follows the strong upward trends is

preferable to satisfy the shareholders and other stakeholders.

5.5 The Layered Basket Option approach

Buying options is a well-known hedging strategy, not at least when it comes to currency

risk management. A basket option is an extension of the vanilla option that captures the

diversification effect. The theory of basket options states that due to the correlation

between the currencies the overall volatility decreases when they are hedged together

instead of separately. The basket put option combined with a layered approach could lead

to an optimal hedging strategy for corporations that are exposed to foreign currencies.

The benefits of buying put options as a hedging tool are several; firstly the owner only buys

the right to sell the underlying asset and not the obligation to do so. This means that when


38

a strengthening in the foreign currencies occurs, the owner of the option can let the

contract default and be a part of the upward trend and only realize the loss of the premium

paid. When a drop in the currency market occurs, the owner still possesses the right to sell

the currencies for the already predetermined strike price. This allows the owner of a put

option to secure itself from downward trends in the foreign exchange market and at the

same time earn profits when the market is strong.

We have argued that a strong incentive for corporations, such as Sandvik, to hedge risks in

the foreign exchange market is to decrease the volatility and to eliminate fluctuations in the

rates. According to our result, the layered basket approach has clearly reduced the volatility

compared to the spot rates (see table 10).

Strategy Spot Rate Layered Basket Option Hedging

Average 2 846 458 450 2 871 759 272

St. Deviation 5,03% 2,67%

Table 10, Spot vs. Layered Basket Option

The effectiveness of the strategy is shown in figure 8 where the basket put option avoids

losses due to drops in the spot rates. Contrary to the layered forward approach there

cannot be discovered any obvious deviations when the spot rates strongly outperform the

layered basket option approach (see figure 11). During the years 2005 and 2008-2009

where the layered forward hedge was clearly outperformed by the foreign exchange market,

the layered basket option approach made it possible to make earnings from the positive

movements in the spot rates that covered the premiums paid and realized profits.

Figure 11, Layered Forward vs. Layered Basket

A comparison between the Layered Forward and the Layered Basket Option hedging

methods is necessary to draw relevant conclusions regarding the currency risk management

within Sandvik AB because of the similar reduction in volatility. The investigated time

period is a relatively long period, which involves two financial crises and large fluctuations

in the foreign exchange market. During this period the Layered Forward strategy has

performed slightly better in terms of volatility, than the Layered Basket Option hedging

method. This is because of the unpredictable downward fluctuations that have occurred

during this time period. A shorter investigated time period where the foreign exchange


39

market performs stronger would clearly show unfavorable results for the forward contracts.

A hedging strategy that yields consistency with the spot rates should probably satisfy the

stakeholders in a short- as well as a long-term perspective. As mentioned earlier, the

shareholders play a central role in the decision making of what kind of risk management

program the corporation should undertake. Even though it may be difficult to justify high

premium costs a Layered Basket Option hedging approach would be in all stakeholders’

interest. The company secures itself from large drops in their foreign currency but at the

same time follows the upward trend, while a forward contract adds a risk to the currency

risk program in the form of lost profits.

We believe that a layered approach combined with basket options would be an optimal

hedging strategy for Sandvik and other multinational corporations. To communicate the

strategy to the stakeholders is of great importance. To make it even more attractive to

implement, improvements that creates lower premiums should be of great interest for risk

managers.

5.6 Improvements

According to our findings, there are improvement possibilities in the third and fourth

quarters in 2011 (see table 6 and 7)

The USD and the CNY have a correlation of approximately 1 (see appendix 1-10). If two

currencies have a correlation of 1, their correlation with other currencies coincides. The

explanation is the current peg, which is placed on the USD by the Chinese government.

This creates a problem, since the pegging makes the currencies move in identical patterns.

The pegging results in a correlation close to 1 and a similar standard deviation. There is no

effect of including the USD and CNY in one basket since they move in identical patterns.

Furthermore, the USD and the CNY consistently represent the largest weight in the basket.

The two currencies combined represent approximately 60% of the weights in the baskets

(see appendix 1-10). If a currency represents a large weight, it will obviously have a larger

effect on the basket variance. If the American and Chinese currencies represent 60% of the

basket’s weight, the basket will be strongly reflected in those currencies. A large weight

equals a strong influence on the basket’s variance. If a currency has a low standard

deviation and is negatively correlated with several currencies, the impact will still be

strongly determined by the weight it represents. Therefore, when building new baskets, the

foundation should be to split currencies with large weights that are highly correlated. In our

case, the primer idea has been to split American and Chinese currencies.

Table 6 illustrates an example when a larger basket was divided into two smaller baskets.

The idea was to separate the USD from the CNY, and thereafter place currencies

strategically in the best-suited basket. The goal was to capture the diversification effect to

maximally reduce the non-systematic risk, where the correlation between currencies was

the benchmark. The original basket consists of both positive and negative weights, where

the negative weighted currencies will lower the exposed amount, leading to a reduction in

premium. The negatively weighted currencies need to be highly correlated with other


40

currencies for the diversification effect to be seized. The CHF is the largest negatively

weighted currency (see appendix 1-10), which allows us to lower the exposed amount in a

basket. The optimal situation would be to have a correlation of 1 between the CHF and a

currency that represents a large positive weight. That would lead to a variance reduction as

well as a decrease in the exposed amount.

The outcome from dividing the basket seen in table 11 illustrates a premium reduction by

12,5% in comparison to the original basket. The example proves that active choices can

lead to distinguishable effects on the premiums. If Sandvik would hedge their entire

exposed amount through the Layered Basket Option hedging, the yearly premiums would

correspond to approximately 300.000.000 SEK. If Sandvik could manage to lower their

premiums by 12,5%, they would reduce their premium expenditures by approximately

37.500.000 SEK a year.

Divided Baskets Original Basket Improvement

40 007 985

39 906 567

79 914 552 91 339 419 12,5%

Table 11, Premium reduction

The improvement-strategy includes dividing larger basket into smaller baskets. The

interesting factor concerns portfolio theory and the concept behind the diversification

effect. When additional assets are added to a basket, the risk is generally reduced. If the

correlations between currencies are too high, the diversification effect will not be fully

exploited. Instead we are separating currencies to correct the misuse of the concept of

applying a basket theory. As seen in “2011 Q2 - Q4”, an incorrect structure of a basket

will lead to a reduction of the diversification effect, which will increase the basket’s

variance in comparison to vanilla options (see table 12). Organizations that apply basket

options should carefully plan and investigate the structure of their baskets to understand

the actual effects.

Date Diversification Improvements

2011 Q2 -3%

2011 Q3 -9%

2011 Q4 -10%

Table 12, Reduction in diversification effect

Overall, organizations that are exposed to currency risks should constantly strive to find

the best hedging alternative. If the strategy involves a basket option, it is important to

realize the actual effects from the basket. The structure of the basket builds the foundation

of the hedging strategy’s outcome.

Chapter 6 G.Carlsson & R.Ericsson Concluding Remarks

41

6 Concluding Remarks

In this last chapter, the research questions will be answered along with the purpose of this thesis. A

conclusion will be drawn from the empirical findings and the discussion in the analysis section. A shorter

section will present and discuss recommendations of further studies within this subject.

6.1 Conclusions

The range of hedging strategies is wide and complex, and it is difficult to select one strategy

as superior. The fundamental issue within corporations is to determine the most suitable

strategy according to their objectives and goals. Furthermore, corporations need to adapt

their strategy to the external environment. That is, corporations need to be aware that

hedging instruments behave differently in diverse environments. This thesis has mainly

focused on forward contracts and options, where some distinctive disparities are

recognized considering external circumstances. The connection between the objectives,

goals and the environment need to be linked before a strategy is selected and implemented.

The volatility of the market has a large impact of what hedging strategy a corporation

should implement. A high volatility will be reflected in an option’s premium, while a

forward contract is cost-free regardless of the financial climate. On the contrary, an option

has the possibility to capture rises, while a forward contract only protects corporations

from drops in the exchange market.

Multinational corporations ought to constantly seek for improved hedging strategies. An

innovative procedure is to combine hedging strategies to seize the benefits from several

alternatives. This thesis suggests that there is no superior hedging strategy, since

corporations need to adapt their strategy accordingly to their objectives.

To hedge or not to hedge has been actively discussed in this thesis among others. An in-

depth evaluation of the Layered Basket Option hedging model has been conducted

together with comparisons with other hedging strategies. The question still lies at hand, is

the Layered Basket Option hedging model the optimal strategy for a corporation such as

Sandvik AB? The role of the shareholders has been discussed in the analysis. The hedging

model must correspond to the overall goals and strategies throughout the organization as

well as the shareholders expectations.

The results have undoubtedly stated that the Layered Basket Option hedging strategy

should be implemented instead of following a spot rate strategy. The volatility in the

exchange rates becomes substantially diminished when this strategy is implemented. The

strategy of layering basket options of currencies allows the corporation to capture upward

trends and at the same time be secured from drops in the exchange rates. Improvements of

actively allocating optimal baskets allow lower premiums to be paid which will make it even

more attractive to the shareholders.

Chapter 6 G.Carlsson & R.Ericsson Concluding Remarks

42

According to our results and discussions in our analysis the Layered Basket Option hedging

strategy is indeed an optimal strategy for Sandvik AB and other organizations with similar

currency risk management strategies.

6.2 Discussion and further studies

We have stated that the Layered Basket Option is the most suitable hedging strategy for

Sandvik AB and there are several motives in why this is stated. The layered approach

generates a lower volatility but the Layered Basket Option hedging strategy contributes

with certain attributes that cannot be ignored. The improvement possibilities sometimes

generate such favorable outcomes that cannot be overlooked. Also, during some time-

periods the layered forward approach is outperformed by the market, which is not

acceptable from a shareholders perspective. A layered forward approach also results in a

fixed cash flow since the corporation is obligated to fulfill the contract. Another downside

with the layered approach is the process of finding a second party in an agreement. A

counterpart may be in an unfavorable position in the market. Therefore, a corporation may

not always find a contract that meets their terms of conditions.

The Layered Basket Option hedging requires further investigations since it is a recently

developed model. It has been proven that there exist great potential with this model as far

as hedging currency risk is concerned. Furthermore, improvement possibilities have been

discovered and additional studies are required regarding this interesting finding.

This thesis has further shown evidence that currency risk hedging is a crucial process for

Sandvik and other corporations that are active on the global market. The investigated

effectiveness of the hedging strategies depends on how the volatility in the foreign

exchange market is calculated. To get the volatility right when pricing the premiums for the

basket options is fundamental to achieve fair evaluations of the Layered Basket Option

hedging model. The volatility we based our calculations on was received through portfolio

theory and we suggest that further studies regarding the estimation of the volatility are

conducted. Other models, such as a Monte Carlo simulation to determine the volatility

would provide further insight into the premium pricing of the Layered Basket Option.

“…stochastic volatility does not make a huge difference as far as the pricing is concerned if you get the

average volatility right. It makes a big difference as far as hedging is concerned.”

- John Hull –

Chapter 7 G.Carlsson & R.Ericsson List of References

43

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46

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Chapter 8 G.Carlsson & R.Ericsson Appendices

47

8 Appendices

8.1 Appendix 1-10 Basket Variance, Weights and Premiums 2003-2012

Appendix 1 - 2003

2003 Q1 Weight (wn) Annual volatil ity (σn) wnσn 2003 Q2 Weight (wn) Annual volatil ity (σn) wnσn

USD 35,94% 12,04% 4,33% USD 35,30% 11,59% 4,09%

AUD 10,95% 12,28% 1,34% AUD 11,56% 12,04% 1,39%

CAD 1,23% 11,86% 0,15% CAD 1,30% 11,61% 0,15%

CHF -19,50% 9,24% -1,80% CHF -19,58% 8,91% -1,74%

CZK 1,66% 11,72% 0,19% CZK 1,67% 11,59% 0,19%

EUR 1,73% 7,85% 0,14% EUR 1,77% 7,61% 0,13%

GBP 6,46% 10,16% 0,66% GBP 6,23% 10,13% 0,63%

ZAR 16,74% 22,56% 3,78% ZAR 17,87% 22,06% 3,94%

SGD -5,75% 10,88% -0,63% SGD -5,55% 10,81% -0,60%

PLN 3,40% 11,90% 0,41% PLN 3,12% 12,29% 0,38%

NOK -3,19% 7,82% -0,25% NOK -2,99% 8,86% -0,26%

KRW 5,80% 14,02% 0,81% KRW 5,41% 15,08% 0,82%

JPY 4,79% 13,61% 0,65% JPY 4,73% 12,53% 0,59%

CNY 27,45% 12,05% 3,31% CNY 26,97% 11,54% 3,11%

CPL 6,78% 15,58% 1,06% CPL 6,53% 16,92% 1,10%

INR -4,95% 12,35% -0,61% INR -4,92% 11,51% -0,57%

BRL 2,72% 32,97% 0,90% BRL 2,84% 34,65% 0,98%

RUB 7,74% 12,01% 0,93% RUB 7,75% 11,72% 0,91%

100% Indv. Std 15,36% 100% Indv. Std 15,26%

Basket Variance 1,72% Basket Variance 1,25%

Std. Basket 13,11% Std. Basket 11,17%

Premium using Black & Scholes Premium using Black & Scholes

3 months 14 007 115 3 months 13 909 690

6 months 19 127 601 6 months 13 320 801

9 months 21 467 996 9 months 18 499 389

12 months 23798439,4 12 months 18 200 476

TOTAL 78 401 151 TOTAL 63 930 356


USD 33,91% 11,91% 4,04% USD 33,34% 12,01% 4,00%

AUD 12,33% 11,80% 1,45% AUD 12,28% 12,71% 1,56%

CAD 1,35% 12,08% 0,16% CAD 1,33% 12,70% 0,17%

CHF -18,83% 8,79% -1,65% CHF -18,97% 7,62% -1,45%

CZK 1,72% 10,52% 0,18% CZK 1,69% 8,79% 0,15%

EUR 1,79% 6,98% 0,13% EUR 1,78% 6,18% 0,11%

GBP 6,27% 10,26% 0,64% GBP 6,20% 9,50% 0,59%

ZAR 18,06% 23,42% 4,23% ZAR 19,16% 23,11% 4,43%

SGD -5,35% 11,08% -0,59% SGD -5,35% 11,48% -0,61%

PLN 3,16% 12,88% 0,41% PLN 3,07% 11,92% 0,37%

NOK -2,89% 9,19% -0,27% NOK -2,91% 8,55% -0,25%

KRW 5,44% 15,75% 0,86% KRW 5,55% 15,39% 0,85%

JPY 4,48% 12,33% 0,55% JPY 4,74% 12,36% 0,59%

CNY 25,91% 11,86% 3,07% CNY 25,49% 12,03% 3,07%

CPL 6,62% 16,51% 1,09% CPL 6,86% 16,60% 1,14%

INR -4,84% 11,86% -0,57% INR -4,83% 12,14% -0,59%

BRL 3,18% 34,42% 1,09% BRL 3,05% 26,07% 0,80%

RUB 7,70% 12,01% 0,92% RUB 7,51% 12,21% 0,92%

100% Indv. Std 15,75% 100% Indv. Std 15,84%




3 months 7 940 205 3 months 7 867 151

6 months 7 715 071 6 months 7 630 072

9 months 10 200 431 9 months 10 098 378

12 months 10 210 859 12 months 7 751 668

TOTAL 36 066 565 TOTAL 33 347 270


48

Appendix 2 - 2004


USD 32,48% 12,71% 4,13% USD 31,91% 14,34% 4,58%

AUD 13,24% 12,71% 1,68% AUD 13,18% 13,07% 1,72%

CAD 1,36% 12,16% 0,16% CAD 1,31% 12,89% 0,17%

CHF -19,70% 7,90% -1,56% CHF -18,90% 8,04% -1,52%

CZK 1,76% 8,64% 0,15% CZK 1,66% 8,34% 0,14%

EUR 1,88% 6,09% 0,11% EUR 1,80% 6,06% 0,11%

GBP 6,48% 10,07% 0,65% GBP 6,57% 10,26% 0,67%

ZAR 19,42% 23,93% 4,65% ZAR 20,21% 24,54% 4,96%

SGD -5,31% 11,51% -0,61% SGD -5,29% 12,74% -0,67%

PLN 3,16% 12,41% 0,39% PLN 3,00% 12,38% 0,37%

NOK -3,00% 8,38% -0,25% NOK -2,86% 9,02% -0,26%

KRW 5,22% 15,27% 0,80% KRW 5,33% 15,51% 0,83%

JPY 4,80% 12,15% 0,58% JPY 4,85% 13,67% 0,66%

CNY 24,82% 12,74% 3,16% CNY 24,38% 14,35% 3,50%

CPL 7,46% 17,82% 1,33% CPL 7,07% 17,35% 1,23%

INR -4,72% 13,04% -0,62% INR -4,87% 14,99% -0,73%

BRL 3,01% 22,06% 0,66% BRL 2,94% 20,44% 0,60%

RUB 7,65% 13,14% 1,01% RUB 7,70% 14,68% 1,13%

100% Indv. Std 16,44% 100% Indv. Std 17,49%




3 months 7 449 896 3 months 13 673 055

6 months 9 750 897 6 months 15 926 486

9 months 12 072 467 9 months 18 258 958

12 months 12 001 268 12 months 17 920 955

TOTAL 41 274 528 TOTAL 65 779 454


USD 32,40% 14,71% 4,77% USD 32,32% 13,97% 4,51%

AUD 12,19% 13,98% 1,70% AUD 12,68% 12,29% 1,56%

CAD 1,30% 12,89% 0,17% CAD 1,38% 11,51% 0,16%

CHF -19,42% 8,01% -1,56% CHF -19,47% 7,08% -1,38%

CZK 1,72% 9,26% 0,16% CZK 1,77% 9,19% 0,16%

EUR 1,81% 6,19% 0,11% EUR 1,84% 5,16% 0,10%

GBP 6,57% 10,28% 0,68% GBP 6,55% 9,32% 0,61%

ZAR 20,79% 23,46% 4,88% ZAR 19,95% 22,64% 4,52%

SGD -5,23% 12,68% -0,66% SGD -5,33% 11,65% -0,62%

PLN 3,18% 11,77% 0,37% PLN 3,34% 11,56% 0,39%

NOK -2,87% 8,39% -0,24% NOK -2,96% 8,44% -0,25%

KRW 5,37% 15,37% 0,83% KRW 5,38% 14,58% 0,78%

JPY 4,69% 13,97% 0,66% JPY 4,64% 12,62% 0,59%

CNY 24,77% 14,72% 3,65% CNY 24,70% 13,98% 3,45%

CPL 6,92% 17,38% 1,20% CPL 7,21% 16,62% 1,20%

INR -4,66% 15,42% -0,72% INR -4,66% 14,64% -0,68%

BRL 2,80% 17,67% 0,49% BRL 3,03% 16,09% 0,49%

RUB 7,67% 15,02% 1,15% RUB 7,62% 14,25% 1,09%

100% Indv. Std 17,64% 100% Indv. Std 16,66%




3 months 10 645 160 3 months 13 074 728

6 months 12 950 451 6 months 17 803 388

9 months 15 299 604 9 months 19 963 346

12 months 15 092 797 12 months 22 186 488

TOTAL 53 988 012 TOTAL 73 027 950


49

Appendix 3 – 2005


USD 30,80% 14,34% 4,42% USD 31,39% 13,09% 4,11%

AUD 13,00% 12,31% 1,60% AUD 13,13% 11,50% 1,51%

CAD 1,38% 11,81% 0,16% CAD 1,40% 10,84% 0,15%

CHF -20,26% 6,58% -1,33% CHF -19,70% 5,99% -1,18%

CZK 1,91% 9,12% 0,17% CZK 1,89% 8,52% 0,16%

EUR 1,91% 5,17% 0,10% EUR 1,87% 4,63% 0,09%

GBP 6,60% 9,33% 0,62% GBP 6,63% 8,54% 0,57%

ZAR 21,73% 20,87% 4,53% ZAR 20,16% 18,97% 3,82%

SGD -5,24% 11,69% -0,61% SGD -5,28% 10,42% -0,55%

PLN 3,72% 11,47% 0,43% PLN 3,61% 11,54% 0,42%

NOK -3,12% 8,43% -0,26% NOK -3,04% 6,88% -0,21%

KRW 5,70% 14,81% 0,84% KRW 5,91% 13,60% 0,80%

JPY 4,75% 12,75% 0,61% JPY 4,63% 10,79% 0,50%

CNY 23,53% 14,32% 3,37% CNY 23,97% 13,12% 3,15%

CPL 7,54% 15,98% 1,20% CPL 7,28% 14,93% 1,09%

INR -4,70% 14,90% -0,70% INR -4,75% 13,22% -0,63%

BRL 3,11% 15,91% 0,49% BRL 3,15% 15,53% 0,49%

RUB 7,65% 14,33% 1,10% RUB 7,75% 12,91% 1,00%

100% Indv. Std 16,73% 100% Indv. Std 15,28%




3 months 9 966 011 3 months 10 311 472

6 months 14 587 989 6 months 12 534 323

9 months 14 233 819 9 months 12 225 379

12 months 16 414 838 12 months 14 623 124

TOTAL 55 202 657 TOTAL 49 694 299


USD 31,64% 12,63% 4,00% USD 30,80% 12,86% 3,96%

AUD 13,05% 10,22% 1,33% AUD 12,75% 9,87% 1,26%

CAD 1,39% 10,90% 0,15% CAD 1,43% 11,26% 0,16%

CHF -18,52% 5,38% -1,00% CHF -17,95% 5,49% -0,99%

CZK 1,77% 7,99% 0,14% CZK 1,75% 8,22% 0,14%

EUR 1,75% 4,58% 0,08% EUR 1,70% 4,90% 0,08%

GBP 6,34% 8,12% 0,52% GBP 6,10% 8,28% 0,50%

ZAR 18,93% 16,44% 3,11% ZAR 19,38% 14,73% 2,85%

SGD -5,21% 10,11% -0,53% SGD -5,06% 10,37% -0,52%

PLN 3,44% 12,00% 0,41% PLN 3,44% 12,75% 0,44%

NOK -2,98% 6,76% -0,20% NOK -2,90% 6,81% -0,20%

KRW 5,86% 12,63% 0,74% KRW 5,66% 12,76% 0,72%

JPY 4,52% 10,13% 0,46% JPY 4,30% 10,43% 0,45%

CNY 24,18% 12,65% 3,06% CNY 24,13% 12,95% 3,13%

CPL 7,43% 13,60% 1,01% CPL 7,92% 13,53% 1,07%

INR -4,81% 12,53% -0,60% INR -4,63% 12,63% -0,59%

BRL 3,59% 15,54% 0,56% BRL 3,73% 17,34% 0,65%

RUB 7,61% 12,01% 0,91% RUB 7,45% 11,58% 0,86%

100% Indv. Std 14,16% 100% Indv. Std 13,99%




3 months 11 289 950 3 months 14 515 511

6 months 13 711 893 6 months 16 840 614

9 months 13 402 933 9 months 19 309 636

12 months 15 982 254 12 months 21 846 583

TOTAL 54 387 030 TOTAL 72 512 345


50

Appendix 4 - 2006


USD 30,88% 12,45% 3,84% USD 30,63% 12,11% 3,71%

AUD 12,26% 9,63% 1,18% AUD 11,88% 9,72% 1,16%

CAD 1,43% 11,15% 0,16% CAD 1,41% 11,71% 0,17%

CHF -17,61% 5,75% -1,01% CHF -17,66% 6,06% -1,07%

CZK 1,75% 8,47% 0,15% CZK 1,82% 8,66% 0,16%

EUR 1,68% 4,98% 0,08% EUR 1,71% 5,40% 0,09%

GBP 5,93% 8,28% 0,49% GBP 5,96% 8,49% 0,51%

ZAR 19,45% 13,80% 2,68% ZAR 19,88% 12,97% 2,58%

SGD -5,15% 10,17% -0,52% SGD -5,26% 10,35% -0,54%

PLN 3,45% 12,66% 0,44% PLN 3,44% 12,05% 0,41%

NOK -2,82% 7,44% -0,21% NOK -2,88% 8,00% -0,23%

KRW 5,84% 12,18% 0,71% KRW 6,03% 12,58% 0,76%

JPY 4,14% 10,27% 0,43% JPY 4,13% 11,00% 0,45%

CNY 24,20% 12,50% 3,02% CNY 24,17% 12,16% 2,94%

CPL 8,16% 13,61% 1,11% CPL 7,90% 13,91% 1,10%

INR -4,54% 11,93% -0,54% INR -4,55% 11,61% -0,53%

BRL 3,54% 19,59% 0,69% BRL 3,78% 19,84% 0,75%

RUB 7,40% 10,54% 0,78% RUB 7,61% 9,95% 0,76%

100% Indv. Std 13,48% 100% Indv. Std 13,16%




3 months 14 938 619 3 months 14 675 800

6 months 20 341 383 6 months 17 026 577

9 months 22 809 257 9 months 19 522 864

12 months 22 469 322 12 months 22 087 826

TOTAL 80 558 581 TOTAL 73 313 068


USD 31,43% 12,29% 3,86% USD 31,55% 11,84% 3,74%

AUD 12,63% 10,09% 1,27% AUD 12,74% 9,96% 1,27%

CAD 1,52% 11,98% 0,18% CAD 1,52% 11,65% 0,18%

CHF -19,27% 6,17% -1,19% CHF -18,93% 6,32% -1,20%

CZK 1,96% 8,43% 0,17% CZK 1,97% 7,48% 0,15%

EUR 1,84% 5,45% 0,10% EUR 1,83% 5,54% 0,10%

GBP 6,50% 8,31% 0,54% GBP 6,60% 8,46% 0,56%

ZAR 17,51% 14,70% 2,57% ZAR 16,27% 15,71% 2,56%

SGD -5,51% 10,48% -0,58% SGD -5,52% 10,05% -0,55%

PLN 3,58% 11,77% 0,42% PLN 3,66% 10,53% 0,38%

NOK -3,11% 8,15% -0,25% NOK -2,98% 8,75% -0,26%

KRW 6,34% 13,03% 0,83% KRW 6,38% 12,86% 0,82%

JPY 4,34% 10,93% 0,48% JPY 4,23% 10,63% 0,45%

CNY 24,87% 12,35% 3,07% CNY 25,22% 11,73% 2,96%

CPL 7,94% 14,24% 1,13% CPL 8,00% 13,60% 1,09%

INR -4,53% 12,07% -0,55% INR -4,56% 11,69% -0,53%

BRL 3,89% 21,44% 0,83% BRL 3,90% 19,95% 0,78%

RUB 8,06% 9,77% 0,79% RUB 8,11% 9,41% 0,76%

100% Indv. Std 13,68% 100% Indv. Std 13,24%




3 months 13 282 513 3 months 13 412 561

6 months 15 410 113 6 months 18 308 072

9 months 17 669 408 9 months 20 558 756

12 months 17 399 143 12 months 20 186 587

TOTAL 63 761 175 TOTAL 72 465 976


51

Appendix 5 - 2007


USD 30,70% 11,11% 3,41% USD 30,74% 10,83% 3,33%

AUD 13,10% 9,63% 1,26% AUD 13,49% 9,76% 1,32%

CAD 1,42% 11,49% 0,16% CAD 1,44% 11,34% 0,16%

CHF -18,89% 5,89% -1,11% CHF -19,03% 6,35% -1,21%

CZK 2,05% 6,92% 0,14% CZK 2,04% 7,26% 0,15%

EUR 1,86% 5,15% 0,10% EUR 1,88% 5,28% 0,10%

GBP 6,72% 7,64% 0,51% GBP 6,77% 7,99% 0,54%

ZAR 17,39% 16,69% 2,90% ZAR 16,83% 17,36% 2,92%

SGD -5,55% 9,59% -0,53% SGD -5,62% 9,25% -0,52%

PLN 3,84% 9,68% 0,37% PLN 3,86% 9,67% 0,37%

NOK -3,03% 8,44% -0,26% NOK -3,11% 8,41% -0,26%

KRW 6,32% 12,49% 0,79% KRW 6,25% 11,20% 0,70%

JPY 4,08% 9,93% 0,41% JPY 4,14% 10,40% 0,43%

CNY 24,87% 11,08% 2,76% CNY 25,14% 10,73% 2,70%

CPL 7,84% 12,08% 0,95% CPL 7,74% 11,43% 0,89%

INR -4,60% 11,33% -0,52% INR -4,71% 11,59% -0,55%

BRL 3,85% 17,36% 0,67% BRL 4,00% 16,03% 0,64%

RUB 8,03% 8,59% 0,69% RUB 8,15% 8,22% 0,67%

100% Indv. Std 12,70% 100% Indv. Std 12,38%




3 months 12 889 667 3 months 10 372 898

6 months 14 954 340 6 months 12 646 431

9 months 17 146 814 9 months 14 928 286

12 months 16 884 542 12 months 12 283 109

TOTAL 61 875 363 TOTAL 50 230 723


USD 30,05% 9,85% 2,96% USD 29,56% 9,78% 2,89%

AUD 13,81% 9,37% 1,29% AUD 14,18% 11,55% 1,64%

CAD 1,52% 10,51% 0,16% CAD 1,60% 10,53% 0,17%

CHF -18,42% 6,62% -1,22% CHF -19,01% 7,01% -1,33%

CZK 1,97% 7,59% 0,15% CZK 2,13% 8,00% 0,17%

EUR 1,86% 5,63% 0,10% EUR 1,93% 5,56% 0,11%

GBP 6,74% 8,00% 0,54% GBP 6,74% 8,13% 0,55%

ZAR 17,03% 15,45% 2,63% ZAR 17,15% 14,71% 2,52%

SGD -5,45% 8,83% -0,48% SGD -5,53% 8,57% -0,47%

PLN 3,91% 8,94% 0,35% PLN 4,04% 8,29% 0,34%

NOK -3,14% 8,07% -0,25% NOK -3,36% 7,46% -0,25%

KRW 6,23% 10,33% 0,64% KRW 6,19% 10,13% 0,63%

JPY 3,85% 10,42% 0,40% JPY 4,07% 12,81% 0,52%

CNY 24,96% 9,78% 2,44% CNY 24,90% 9,72% 2,42%

CPL 7,76% 10,46% 0,81% CPL 7,87% 10,39% 0,82%

INR -4,89% 10,88% -0,53% INR -4,93% 10,81% -0,53%

BRL 4,17% 13,25% 0,55% BRL 4,31% 15,02% 0,65%

RUB 8,03% 7,76% 0,62% RUB 8,17% 7,62% 0,62%

100% Indv. Std 11,18% 100% Indv. Std 11,45%




3 months 7 788 630 3 months 7 382 059

6 months 10 034 970 6 months 7 172 750

9 months 7 441 548 9 months 7 179 094

12 months 9 941 779 12 months 9 493 100

TOTAL 35 206 928 TOTAL 31 227 002


52

Appendix 6- 2008


USD 29,39% 10,29% 3,02% USD 29,84% 11,77% 3,51%

AUD 13,96% 12,85% 1,79% AUD 14,76% 14,01% 2,07%

CAD 1,60% 11,62% 0,19% CAD 1,56% 12,85% 0,20%

CHF -19,46% 7,62% -1,48% CHF -22,57% 9,00% -2,03%

CZK 2,24% 8,58% 0,19% CZK 2,60% 8,56% 0,22%

EUR 1,97% 5,62% 0,11% EUR 2,16% 5,58% 0,12%

GBP 6,52% 9,09% 0,59% GBP 6,63% 10,54% 0,70%

ZAR 17,11% 14,45% 2,47% ZAR 14,64% 16,86% 2,47%

SGD -5,67% 8,88% -0,50% SGD -6,01% 10,10% -0,61%

PLN 4,32% 8,42% 0,36% PLN 4,86% 7,65% 0,37%

NOK -3,33% 7,71% -0,26% NOK -3,61% 7,47% -0,27%

KRW 6,01% 10,53% 0,63% KRW 5,77% 13,26% 0,77%

JPY 4,16% 14,81% 0,62% JPY 4,73% 16,92% 0,80%

CNY 25,44% 10,02% 2,55% CNY 26,92% 11,60% 3,12%

CPL 8,02% 10,98% 0,88% CPL 9,32% 11,68% 1,09%

INR -4,94% 11,20% -0,55% INR -4,92% 12,27% -0,60%

BRL 4,42% 15,98% 0,71% BRL 4,58% 16,37% 0,75%

RUB 8,23% 7,76% 0,64% RUB 8,75% 8,12% 0,71%

100% Indv. Std 11,97% 100% Indv. Std 13,39%




3 months 7 413 885 3 months 9 085 759

6 months 9 689 633 6 months 11 024 897

9 months 7 231 507 9 months 13 061 790

12 months 7 296 775 12 months 12 946 145

TOTAL 31 631 800 TOTAL 46 118 590


USD 29,41% 12,46% 3,66% USD 30,97% 14,07% 4,36%

AUD 15,23% 13,94% 2,12% AUD 13,25% 13,44% 1,78%

CAD 1,56% 13,61% 0,21% CAD 1,58% 14,05% 0,22%

CHF -21,63% 9,33% -2,02% CHF -20,78% 10,20% -2,12%

CZK 2,69% 8,31% 0,22% CZK 2,47% 10,22% 0,25%

EUR 2,12% 5,11% 0,11% EUR 2,00% 5,40% 0,11%

GBP 6,55% 11,36% 0,74% GBP 6,17% 11,80% 0,73%

ZAR 15,05% 19,06% 2,87% ZAR 14,88% 20,71% 3,08%

SGD -6,00% 10,36% -0,62% SGD -6,00% 11,56% -0,69%

PLN 5,01% 7,06% 0,35% PLN 4,66% 9,67% 0,45%

NOK -3,55% 7,53% -0,27% NOK -3,24% 7,55% -0,24%

KRW 5,38% 14,81% 0,80% KRW 4,91% 20,08% 0,99%

JPY 4,38% 17,25% 0,76% JPY 4,63% 18,02% 0,83%

CNY 27,13% 12,34% 3,35% CNY 28,61% 13,90% 3,98%

CPL 7,62% 14,35% 1,09% CPL 7,67% 16,72% 1,28%

INR -4,53% 12,77% -0,58% INR -4,41% 15,30% -0,67%

BRL 4,94% 16,55% 0,82% BRL 4,32% 16,80% 0,73%

RUB 8,63% 7,92% 0,68% RUB 8,31% 8,64% 0,72%

100% Indv. Std 14,31% 100% Indv. Std 15,77%




3 months 9 395 171 3 months 12 972 672

6 months 13 801 475 6 months 12 451 870

9 months 15 779 845 9 months 14 762 020

12 months 17 813 368 12 months 14 536 645

TOTAL 56 789 859 TOTAL 54 723 207


53

Appendix 7 - 2009


USD 33,80% 23,10% 7,81% USD 33,97% 27,07% 9,19%

AUD 12,77% 25,01% 3,19% AUD 12,74% 26,01% 3,31%

CAD 1,49% 18,07% 0,27% CAD 1,45% 20,40% 0,30%

CHF -23,76% 16,99% -4,04% CHF -22,38% 20,94% -4,69%

CZK 2,44% 15,30% 0,37% CZK 2,29% 17,55% 0,40%

EUR 2,16% 11,49% 0,25% EUR 2,07% 14,61% 0,30%

GBP 5,53% 18,37% 1,02% GBP 5,44% 21,87% 1,19%

ZAR 14,46% 26,71% 3,86% ZAR 14,24% 26,93% 3,84%

SGD -6,52% 18,96% -1,24% SGD -6,20% 21,95% -1,36%

PLN 4,13% 18,21% 0,75% PLN 3,53% 21,51% 0,76%

NOK -2,98% 11,35% -0,34% NOK -3,10% 14,20% -0,44%

KRW 5,13% 37,10% 1,90% KRW 4,73% 38,72% 1,83%

JPY 5,89% 30,97% 1,83% JPY 5,42% 34,41% 1,87%

CNY 31,34% 22,87% 7,17% CNY 31,44% 26,84% 8,44%

CPL 7,20% 24,42% 1,76% CPL 7,92% 28,50% 2,26%

INR -4,60% 23,58% -1,08% INR -4,42% 25,82% -1,14%

BRL 3,91% 31,94% 1,25% BRL 3,95% 34,17% 1,35%

RUB 7,62% 17,80% 1,36% RUB 6,89% 22,73% 1,57%

100% Indv. Std 26,08% 100% Indv. Std 28,98%




3 months 13 487 810 3 months 22 874 392

6 months 15 648 295 6 months 27 944 462

9 months 20 622 973 9 months 32 919 168

12 months 17 668 068 12 months 32 311 506

TOTAL 67 427 145 TOTAL 116 049 529


USD 31,52% 29,47% 9,29% USD 30,86% 30,02% 9,26%

AUD 13,75% 27,14% 3,73% AUD 14,75% 27,05% 3,99%

CAD 1,46% 21,45% 0,31% CAD 1,55% 21,73% 0,34%

CHF -21,77% 22,58% -4,92% CHF -22,32% 22,90% -5,11%

CZK 2,36% 18,72% 0,44% CZK 2,48% 18,22% 0,45%

EUR 2,03% 16,65% 0,34% EUR 2,07% 17,52% 0,36%

GBP 5,80% 23,11% 1,34% GBP 5,53% 23,67% 1,31%

ZAR 16,27% 26,81% 4,36% ZAR 16,36% 26,26% 4,30%

SGD -6,04% 23,84% -1,44% SGD -6,08% 24,29% -1,48%

PLN 3,59% 23,55% 0,85% PLN 3,89% 23,08% 0,90%

NOK -3,01% 15,44% -0,47% NOK -3,29% 15,81% -0,52%

KRW 4,73% 40,29% 1,91% KRW 5,02% 38,73% 1,95%

JPY 5,18% 36,89% 1,91% JPY 5,46% 37,76% 2,06%

CNY 29,19% 29,20% 8,52% CNY 28,59% 29,75% 8,50%

CPL 8,06% 29,57% 2,38% CPL 7,64% 29,24% 2,23%

INR -4,37% 27,57% -1,20% INR -4,24% 27,17% -1,15%

BRL 4,30% 34,69% 1,49% BRL 4,66% 33,97% 1,58%

RUB 6,96% 24,27% 1,69% RUB 7,08% 25,28% 1,79%

100% Indv. Std 30,54% 100% Indv. Std 30,76%




3 months 23 152 221 3 months 21 281 054

6 months 31 148 399 6 months 25 997 962

9 months 36 236 007 9 months 27 957 956

12 months 41 267 732 12 months 32 477 352

TOTAL 131 804 359 TOTAL 107 714 324


54

Appendix 8 - 2010


USD 30,61% 24,87% 7,61% USD 30,54% 20,20% 6,17%

AUD 14,88% 16,33% 2,43% AUD 15,16% 13,76% 2,09%

CAD 1,58% 18,62% 0,29% CAD 1,62% 15,23% 0,25%

CHF -22,18% 18,66% -4,14% CHF -21,76% 13,53% -2,95%

CZK 2,32% 14,27% 0,33% CZK 2,26% 11,21% 0,25%

EUR 2,01% 14,93% 0,30% EUR 1,89% 12,15% 0,23%

GBP 5,54% 20,02% 1,11% GBP 5,19% 15,83% 0,82%

ZAR 16,57% 19,83% 3,29% ZAR 16,63% 16,70% 2,78%

SGD -6,05% 19,86% -1,20% SGD -6,06% 16,22% -0,98%

PLN 3,88% 17,63% 0,68% PLN 3,88% 13,79% 0,54%

NOK -3,25% 13,34% -0,43% NOK -3,16% 10,33% -0,33%

KRW 5,03% 23,95% 1,20% KRW 5,17% 20,39% 1,05%

JPY 5,20% 28,97% 1,51% JPY 5,17% 24,65% 1,27%

CNY 28,36% 24,70% 7,01% CNY 28,29% 20,07% 5,68%

CPL 8,20% 23,88% 1,96% CPL 7,93% 19,84% 1,57%

INR -4,36% 20,87% -0,91% INR -4,49% 17,55% -0,79%

BRL 4,70% 19,83% 0,93% BRL 4,60% 15,49% 0,71%

RUB 6,95% 21,26% 1,48% RUB 7,14% 16,23% 1,16%

100% Indv. Std 23,45% 100% Indv. Std 19,53%




3 months 13 558 952 3 months 13 688 879

6 months 15 693 893 6 months 18 639 657

9 months 20 702 691 9 months 20 952 807

12 months 23 008 168 12 months 23 252 679

TOTAL 72 963 705 TOTAL 76 534 021


USD 31,39% 18,17% 5,70% USD 30,10% 17,19% 5,17%

AUD 14,41% 13,02% 1,88% AUD 15,71% 12,31% 1,93%

CAD 1,60% 14,12% 0,23% CAD 1,58% 14,05% 0,22%

CHF -21,86% 12,25% -2,68% CHF -23,03% 12,84% -2,96%

CZK 2,09% 9,92% 0,21% CZK 2,32% 9,32% 0,22%

EUR 1,77% 10,13% 0,18% EUR 1,88% 8,80% 0,17%

GBP 5,25% 14,29% 0,75% GBP 5,30% 13,87% 0,73%

ZAR 16,44% 15,12% 2,48% ZAR 17,18% 13,78% 2,37%

SGD -6,24% 14,26% -0,89% SGD -6,35% 13,20% -0,84%

PLN 3,39% 11,51% 0,39% PLN 3,74% 11,25% 0,42%

NOK -2,98% 8,89% -0,26% NOK -3,14% 7,94% -0,25%

KRW 4,92% 18,70% 0,92% KRW 5,05% 17,79% 0,90%

JPY 5,61% 24,25% 1,36% JPY 5,70% 22,58% 1,29%

CNY 29,27% 18,07% 5,29% CNY 28,45% 17,08% 4,86%

CPL 7,82% 17,36% 1,36% CPL 8,46% 16,71% 1,41%

INR -4,47% 14,98% -0,67% INR -4,47% 14,36% -0,64%

BRL 4,68% 13,08% 0,61% BRL 4,75% 12,97% 0,62%

RUB 6,93% 14,67% 1,02% RUB 6,77% 13,24% 0,90%

100% Indv. Std 17,87% 100% Indv. Std 16,52%




3 months 17 266 535 3 months 18 436 981

6 months 25 482 945 6 months 23 112 581

9 months 27 711 757 9 months 25 171 414

12 months 29 957 371 12 months 27 242 123

TOTAL 100 418 608 TOTAL 93 963 099


55

Appendix 9 - 2011


USD 29,61% 16,20% 4,80% USD 29,55% 15,98% 4,72%

AUD 16,41% 12,45% 2,04% AUD 16,58% 13,05% 2,16%

CAD 1,60% 13,30% 0,21% CAD 1,64% 13,56% 0,22%

CHF -23,79% 13,58% -3,23% CHF -24,23% 14,84% -3,60%

CZK 2,21% 9,24% 0,20% CZK 2,38% 9,54% 0,23%

EUR 1,82% 8,13% 0,15% EUR 1,92% 8,33% 0,16%

GBP 5,17% 13,22% 0,68% GBP 5,31% 12,97% 0,69%

ZAR 17,96% 13,43% 2,41% ZAR 17,45% 14,02% 2,45%

SGD -6,40% 12,17% -0,78% SGD -6,51% 11,94% -0,78%

PLN 3,64% 11,55% 0,42% PLN 3,77% 11,44% 0,43%

NOK -3,13% 7,56% -0,24% NOK -3,29% 7,76% -0,26%

KRW 5,05% 16,94% 0,86% KRW 5,15% 16,61% 0,86%

JPY 5,78% 20,86% 1,21% JPY 5,65% 20,75% 1,17%

CNY 28,41% 16,04% 4,56% CNY 28,56% 15,79% 4,51%

CPL 8,60% 16,31% 1,40% CPL 8,43% 15,27% 1,29%

INR -4,38% 13,85% -0,61% INR -4,39% 13,98% -0,61%

BRL 4,78% 12,44% 0,59% BRL 4,86% 12,41% 0,60%

RUB 6,68% 12,16% 0,81% RUB 7,16% 12,14% 0,87%

100% Indv. Std 15,49% 100% Indv. Std 15,12%




3 months 15 951 092 3 months 14 935 091

6 months 18 045 942 6 months 22 042 066

9 months 22 760 764 9 months 26 473 153

12 months 22 375 153 12 months 28 387 546

TOTAL 79 132 951 TOTAL 91 837 856


USD 29,65% 15,32% 4,54% USD 31,28% 16,97% 5,31%

AUD 17,22% 11,90% 2,05% AUD 16,51% 12,72% 2,10%

CAD 1,66% 12,87% 0,21% CAD 1,62% 13,48% 0,22%

CHF -26,45% 15,22% -4,03% CHF -25,94% 21,70% -5,63%

CZK 2,46% 8,67% 0,21% CZK 2,37% 10,18% 0,24%

EUR 1,98% 7,80% 0,15% EUR 1,93% 9,26% 0,18%

GBP 5,33% 12,86% 0,69% GBP 5,47% 13,42% 0,73%

ZAR 17,53% 13,46% 2,36% ZAR 15,58% 15,30% 2,38%

SGD -6,70% 11,51% -0,77% SGD -6,67% 12,47% -0,83%

PLN 3,93% 10,30% 0,40% PLN 3,46% 11,79% 0,41%

NOK -3,40% 7,60% -0,26% NOK -3,30% 8,02% -0,26%

KRW 5,32% 14,27% 0,76% KRW 5,07% 16,07% 0,81%

JPY 5,82% 17,84% 1,04% JPY 6,43% 18,81% 1,21%

CNY 29,01% 15,10% 4,38% CNY 31,00% 16,70% 5,18%

CPL 8,62% 14,56% 1,26% CPL 8,19% 15,72% 1,29%

INR -4,40% 14,30% -0,63% INR -4,22% 15,03% -0,63%

BRL 5,09% 12,85% 0,65% BRL 4,53% 14,09% 0,64%

RUB 7,33% 12,06% 0,88% RUB 6,69% 13,23% 0,88%

100% Indv. Std 13,91% 100% Indv. Std 14,22%




3 months 17 434 378 3 months 17 924 931

6 months 21 929 035 6 months 22 498 961

9 months 23 847 012 9 months 24 446 843

12 months 25 779 448 12 months 26 468 683

TOTAL 88 989 872 TOTAL 91 339 419


56

Appendix 10 - 2012

2012 Q1 Weight (wn) Annual volatil ity (σn) wnσn

USD 30,47% 17,58% 5,36%

AUD 17,13% 12,80% 2,19%

CAD 1,63% 13,34% 0,22%

CHF -24,54% 21,18% -5,20%

CZK 2,15% 10,64% 0,23%

EUR 1,82% 9,12% 0,17%

GBP 5,34% 12,92% 0,69%

ZAR 15,17% 16,45% 2,50%

SGD -6,60% 12,26% -0,81%

PLN 3,24% 11,76% 0,38%

NOK -3,18% 7,71% -0,24%

KRW 5,09% 16,49% 0,84%

JPY 6,29% 19,49% 1,23%

CNY 30,62% 17,39% 5,33%

CPL 8,09% 15,85% 1,28%

INR -3,79% 15,96% -0,61%

BRL 4,45% 14,84% 0,66%

RUB 6,62% 13,03% 0,86%

100% Indv. Std 15,07%

Basket Variance 1,28%

Std. Basket 11,33%

Premium using Black & Scholes

3 months 13 019 345

6 months 15 128 460

9 months 17 297 047

12 months 16 991 664

TOTAL 62 436 516


57

8.2 Appendix 11-20 – Correlation 2003-2012

Appendix 11- Correlation 2003

2003 Q1 USD AUD CAD CHF CZK EUR GBP ZAR SGD PLN NOK KRW JPY CNY CPL INR BRL RUB

USD 1 0,8672 0,9634 0,0360 -0,1318 0,0421 0,7630 -0,0287 0,9747 0,9072 -0,8161 0,6338 0,6543 1,0000 0,9566 0,9966 0,9495 0,9992

AUD 0,8672 1 0,9408 0,0182 0,0278 0,0334 0,4966 0,2363 0,8477 0,8827 -0,6285 0,6297 0,5872 0,8670 0,9194 0,8359 0,8989 0,8676

CAD 0,9634 0,9408 1 0,0680 -0,0148 0,0875 0,6543 0,0617 0,9604 0,8930 -0,7331 0,7080 0,7083 0,9635 0,9653 0,9424 0,9665 0,9664

CHF 0,0360 0,0182 0,0680 1 0,6463 0,9572 0,4641 0,1182 0,2009 -0,0117 0,4083 0,5412 0,5739 0,0365 0,0378 0,0111 0,0348 0,0304

CZK -0,1318 0,0278 -0,0148 0,6463 1 0,6784 0,1608 -0,0561 -0,0093 -0,2188 0,5306 0,4337 0,4265 -0,1313 -0,1061 -0,1849 -0,0496 -0,1329

EUR 0,0421 0,0334 0,0875 0,9572 0,6784 1 0,4563 0,1125 0,2233 -0,0291 0,4299 0,6052 0,6125 0,0426 0,0442 0,0147 0,0410 0,0382

GBP 0,7630 0,4966 0,6543 0,4641 0,1608 0,4563 1 -0,1194 0,7963 0,6231 -0,4544 0,5974 0,6551 0,7633 0,6489 0,7749 0,6326 0,7532

ZAR -0,0287 0,2363 0,0617 0,1182 -0,0561 0,1125 -0,1194 1 -0,0171 0,2652 0,1505 -0,0021 -0,1435 -0,0293 0,1623 -0,0396 0,0511 -0,0325

SGD 0,9747 0,8477 0,9604 0,2009 -0,0093 0,2233 0,7963 -0,0171 1 0,8639 -0,7146 0,7636 0,7881 0,9749 0,9420 0,9649 0,9432 0,9753

PLN 0,9072 0,8827 0,8930 -0,0117 -0,2188 -0,0291 0,6231 0,2652 0,8639 1 -0,7751 0,4613 0,4705 0,9070 0,9517 0,9047 0,9086 0,9052

NOK -0,8161 -0,6285 -0,7331 0,4083 0,5306 0,4299 -0,4544 0,1505 -0,7146 -0,7751 1 -0,2199 -0,2556 -0,8159 -0,7749 -0,8351 -0,7780 -0,8203

KRW 0,6338 0,6297 0,7080 0,5412 0,4337 0,6052 0,5974 -0,0021 0,7636 0,4613 -0,2199 1 0,9375 0,6342 0,6409 0,5914 0,6693 0,6389

JPY 0,6543 0,5872 0,7083 0,5739 0,4265 0,6125 0,6551 -0,1435 0,7881 0,4705 -0,2556 0,9375 1 0,6548 0,6445 0,6191 0,6884 0,6585

CNY 1,0000 0,8670 0,9635 0,0365 -0,1313 0,0426 0,7633 -0,0293 0,9749 0,9070 -0,8159 0,6342 0,6548 1 0,9565 0,9966 0,9494 0,9993

CPL 0,9566 0,9194 0,9653 0,0378 -0,1061 0,0442 0,6489 0,1623 0,9420 0,9517 -0,7749 0,6409 0,6445 0,9565 1 0,9426 0,9788 0,9578

INR 0,9966 0,8359 0,9424 0,0111 -0,1849 0,0147 0,7749 -0,0396 0,9649 0,9047 -0,8351 0,5914 0,6191 0,9966 0,9426 1 0,9320 0,9950

BRL 0,9495 0,8989 0,9665 0,0348 -0,0496 0,0410 0,6326 0,0511 0,9432 0,9086 -0,7780 0,6693 0,6884 0,9494 0,9788 0,9320 1 0,9552

RUB 0,9992 0,8676 0,9664 0,0304 -0,1329 0,0382 0,7532 -0,0325 0,9753 0,9052 -0,8203 0,6389 0,6585 0,9993 0,9578 0,9950 0,9552 1


USD 1 0,8213 0,9438 0,1559 0,6062 0,0962 0,8628 -0,4621 0,9821 0,8854 0,0122 0,8299 0,8490 1,0000 0,9679 0,9975 0,9022 0,9971

AUD 0,8213 1 0,9330 0,1079 0,4078 0,1064 0,4858 -0,0313 0,7773 0,8218 -0,2986 0,5863 0,6263 0,8212 0,8710 0,8160 0,9079 0,8489

CAD 0,9438 0,9330 1 0,1892 0,5833 0,1730 0,6949 -0,2682 0,9215 0,8383 -0,1750 0,7469 0,8124 0,9439 0,9488 0,9376 0,9474 0,9614

CHF 0,1559 0,1079 0,1892 1 0,4443 0,9456 0,3413 0,0600 0,2608 0,1013 0,1568 0,3288 0,4335 0,1563 0,1401 0,1553 0,1961 0,1684

CZK 0,6062 0,4078 0,5833 0,4443 1 0,4552 0,6981 -0,5655 0,6819 0,3686 0,3546 0,7774 0,8133 0,6068 0,5420 0,5739 0,5254 0,5981

EUR 0,0962 0,1064 0,1730 0,9456 0,4552 1 0,2567 0,1049 0,2001 0,0136 0,0926 0,2725 0,3938 0,0966 0,0892 0,0945 0,1573 0,1147

GBP 0,8628 0,4858 0,6949 0,3413 0,6981 0,2567 1 -0,6284 0,8918 0,7268 0,3472 0,8438 0,8220 0,8628 0,7799 0,8615 0,6545 0,8344

ZAR -0,4621 -0,0313 -0,2682 0,0600 -0,5655 0,1049 -0,6284 1 -0,5013 -0,1953 -0,4660 -0,5990 -0,5636 -0,4624 -0,3086 -0,4410 -0,2053 -0,4224

SGD 0,9821 0,7773 0,9215 0,2608 0,6819 0,2001 0,8918 -0,5013 1 0,8553 0,1311 0,9047 0,9209 0,9822 0,9519 0,9732 0,8818 0,9746

PLN 0,8854 0,8218 0,8383 0,1013 0,3686 0,0136 0,7268 -0,1953 0,8553 1 -0,0112 0,6756 0,6368 0,8851 0,9340 0,8871 0,8838 0,8835

NOK 0,0122 -0,2986 -0,1750 0,1568 0,3546 0,0926 0,3472 -0,4660 0,1311 -0,0112 1 0,4306 0,2544 0,0123 -0,0274 -0,0216 -0,1838 -0,0485

KRW 0,8299 0,5863 0,7469 0,3288 0,7774 0,2725 0,8438 -0,5990 0,9047 0,6756 0,4306 1 0,9412 0,8299 0,7997 0,8000 0,7109 0,8079

JPY 0,8490 0,6263 0,8124 0,4335 0,8133 0,3938 0,8220 -0,5636 0,9209 0,6368 0,2544 0,9412 1 0,8494 0,8090 0,8269 0,7629 0,8425

CNY 1,0000 0,8212 0,9439 0,1563 0,6068 0,0966 0,8628 -0,4624 0,9822 0,8851 0,0123 0,8299 0,8494 1 0,9678 0,9974 0,9021 0,9971

CPL 0,9679 0,8710 0,9488 0,1401 0,5420 0,0892 0,7799 -0,3086 0,9519 0,9340 -0,0274 0,7997 0,8090 0,9678 1 0,9620 0,9526 0,9708

INR 0,9975 0,8160 0,9376 0,1553 0,5739 0,0945 0,8615 -0,4410 0,9732 0,8871 -0,0216 0,8000 0,8269 0,9974 0,9620 1 0,8969 0,9955

BRL 0,9022 0,9079 0,9474 0,1961 0,5254 0,1573 0,6545 -0,2053 0,8818 0,8838 -0,1838 0,7109 0,7629 0,9021 0,9526 0,8969 1 0,9232

RUB 0,9971 0,8489 0,9614 0,1684 0,5981 0,1147 0,8344 -0,4224 0,9746 0,8835 -0,0485 0,8079 0,8425 0,9971 0,9708 0,9955 0,9232 1


USD 1 -0,0659 0,6415 0,7357 0,6863 0,2336 0,9605 -0,6776 0,9872 0,8430 0,8459 0,9518 0,9522 1,0000 0,9284 0,9975 0,3296 0,9876

AUD -0,0659 1 0,5928 -0,2057 0,2767 0,2437 -0,1528 0,0668 -0,0819 -0,3622 -0,3971 -0,0751 -0,0045 -0,0648 0,0302 -0,0405 0,4742 0,0450

CAD 0,6415 0,5928 1 0,3182 0,7544 0,3921 0,5358 -0,5134 0,6280 0,2658 0,2509 0,6014 0,6795 0,6425 0,7115 0,6540 0,7293 0,7392

CHF 0,7357 -0,2057 0,3182 1 0,5286 0,6447 0,7549 -0,3328 0,7792 0,6792 0,7581 0,7614 0,8155 0,7353 0,6192 0,7196 0,1915 0,6845

CZK 0,6863 0,2767 0,7544 0,5286 1 0,4949 0,6857 -0,6549 0,7140 0,4812 0,5383 0,7476 0,7665 0,6869 0,7375 0,6674 0,7075 0,7380

EUR 0,2336 0,2437 0,3921 0,6447 0,4949 1 0,2696 -0,0551 0,3004 0,0861 0,1598 0,3258 0,4296 0,2337 0,2638 0,2293 0,4842 0,2708

GBP 0,9605 -0,1528 0,5358 0,7549 0,6857 0,2696 1 -0,7177 0,9665 0,8815 0,8773 0,9559 0,9168 0,9603 0,8888 0,9551 0,2659 0,9377

ZAR -0,6776 0,0668 -0,5134 -0,3328 -0,6549 -0,0551 -0,7177 1 -0,7025 -0,5649 -0,5888 -0,7015 -0,6488 -0,6781 -0,6323 -0,6653 -0,3096 -0,7020

SGD 0,9872 -0,0819 0,6280 0,7792 0,7140 0,3004 0,9665 -0,7025 1 0,8634 0,8727 0,9783 0,9750 0,9872 0,9325 0,9789 0,3668 0,9711

PLN 0,8430 -0,3622 0,2658 0,6792 0,4812 0,0861 0,8815 -0,5649 0,8634 1 0,9315 0,8705 0,7879 0,8425 0,8166 0,8255 0,1111 0,7748

NOK 0,8459 -0,3971 0,2509 0,7581 0,5383 0,1598 0,8773 -0,5888 0,8727 0,9315 1 0,8758 0,8178 0,8453 0,7802 0,8216 0,1286 0,7721

KRW 0,9518 -0,0751 0,6014 0,7614 0,7476 0,3258 0,9559 -0,7015 0,9783 0,8705 0,8758 1 0,9643 0,9517 0,9305 0,9382 0,4328 0,9371

JPY 0,9522 -0,0045 0,6795 0,8155 0,7665 0,4296 0,9168 -0,6488 0,9750 0,7879 0,8178 0,9643 1 0,9522 0,9206 0,9417 0,4928 0,9491

CNY 1,0000 -0,0648 0,6425 0,7353 0,6869 0,2337 0,9603 -0,6781 0,9872 0,8425 0,8453 0,9517 0,9522 1 0,9286 0,9975 0,3304 0,9878

CPL 0,9284 0,0302 0,7115 0,6192 0,7375 0,2638 0,8888 -0,6323 0,9325 0,8166 0,7802 0,9305 0,9206 0,9286 1 0,9227 0,5451 0,9380

INR 0,9975 -0,0405 0,6540 0,7196 0,6674 0,2293 0,9551 -0,6653 0,9789 0,8255 0,8216 0,9382 0,9417 0,9975 0,9227 1 0,3225 0,9895

BRL 0,3296 0,4742 0,7293 0,1915 0,7075 0,4842 0,2659 -0,3096 0,3668 0,1111 0,1286 0,4328 0,4928 0,3304 0,5451 0,3225 1 0,4271

RUB 0,9876 0,0450 0,7392 0,6845 0,7380 0,2708 0,9377 -0,7020 0,9711 0,7748 0,7721 0,9371 0,9491 0,9878 0,9380 0,9895 0,4271 1


USD 1 -0,4312 0,0534 0,7224 0,5923 -0,1064 0,9477 -0,5447 0,9858 0,8647 0,8112 0,9185 0,9386 1,0000 0,8322 0,9603 -0,5846 0,9604

AUD -0,4312 1 0,7694 -0,6902 -0,5784 0,2608 -0,5180 0,5974 -0,4777 -0,6428 -0,8044 -0,3254 -0,3748 -0,4309 -0,1637 -0,1909 0,7225 -0,1943

CAD 0,0534 0,7694 1 -0,4072 -0,2156 0,1335 -0,0922 0,2762 -0,0254 -0,2933 -0,4717 0,0139 0,0406 0,0543 0,2541 0,2636 0,5067 0,2875

CHF 0,7224 -0,6902 -0,4072 1 0,6131 0,2675 0,7307 -0,4345 0,7662 0,7719 0,8511 0,6151 0,7159 0,7220 0,3308 0,5726 -0,7567 0,5603

CZK 0,5923 -0,5784 -0,2156 0,6131 1 0,0256 0,6542 -0,7537 0,5932 0,6512 0,6784 0,4204 0,4397 0,5924 0,3004 0,4235 -0,5171 0,5099

EUR -0,1064 0,2608 0,1335 0,2675 0,0256 1 -0,1365 0,3205 -0,0957 -0,1072 -0,1471 -0,1400 -0,1104 -0,1069 -0,3242 -0,0521 0,1153 -0,0496

GBP 0,9477 -0,5180 -0,0922 0,7307 0,6542 -0,1365 1 -0,6621 0,9605 0,8951 0,8639 0,9182 0,8880 0,9475 0,7732 0,8774 -0,6549 0,8771

ZAR -0,5447 0,5974 0,2762 -0,4345 -0,7537 0,3205 -0,6621 1 -0,5777 -0,6045 -0,6633 -0,4788 -0,4285 -0,5450 -0,3404 -0,3916 0,5983 -0,4475

SGD 0,9858 -0,4777 -0,0254 0,7662 0,5932 -0,0957 0,9605 -0,5777 1 0,9027 0,8561 0,9402 0,9506 0,9858 0,8120 0,9316 -0,6375 0,9221

PLN 0,8647 -0,6428 -0,2933 0,7719 0,6512 -0,1072 0,8951 -0,6045 0,9027 1 0,9316 0,8584 0,7904 0,8642 0,6992 0,7511 -0,6347 0,7455

NOK 0,8112 -0,8044 -0,4717 0,8511 0,6784 -0,1471 0,8639 -0,6633 0,8561 0,9316 1 0,7656 0,7645 0,8108 0,5802 0,6452 -0,7558 0,6365

KRW 0,9185 -0,3254 0,0139 0,6151 0,4204 -0,1400 0,9182 -0,4788 0,9402 0,8584 0,7656 1 0,9179 0,9182 0,8489 0,9181 -0,5191 0,8826

JPY 0,9386 -0,3748 0,0406 0,7159 0,4397 -0,1104 0,8880 -0,4285 0,9506 0,7904 0,7645 0,9179 1 0,9385 0,8180 0,9195 -0,5606 0,8848

CNY 1,0000 -0,4309 0,0543 0,7220 0,5924 -0,1069 0,9475 -0,5450 0,9858 0,8642 0,8108 0,9182 0,9385 1 0,8322 0,9604 -0,5843 0,9605

CPL 0,8322 -0,1637 0,2541 0,3308 0,3004 -0,3242 0,7732 -0,3404 0,8120 0,6992 0,5802 0,8489 0,8180 0,8322 1 0,8743 -0,2227 0,8504

INR 0,9603 -0,1909 0,2636 0,5726 0,4235 -0,0521 0,8774 -0,3916 0,9316 0,7511 0,6452 0,9181 0,9195 0,9604 0,8743 1 -0,4175 0,9879

BRL -0,5846 0,7225 0,5067 -0,7567 -0,5171 0,1153 -0,6549 0,5983 -0,6375 -0,6347 -0,7558 -0,5191 -0,5606 -0,5843 -0,2227 -0,4175 1 -0,4057

RUB 0,9604 -0,1943 0,2875 0,5603 0,5099 -0,0496 0,8771 -0,4475 0,9221 0,7455 0,6365 0,8826 0,8848 0,9605 0,8504 0,9879 -0,4057 1


58

Appendix 12 - Correlation 2004


USD 1 -0,5734 0,0822 0,8628 0,6123 0,6919 0,8318 -0,3166 0,9839 0,8793 0,7639 0,9136 0,6597 1,0000 -0,1137 0,9396 -0,1348 0,9312

AUD -0,5734 1 0,5689 -0,7748 -0,7200 -0,3558 -0,5139 0,7223 -0,5999 -0,7612 -0,8281 -0,4603 -0,1441 -0,5736 0,5676 -0,3015 0,4503 -0,2683

CAD 0,0822 0,5689 1 -0,2969 -0,1699 0,1466 -0,1805 0,4377 -0,0052 -0,2317 -0,4855 0,1043 0,0859 0,0825 0,2083 0,3390 0,7067 0,3304

CHF 0,8628 -0,7748 -0,2969 1 0,7582 0,7195 0,8109 -0,5196 0,8917 0,8889 0,9004 0,7150 0,5197 0,8628 -0,3274 0,6695 -0,4680 0,6837

CZK 0,6123 -0,7200 -0,1699 0,7582 1 0,6994 0,5197 -0,6685 0,6136 0,7511 0,6793 0,4657 0,0447 0,6123 -0,6386 0,3987 -0,1475 0,4391

EUR 0,6919 -0,3558 0,1466 0,7195 0,6994 1 0,5345 -0,3527 0,6756 0,6843 0,4688 0,5823 0,1884 0,6920 -0,3594 0,6458 0,0221 0,7010

GBP 0,8318 -0,5139 -0,1805 0,8109 0,5197 0,5345 1 -0,3803 0,8696 0,7827 0,8086 0,8004 0,7047 0,8315 0,0627 0,7381 -0,4027 0,7450

ZAR -0,3166 0,7223 0,4377 -0,5196 -0,6685 -0,3527 -0,3803 1 -0,3821 -0,5585 -0,5705 -0,3115 0,1048 -0,3168 0,6332 -0,0974 0,3195 -0,0809

SGD 0,9839 -0,5999 -0,0052 0,8917 0,6136 0,6756 0,8696 -0,3821 1 0,9021 0,8168 0,9276 0,6913 0,9838 -0,1173 0,9045 -0,2325 0,8897

PLN 0,8793 -0,7612 -0,2317 0,8889 0,7511 0,6843 0,7827 -0,5585 0,9021 1 0,8890 0,8382 0,4082 0,8791 -0,3303 0,7221 -0,2323 0,7177

NOK 0,7639 -0,8281 -0,4855 0,9004 0,6793 0,4688 0,8086 -0,5705 0,8168 0,8890 1 0,6856 0,4985 0,7636 -0,2186 0,5377 -0,5141 0,5273

KRW 0,9136 -0,4603 0,1043 0,7150 0,4657 0,5823 0,8004 -0,3115 0,9276 0,8382 0,6856 1 0,6556 0,9134 -0,0502 0,9140 -0,0626 0,8559

JPY 0,6597 -0,1441 0,0859 0,5197 0,0447 0,1884 0,7047 0,1048 0,6913 0,4082 0,4985 0,6556 1 0,6596 0,4834 0,7016 -0,2881 0,6604

CNY 1,0000 -0,5736 0,0825 0,8628 0,6123 0,6920 0,8315 -0,3168 0,9838 0,8791 0,7636 0,9134 0,6596 1 -0,1140 0,9397 -0,1345 0,9312

CPL -0,1137 0,5676 0,2083 -0,3274 -0,6386 -0,3594 0,0627 0,6332 -0,1173 -0,3303 -0,2186 -0,0502 0,4834 -0,1140 1 0,0725 0,1452 0,0805

INR 0,9396 -0,3015 0,3390 0,6695 0,3987 0,6458 0,7381 -0,0974 0,9045 0,7221 0,5377 0,9140 0,7016 0,9397 0,0725 1 0,0693 0,9771

BRL -0,1348 0,4503 0,7067 -0,4680 -0,1475 0,0221 -0,4027 0,3195 -0,2325 -0,2323 -0,5141 -0,0626 -0,2881 -0,1345 0,1452 0,0693 1 0,0665

RUB 0,9312 -0,2683 0,3304 0,6837 0,4391 0,7010 0,7450 -0,0809 0,8897 0,7177 0,5273 0,8559 0,6604 0,9312 0,0805 0,9771 0,0665 1


USD 1 -0,5750 0,7733 0,7231 0,6255 0,2748 -0,0642 0,0807 0,9841 0,8770 0,7525 0,9364 0,3868 1,0000 -0,4744 0,9528 0,8385 0,8375

AUD -0,5750 1 -0,2888 -0,5385 -0,7001 0,1952 0,6463 0,3823 -0,4989 -0,7436 -0,8209 -0,4195 0,2209 -0,5754 0,8359 -0,3576 -0,4628 -0,0824

CAD 0,7733 -0,2888 1 0,2819 0,3606 0,0249 -0,1526 0,2198 0,7608 0,5721 0,4500 0,8214 0,4911 0,7733 -0,2906 0,8413 0,8364 0,6618

CHF 0,7231 -0,5385 0,2819 1 0,7319 0,6180 0,1432 -0,1608 0,7454 0,8139 0,7721 0,5571 0,1040 0,7232 -0,4738 0,5853 0,4415 0,6175

CZK 0,6255 -0,7001 0,3606 0,7319 1 0,3046 -0,1718 -0,3688 0,6057 0,7894 0,7602 0,4787 -0,2269 0,6254 -0,7857 0,4414 0,5369 0,3373

EUR 0,2748 0,1952 0,0249 0,6180 0,3046 1 0,6605 -0,1073 0,3650 0,3270 0,0778 0,2720 -0,0051 0,2746 -0,0043 0,2983 0,1744 0,5716

GBP -0,0642 0,6463 -0,1526 0,1432 -0,1718 0,6605 1 0,2528 0,0280 -0,2335 -0,3443 -0,0112 0,2733 -0,0645 0,5101 0,0601 -0,1590 0,4187

ZAR 0,0807 0,3823 0,2198 -0,1608 -0,3688 -0,1073 0,2528 1 0,0922 -0,1845 -0,0807 0,1577 0,6112 0,0802 0,4906 0,2492 0,0103 0,2799

SGD 0,9841 -0,4989 0,7608 0,7454 0,6057 0,3650 0,0280 0,0922 1 0,8598 0,7174 0,9473 0,4292 0,9841 -0,4409 0,9579 0,8130 0,8753

PLN 0,8770 -0,7436 0,5721 0,8139 0,7894 0,3270 -0,2335 -0,1845 0,8598 1 0,8480 0,7726 0,0407 0,8770 -0,6849 0,7419 0,7413 0,6133

NOK 0,7525 -0,8209 0,4500 0,7721 0,7602 0,0778 -0,3443 -0,0807 0,7174 0,8480 1 0,5685 0,0890 0,7524 -0,6593 0,5796 0,5311 0,4048

KRW 0,9364 -0,4195 0,8214 0,5571 0,4787 0,2720 -0,0112 0,1577 0,9473 0,7726 0,5685 1 0,4543 0,9364 -0,4058 0,9684 0,8779 0,8473

JPY 0,3868 0,2209 0,4911 0,1040 -0,2269 -0,0051 0,2733 0,6112 0,4292 0,0407 0,0890 0,4543 1 0,3867 0,4225 0,5556 0,2732 0,5509

CNY 1,0000 -0,5754 0,7733 0,7232 0,6254 0,2746 -0,0645 0,0802 0,9841 0,8770 0,7524 0,9364 0,3867 1 -0,4747 0,9528 0,8384 0,8373

CPL -0,4744 0,8359 -0,2906 -0,4738 -0,7857 -0,0043 0,5101 0,4906 -0,4409 -0,6849 -0,6593 -0,4058 0,4225 -0,4747 1 -0,2988 -0,4599 -0,0793

INR 0,9528 -0,3576 0,8413 0,5853 0,4414 0,2983 0,0601 0,2492 0,9579 0,7419 0,5796 0,9684 0,5556 0,9528 -0,2988 1 0,8370 0,9088

BRL 0,8385 -0,4628 0,8364 0,4415 0,5369 0,1744 -0,1590 0,0103 0,8130 0,7413 0,5311 0,8779 0,2732 0,8384 -0,4599 0,8370 1 0,6806

RUB 0,8375 -0,0824 0,6618 0,6175 0,3373 0,5716 0,4187 0,2799 0,8753 0,6133 0,4048 0,8473 0,5509 0,8373 -0,0793 0,9088 0,6806 1


USD 1 -0,3184 0,8326 0,4217 0,4112 0,2300 -0,1667 0,0911 0,9634 0,8444 0,6631 0,9637 0,4189 1,0000 -0,4665 0,9486 0,8218 0,8186

AUD -0,3184 1 -0,1012 -0,2915 -0,4744 0,3379 0,4000 -0,0147 -0,1448 -0,4779 -0,5134 -0,2787 0,2603 -0,3188 0,8287 -0,1360 -0,0044 0,0475

CAD 0,8326 -0,1012 1 0,0563 0,1344 -0,0150 -0,3683 0,0901 0,7784 0,6727 0,4794 0,7767 0,5841 0,8323 -0,2062 0,7941 0,8945 0,5678

CHF 0,4217 -0,2915 0,0563 1 0,7093 0,7045 0,5231 0,2900 0,4764 0,5542 0,4563 0,4667 0,0656 0,4219 -0,4343 0,4260 0,0198 0,6221

CZK 0,4112 -0,4744 0,1344 0,7093 1 0,3193 0,2884 0,2664 0,3888 0,4996 0,5452 0,4185 -0,0808 0,4110 -0,6279 0,3689 0,0454 0,4131

EUR 0,2300 0,3379 -0,0150 0,7045 0,3193 1 0,6517 0,0003 0,3486 0,2979 -0,0258 0,2611 0,0180 0,2299 0,0764 0,2884 0,1080 0,6125

GBP -0,1667 0,4000 -0,3683 0,5231 0,2884 0,6517 1 0,3720 0,0194 -0,2324 -0,0966 -0,0315 0,1171 -0,1667 0,2665 0,0138 -0,3734 0,3746

ZAR 0,0911 -0,0147 0,0901 0,2900 0,2664 0,0003 0,3720 1 0,1835 0,0100 0,4066 0,1705 0,4002 0,0911 -0,0313 0,2126 -0,1819 0,2488

SGD 0,9634 -0,1448 0,7784 0,4764 0,3888 0,3486 0,0194 0,1835 1 0,7703 0,6446 0,9726 0,5322 0,9635 -0,3391 0,9830 0,7819 0,9025

PLN 0,8444 -0,4779 0,6727 0,5542 0,4996 0,2979 -0,2324 0,0100 0,7703 1 0,5732 0,8004 0,1712 0,8444 -0,6213 0,7131 0,6415 0,6132

NOK 0,6631 -0,5134 0,4794 0,4563 0,5452 -0,0258 -0,0966 0,4066 0,6446 0,5732 1 0,6406 0,2557 0,6632 -0,5725 0,6763 0,3555 0,5213

KRW 0,9637 -0,2787 0,7767 0,4667 0,4185 0,2611 -0,0315 0,1705 0,9726 0,8004 0,6406 1 0,5096 0,9638 -0,4500 0,9599 0,7709 0,8404

JPY 0,4189 0,2603 0,5841 0,0656 -0,0808 0,0180 0,1171 0,4002 0,5322 0,1712 0,2557 0,5096 1 0,4193 0,2268 0,5715 0,4606 0,4820

CNY 1,0000 -0,3188 0,8323 0,4219 0,4110 0,2299 -0,1667 0,0911 0,9635 0,8444 0,6632 0,9638 0,4193 1 -0,4665 0,9487 0,8216 0,8186

CPL -0,4665 0,8287 -0,2062 -0,4343 -0,6279 0,0764 0,2665 -0,0313 -0,3391 -0,6213 -0,5725 -0,4500 0,2268 -0,4665 1 -0,3113 -0,1588 -0,1642

INR 0,9486 -0,1360 0,7941 0,4260 0,3689 0,2884 0,0138 0,2126 0,9830 0,7131 0,6763 0,9599 0,5715 0,9487 -0,3113 1 0,7862 0,8890

BRL 0,8218 -0,0044 0,8945 0,0198 0,0454 0,1080 -0,3734 -0,1819 0,7819 0,6415 0,3555 0,7709 0,4606 0,8216 -0,1588 0,7862 1 0,5819

RUB 0,8186 0,0475 0,5678 0,6221 0,4131 0,6125 0,3746 0,2488 0,9025 0,6132 0,5213 0,8404 0,4820 0,8186 -0,1642 0,8890 0,5819 1


USD 1 -0,1093 0,6000 0,1481 0,2157 -0,0797 0,1521 0,3818 0,8945 0,1199 0,6468 0,8750 0,6382 0,9999 -0,1550 0,8706 0,5026 0,7262

AUD -0,1093 1 -0,0711 -0,3496 -0,5655 0,3377 0,1689 -0,2416 0,1157 -0,6244 -0,3962 -0,1674 0,3895 -0,1098 0,8098 0,2369 0,3362 0,2792

CAD 0,6000 -0,0711 1 -0,1717 0,1208 -0,2870 -0,2154 0,2876 0,4860 0,3896 0,3204 0,5400 0,5160 0,5990 0,0270 0,4106 0,7346 0,1909

CHF 0,1481 -0,3496 -0,1717 1 0,7705 0,6581 0,7638 0,5689 0,2112 0,5356 0,3412 0,3617 -0,0517 0,1483 -0,5179 0,0298 -0,5271 0,3846

CZK 0,2157 -0,5655 0,1208 0,7705 1 0,3163 0,5171 0,6321 0,1792 0,7652 0,4076 0,3972 -0,2014 0,2152 -0,6439 -0,0448 -0,3930 0,1607

EUR -0,0797 0,3377 -0,2870 0,6581 0,3163 1 0,8671 0,1942 0,1397 0,1346 -0,1504 0,1109 0,0017 -0,0797 0,1407 0,0114 -0,2920 0,5041

GBP 0,1521 0,1689 -0,2154 0,7638 0,5171 0,8671 1 0,4543 0,3669 0,2391 0,0757 0,3811 0,0671 0,1518 -0,0633 0,2078 -0,3491 0,6642

ZAR 0,3818 -0,2416 0,2876 0,5689 0,6321 0,1942 0,4543 1 0,3890 0,5248 0,4684 0,4961 0,1742 0,3808 -0,4401 0,2344 -0,1833 0,3281

SGD 0,8945 0,1157 0,4860 0,2112 0,1792 0,1397 0,3669 0,3890 1 0,0632 0,5822 0,9073 0,7086 0,8945 0,0259 0,9262 0,4879 0,8583

PLN 0,1199 -0,6244 0,3896 0,5356 0,7652 0,1346 0,2391 0,5248 0,0632 1 0,2610 0,3446 -0,1757 0,1197 -0,5403 -0,2201 -0,1386 -0,0395

NOK 0,6468 -0,3962 0,3204 0,3412 0,4076 -0,1504 0,0757 0,4684 0,5822 0,2610 1 0,5682 0,2714 0,6465 -0,4580 0,5413 0,0524 0,3789

KRW 0,8750 -0,1674 0,5400 0,3617 0,3972 0,1109 0,3811 0,4961 0,9073 0,3446 0,5682 1 0,5954 0,8748 -0,2555 0,7799 0,3922 0,7316

JPY 0,6382 0,3895 0,5160 -0,0517 -0,2014 0,0017 0,0671 0,1742 0,7086 -0,1757 0,2714 0,5954 1 0,6384 0,2552 0,7606 0,6085 0,5548

CNY 0,9999 -0,1098 0,5990 0,1483 0,2152 -0,0797 0,1518 0,3808 0,8945 0,1197 0,6465 0,8748 0,6384 1 -0,1550 0,8709 0,5021 0,7266

CPL -0,1550 0,8098 0,0270 -0,5179 -0,6439 0,1407 -0,0633 -0,4401 0,0259 -0,5403 -0,4580 -0,2555 0,2552 -0,1550 1 0,1260 0,4673 0,1467

INR 0,8706 0,2369 0,4106 0,0298 -0,0448 0,0114 0,2078 0,2344 0,9262 -0,2201 0,5413 0,7799 0,7606 0,8709 0,1260 1 0,5428 0,7990

BRL 0,5026 0,3362 0,7346 -0,5271 -0,3930 -0,2920 -0,3491 -0,1833 0,4879 -0,1386 0,0524 0,3922 0,6085 0,5021 0,4673 0,5428 1 0,2322

RUB 0,7262 0,2792 0,1909 0,3846 0,1607 0,5041 0,6642 0,3281 0,8583 -0,0395 0,3789 0,7316 0,5548 0,7266 0,1467 0,7990 0,2322 1


59



USD 1 0,3630 0,1630 0,4528 -0,2260 0,7734 0,8480 0,1194 0,9626 -0,5481 0,1772 0,5419 0,7847 1,0000 0,3824 0,8991 0,3138 0,9516

AUD 0,3630 1 -0,0270 -0,2543 -0,7398 0,6015 0,4178 -0,3388 0,4398 -0,7456 -0,4191 -0,0789 0,6361 0,3627 0,8039 0,4987 0,5304 0,4992

CAD 0,1630 -0,0270 1 0,1654 0,1601 -0,0209 -0,0778 0,2732 0,2469 0,4036 0,3689 0,3461 0,1524 0,1634 -0,0467 0,0403 0,5064 0,0398

CHF 0,4528 -0,2543 0,1654 1 0,4816 0,3950 0,5453 0,6226 0,3905 0,1316 0,4999 0,5381 0,3622 0,4529 -0,4501 0,3109 -0,3561 0,3700

CZK -0,2260 -0,7398 0,1601 0,4816 1 -0,2934 -0,1062 0,6711 -0,2551 0,7786 0,5035 0,3091 -0,4185 -0,2260 -0,7244 -0,3123 -0,4087 -0,3282

EUR 0,7734 0,6015 -0,0209 0,3950 -0,2934 1 0,8585 0,0501 0,7199 -0,5886 -0,1749 0,2348 0,7565 0,7727 0,5081 0,6991 0,2474 0,8128

GBP 0,8480 0,4178 -0,0778 0,5453 -0,1062 0,8585 1 0,3093 0,8073 -0,5301 0,0237 0,5098 0,7598 0,8476 0,2852 0,8077 0,0970 0,8807

ZAR 0,1194 -0,3388 0,2732 0,6226 0,6711 0,0501 0,3093 1 0,1482 0,4743 0,4695 0,6175 0,0790 0,1195 -0,4919 0,1188 -0,1795 0,0990

SGD 0,9626 0,4398 0,2469 0,3905 -0,2551 0,7199 0,8073 0,1482 1 -0,5301 0,2480 0,6346 0,8461 0,9627 0,4223 0,9446 0,4427 0,9497

PLN -0,5481 -0,7456 0,4036 0,1316 0,7786 -0,5886 -0,5301 0,4743 -0,5301 1 0,3685 0,1153 -0,5930 -0,5478 -0,6728 -0,6266 -0,1761 -0,6357

NOK 0,1772 -0,4191 0,3689 0,4999 0,5035 -0,1749 0,0237 0,4695 0,2480 0,3685 1 0,6183 0,0382 0,1777 -0,5149 0,2285 -0,0519 0,1143

KRW 0,5419 -0,0789 0,3461 0,5381 0,3091 0,2348 0,5098 0,6175 0,6346 0,1153 0,6183 1 0,4969 0,5424 -0,1346 0,6224 0,2673 0,5757

JPY 0,7847 0,6361 0,1524 0,3622 -0,4185 0,7565 0,7598 0,0790 0,8461 -0,5930 0,0382 0,4969 1 0,7849 0,5181 0,8404 0,4300 0,8419

CNY 1,0000 0,3627 0,1634 0,4529 -0,2260 0,7727 0,8476 0,1195 0,9627 -0,5478 0,1777 0,5424 0,7849 1 0,3821 0,8993 0,3140 0,9517

CPL 0,3824 0,8039 -0,0467 -0,4501 -0,7244 0,5081 0,2852 -0,4919 0,4223 -0,6728 -0,5149 -0,1346 0,5181 0,3821 1 0,4765 0,6952 0,4770

INR 0,8991 0,4987 0,0403 0,3109 -0,3123 0,6991 0,8077 0,1188 0,9446 -0,6266 0,2285 0,6224 0,8404 0,8993 0,4765 1 0,4156 0,9580

BRL 0,3138 0,5304 0,5064 -0,3561 -0,4087 0,2474 0,0970 -0,1795 0,4427 -0,1761 -0,0519 0,2673 0,4300 0,3140 0,6952 0,4156 1 0,3696

RUB 0,9516 0,4992 0,0398 0,3700 -0,3282 0,8128 0,8807 0,0990 0,9497 -0,6357 0,1143 0,5757 0,8419 0,9517 0,4770 0,9580 0,3696 1


USD 1 0,3188 0,1497 0,5938 -0,6241 0,7766 0,8833 0,0824 0,9580 -0,8095 0,0701 -0,1168 0,8310 1,0000 0,4264 0,8661 -0,0550 0,9373

AUD 0,3188 1 0,2773 -0,0179 -0,0729 0,4395 0,3681 0,0823 0,5213 -0,1867 0,2012 0,4838 0,5693 0,3186 0,6477 0,5859 0,5738 0,4912

CAD 0,1497 0,2773 1 -0,0348 -0,1722 0,1091 -0,0521 -0,1033 0,2081 0,0353 -0,0523 -0,0187 0,1891 0,1498 0,2448 -0,0175 0,3700 0,0406

CHF 0,5938 -0,0179 -0,0348 1 -0,2836 0,6774 0,7205 0,4714 0,4538 -0,4972 0,0635 -0,2210 0,5021 0,5935 -0,2184 0,3536 -0,5141 0,4999

CZK -0,6241 -0,0729 -0,1722 -0,2836 1 -0,1395 -0,3920 0,0945 -0,5496 0,8822 -0,0128 0,6456 -0,5409 -0,6248 -0,1918 -0,4578 0,2609 -0,4501

EUR 0,7766 0,4395 0,1091 0,6774 -0,1395 1 0,8738 0,3479 0,7704 -0,4363 0,1192 0,2061 0,7228 0,7759 0,3590 0,7330 0,0323 0,8266

GBP 0,8833 0,3681 -0,0521 0,7205 -0,3920 0,8738 1 0,3893 0,8406 -0,6685 0,0152 0,0349 0,8067 0,8829 0,3026 0,8168 -0,1309 0,8947

ZAR 0,0824 0,0823 -0,1033 0,4714 0,0945 0,3479 0,3893 1 0,0276 0,0447 -0,4449 -0,0065 0,2239 0,0821 -0,0600 0,0173 -0,1609 0,0886

SGD 0,9580 0,5213 0,2081 0,4538 -0,5496 0,7704 0,8406 0,0276 1 -0,7393 0,1343 0,0749 0,8896 0,9579 0,5931 0,9376 0,1578 0,9609

PLN -0,8095 -0,1867 0,0353 -0,4972 0,8822 -0,4363 -0,6685 0,0447 -0,7393 1 -0,1880 0,4603 -0,6864 -0,8099 -0,2181 -0,7093 0,3451 -0,7127

NOK 0,0701 0,2012 -0,0523 0,0635 -0,0128 0,1192 0,0152 -0,4449 0,1343 -0,1880 1 0,1234 0,0497 0,0697 -0,1152 0,1951 -0,1467 0,1593

KRW -0,1168 0,4838 -0,0187 -0,2210 0,6456 0,2061 0,0349 -0,0065 0,0749 0,4603 0,1234 1 0,1011 -0,1175 0,3739 0,2156 0,6237 0,1700

JPY 0,8310 0,5693 0,1891 0,5021 -0,5409 0,7228 0,8067 0,2239 0,8896 -0,6864 0,0497 0,1011 1 0,8311 0,5590 0,8647 0,1461 0,8585

CNY 1,0000 0,3186 0,1498 0,5935 -0,6248 0,7759 0,8829 0,0821 0,9579 -0,8099 0,0697 -0,1175 0,8311 1 0,4264 0,8661 -0,0551 0,9372

CPL 0,4264 0,6477 0,2448 -0,2184 -0,1918 0,3590 0,3026 -0,0600 0,5931 -0,2181 -0,1152 0,3739 0,5590 0,4264 1 0,6534 0,7482 0,5508

INR 0,8661 0,5859 -0,0175 0,3536 -0,4578 0,7330 0,8168 0,0173 0,9376 -0,7093 0,1951 0,2156 0,8647 0,8661 0,6534 1 0,1960 0,9630

BRL -0,0550 0,5738 0,3700 -0,5141 0,2609 0,0323 -0,1309 -0,1609 0,1578 0,3451 -0,1467 0,6237 0,1461 -0,0551 0,7482 0,1960 1 0,0885

RUB 0,9373 0,4912 0,0406 0,4999 -0,4501 0,8266 0,8947 0,0886 0,9609 -0,7127 0,1593 0,1700 0,8585 0,9372 0,5508 0,9630 0,0885 1


USD 1 0,4792 0,6767 0,7168 -0,0436 0,7594 0,8612 0,0453 0,9428 -0,2869 0,3417 0,3012 0,8714 1,0000 0,5486 0,8014 0,4198 0,8818

AUD 0,4792 1 0,7574 0,5830 0,7146 0,7372 0,6074 -0,1537 0,6995 0,5493 0,8530 0,8823 0,6355 0,4793 0,8143 0,8286 0,8785 0,7405

CAD 0,6767 0,7574 1 0,5489 0,2562 0,6105 0,5289 -0,3494 0,7950 0,1619 0,7454 0,5765 0,7060 0,6772 0,7252 0,7683 0,7019 0,7124

CHF 0,7168 0,5830 0,5489 1 0,1589 0,8133 0,8358 0,3098 0,7005 -0,1488 0,5030 0,3838 0,7511 0,7165 0,4053 0,6605 0,4061 0,7205

CZK -0,0436 0,7146 0,2562 0,1589 1 0,4975 0,2614 -0,0992 0,2293 0,8908 0,6544 0,8563 0,1534 -0,0441 0,6079 0,5093 0,7003 0,3976

EUR 0,7594 0,7372 0,6105 0,8133 0,4975 1 0,8943 0,1527 0,8294 0,1703 0,6130 0,6428 0,7547 0,7587 0,6866 0,8705 0,6335 0,9088

GBP 0,8612 0,6074 0,5289 0,8358 0,2614 0,8943 1 0,3008 0,8452 -0,0663 0,4282 0,4719 0,8003 0,8608 0,5473 0,8186 0,4793 0,8973

ZAR 0,0453 -0,1537 -0,3494 0,3098 -0,0992 0,1527 0,3008 1 -0,0896 -0,2054 -0,3627 -0,2838 0,0291 0,0450 -0,2738 -0,1277 -0,3434 -0,0359

SGD 0,9428 0,6995 0,7950 0,7005 0,2293 0,8294 0,8452 -0,0896 1 -0,0005 0,5678 0,5678 0,9137 0,9428 0,7440 0,9305 0,6626 0,9529

PLN -0,2869 0,5493 0,1619 -0,1488 0,8908 0,1703 -0,0663 -0,2054 -0,0005 1 0,5204 0,6997 -0,0568 -0,2872 0,4846 0,2738 0,5788 0,1105

NOK 0,3417 0,8530 0,7454 0,5030 0,6544 0,6130 0,4282 -0,3627 0,5678 0,5204 1 0,8583 0,5067 0,3417 0,7482 0,7283 0,8735 0,6170

KRW 0,3012 0,8823 0,5765 0,3838 0,8563 0,6428 0,4719 -0,2838 0,5678 0,6997 0,8583 1 0,4909 0,3010 0,8341 0,7936 0,9340 0,6861

JPY 0,8714 0,6355 0,7060 0,7511 0,1534 0,7547 0,8003 0,0291 0,9137 -0,0568 0,5067 0,4909 1 0,8715 0,6384 0,8468 0,5717 0,8547

CNY 1,0000 0,4793 0,6772 0,7165 -0,0441 0,7587 0,8608 0,0450 0,9428 -0,2872 0,3417 0,3010 0,8715 1 0,5487 0,8014 0,4200 0,8817

CPL 0,5486 0,8143 0,7252 0,4053 0,6079 0,6866 0,5473 -0,2738 0,7440 0,4846 0,7482 0,8341 0,6384 0,5487 1 0,8834 0,9365 0,7765

INR 0,8014 0,8286 0,7683 0,6605 0,5093 0,8705 0,8186 -0,1277 0,9305 0,2738 0,7283 0,7936 0,8468 0,8014 0,8834 1 0,8420 0,9654

BRL 0,4198 0,8785 0,7019 0,4061 0,7003 0,6335 0,4793 -0,3434 0,6626 0,5788 0,8735 0,9340 0,5717 0,4200 0,9365 0,8420 1 0,7141

RUB 0,8818 0,7405 0,7124 0,7205 0,3976 0,9088 0,8973 -0,0359 0,9529 0,1105 0,6170 0,6861 0,8547 0,8817 0,7765 0,9654 0,7141 1


USD 1 0,9197 0,9310 0,8734 0,6807 0,9174 0,8839 0,1946 0,9865 0,5695 0,9064 0,8366 0,9068 0,9901 0,8879 0,9630 0,9241 0,9617

AUD 0,9197 1 0,8971 0,8955 0,8297 0,9313 0,9211 0,2826 0,9505 0,7400 0,9292 0,9386 0,8856 0,9221 0,8926 0,9544 0,9513 0,9558

CAD 0,9310 0,8971 1 0,8797 0,7124 0,8878 0,8137 0,3672 0,9143 0,6384 0,9323 0,7766 0,8192 0,9565 0,9237 0,8928 0,9029 0,8963

CHF 0,8734 0,8955 0,8797 1 0,7065 0,9035 0,8744 0,3100 0,8786 0,5712 0,9356 0,8302 0,8426 0,8761 0,8264 0,8761 0,8840 0,8789

CZK 0,6807 0,8297 0,7124 0,7065 1 0,8551 0,8192 0,4643 0,7419 0,9301 0,8090 0,8934 0,6311 0,7205 0,8467 0,8120 0,8440 0,8259

EUR 0,9174 0,9313 0,8878 0,9035 0,8551 1 0,9043 0,3678 0,9392 0,7236 0,9289 0,9085 0,8307 0,9241 0,9078 0,9590 0,9391 0,9642

GBP 0,8839 0,9211 0,8137 0,8744 0,8192 0,9043 1 0,2532 0,8968 0,6945 0,8870 0,9169 0,8471 0,8760 0,8453 0,9244 0,9119 0,9395

ZAR 0,1946 0,2826 0,3672 0,3100 0,4643 0,3678 0,2532 1 0,2161 0,5228 0,3367 0,2269 0,1208 0,2766 0,4668 0,2353 0,3516 0,2379

SGD 0,9865 0,9505 0,9143 0,8786 0,7419 0,9392 0,8968 0,2161 1 0,6288 0,9175 0,8885 0,9235 0,9810 0,8962 0,9796 0,9397 0,9750

PLN 0,5695 0,7400 0,6384 0,5712 0,9301 0,7236 0,6945 0,5228 0,6288 1 0,6957 0,7724 0,5468 0,6149 0,7687 0,7003 0,7443 0,7007

NOK 0,9064 0,9292 0,9323 0,9356 0,8090 0,9289 0,8870 0,3367 0,9175 0,6957 1 0,8934 0,8368 0,9273 0,9181 0,9308 0,9522 0,9346

KRW 0,8366 0,9386 0,7766 0,8302 0,8934 0,9085 0,9169 0,2269 0,8885 0,7724 0,8934 1 0,8322 0,8365 0,8490 0,9407 0,9362 0,9431

JPY 0,9068 0,8856 0,8192 0,8426 0,6311 0,8307 0,8471 0,1208 0,9235 0,5468 0,8368 0,8322 1 0,8810 0,7790 0,9107 0,8580 0,8875

CNY 0,9901 0,9221 0,9565 0,8761 0,7205 0,9241 0,8760 0,2766 0,9810 0,6149 0,9273 0,8365 0,8810 1 0,9323 0,9563 0,9374 0,9578

CPL 0,8879 0,8926 0,9237 0,8264 0,8467 0,9078 0,8453 0,4668 0,8962 0,7687 0,9181 0,8490 0,7790 0,9323 1 0,9111 0,9528 0,9127

INR 0,9630 0,9544 0,8928 0,8761 0,8120 0,9590 0,9244 0,2353 0,9796 0,7003 0,9308 0,9407 0,9107 0,9563 0,9111 1 0,9677 0,9915

BRL 0,9241 0,9513 0,9029 0,8840 0,8440 0,9391 0,9119 0,3516 0,9397 0,7443 0,9522 0,9362 0,8580 0,9374 0,9528 0,9677 1 0,9659

RUB 0,9617 0,9558 0,8963 0,8789 0,8259 0,9642 0,9395 0,2379 0,9750 0,7007 0,9346 0,9431 0,8875 0,9578 0,9127 0,9915 0,9659 1


60



USD 1 0,9573 0,9619 0,9382 0,8734 0,9562 0,9184 0,6199 0,9916 0,7697 0,9390 0,9644 0,6639 0,9925 0,9336 0,9511 0,9783 0,9946

AUD 0,9573 1 0,9178 0,9028 0,8453 0,9166 0,9319 0,5815 0,9538 0,7584 0,9316 0,9482 0,6820 0,9507 0,8801 0,9423 0,9523 0,9558

CAD 0,9619 0,9178 1 0,9125 0,9340 0,9371 0,8663 0,7432 0,9533 0,8701 0,9167 0,9067 0,5072 0,9800 0,9772 0,8656 0,9596 0,9582

CHF 0,9382 0,9028 0,9125 1 0,8858 0,9707 0,9402 0,6150 0,9265 0,7391 0,9418 0,9103 0,5721 0,9363 0,8851 0,8545 0,9340 0,9508

CZK 0,8734 0,8453 0,9340 0,8858 1 0,9030 0,8364 0,8065 0,8805 0,9057 0,8524 0,8492 0,3625 0,9071 0,9406 0,7512 0,8872 0,8826

EUR 0,9562 0,9166 0,9371 0,9707 0,9030 1 0,9080 0,6479 0,9490 0,7600 0,9426 0,9130 0,5818 0,9578 0,9038 0,8937 0,9417 0,9670

GBP 0,9184 0,9319 0,8663 0,9402 0,8364 0,9080 1 0,5364 0,9037 0,7002 0,9098 0,9228 0,6630 0,9048 0,8324 0,8809 0,9075 0,9306

ZAR 0,6199 0,5815 0,7432 0,6150 0,8065 0,6479 0,5364 1 0,6430 0,8182 0,5333 0,5741 0,0522 0,6720 0,8000 0,4445 0,6637 0,6125

SGD 0,9916 0,9538 0,9533 0,9265 0,8805 0,9490 0,9037 0,6430 1 0,7754 0,9213 0,9741 0,6579 0,9865 0,9334 0,9435 0,9656 0,9844

PLN 0,7697 0,7584 0,8701 0,7391 0,9057 0,7600 0,7002 0,8182 0,7754 1 0,7244 0,7074 0,2649 0,8123 0,8764 0,6299 0,7907 0,7611

NOK 0,9390 0,9316 0,9167 0,9418 0,8524 0,9426 0,9098 0,5333 0,9213 0,7244 1 0,9092 0,6665 0,9442 0,8705 0,9160 0,9451 0,9500

KRW 0,9644 0,9482 0,9067 0,9103 0,8492 0,9130 0,9228 0,5741 0,9741 0,7074 0,9092 1 0,6621 0,9515 0,8872 0,9357 0,9436 0,9676

JPY 0,6639 0,6820 0,5072 0,5721 0,3625 0,5818 0,6630 0,0522 0,6579 0,2649 0,6665 0,6621 1 0,6153 0,4423 0,8194 0,6050 0,6438

CNY 0,9925 0,9507 0,9800 0,9363 0,9071 0,9578 0,9048 0,6720 0,9865 0,8123 0,9442 0,9515 0,6153 1 0,9634 0,9292 0,9828 0,9887

CPL 0,9336 0,8801 0,9772 0,8851 0,9406 0,9038 0,8324 0,8000 0,9334 0,8764 0,8705 0,8872 0,4423 0,9634 1 0,8189 0,9509 0,9283

INR 0,9511 0,9423 0,8656 0,8545 0,7512 0,8937 0,8809 0,4445 0,9435 0,6299 0,9160 0,9357 0,8194 0,9292 0,8189 1 0,9158 0,9435

BRL 0,9783 0,9523 0,9596 0,9340 0,8872 0,9417 0,9075 0,6637 0,9656 0,7907 0,9451 0,9436 0,6050 0,9828 0,9509 0,9158 1 0,9781

RUB 0,9946 0,9558 0,9582 0,9508 0,8826 0,9670 0,9306 0,6125 0,9844 0,7611 0,9500 0,9676 0,6438 0,9887 0,9283 0,9435 0,9781 1


USD 1 0,8373 0,9179 0,7850 0,7645 0,8980 0,7440 0,5641 0,9061 0,7857 0,8106 0,7794 0,2492 0,9801 0,8803 0,8906 0,9092 0,9541

AUD 0,8373 1 0,7070 0,8062 0,4855 0,7707 0,8186 0,3123 0,6357 0,5948 0,8107 0,4809 0,4929 0,7887 0,6711 0,8009 0,6767 0,6902

CAD 0,9179 0,7070 1 0,6294 0,9210 0,7958 0,5884 0,7964 0,9302 0,9412 0,6637 0,8532 -0,0688 0,9649 0,9702 0,7627 0,9526 0,9368

CHF 0,7850 0,8062 0,6294 1 0,4794 0,8919 0,8923 0,2417 0,5413 0,4955 0,8557 0,3588 0,4096 0,7350 0,6299 0,5979 0,5959 0,6607

CZK 0,7645 0,4855 0,9210 0,4794 1 0,6854 0,4492 0,8870 0,8905 0,9371 0,4829 0,8738 -0,2659 0,8499 0,9175 0,6041 0,8858 0,8580

EUR 0,8980 0,7707 0,7958 0,8919 0,6854 1 0,7881 0,4550 0,7577 0,6534 0,8696 0,5814 0,2932 0,8790 0,7716 0,7630 0,7796 0,8570

GBP 0,7440 0,8186 0,5884 0,8923 0,4492 0,7881 1 0,2020 0,5178 0,4855 0,7988 0,3760 0,5057 0,6805 0,5596 0,6207 0,5617 0,6386

ZAR 0,5641 0,3123 0,7964 0,2417 0,8870 0,4550 0,2020 1 0,7682 0,8587 0,1820 0,7968 -0,4652 0,6676 0,8069 0,4033 0,7412 0,6731

SGD 0,9061 0,6357 0,9302 0,5413 0,8905 0,7577 0,5178 0,7682 1 0,8656 0,5789 0,9587 -0,0020 0,9321 0,8879 0,8310 0,9391 0,9605

PLN 0,7857 0,5948 0,9412 0,4955 0,9371 0,6534 0,4855 0,8587 0,8656 1 0,5148 0,8318 -0,1937 0,8631 0,9291 0,6346 0,8762 0,8311

NOK 0,8106 0,8107 0,6637 0,8557 0,4829 0,8696 0,7988 0,1820 0,5789 0,5148 1 0,3872 0,4972 0,7847 0,6393 0,7337 0,6759 0,7150

KRW 0,7794 0,4809 0,8532 0,3588 0,8738 0,5814 0,3760 0,7968 0,9587 0,8318 0,3872 1 -0,1294 0,8172 0,8049 0,7299 0,8794 0,8793

JPY 0,2492 0,4929 -0,0688 0,4096 -0,2659 0,2932 0,5057 -0,4652 -0,0020 -0,1937 0,4972 -0,1294 1 0,1228 -0,1145 0,4725 -0,0286 0,0837

CNY 0,9801 0,7887 0,9649 0,7350 0,8499 0,8790 0,6805 0,6676 0,9321 0,8631 0,7847 0,8172 0,1228 1 0,9443 0,8497 0,9453 0,9637

CPL 0,8803 0,6711 0,9702 0,6299 0,9175 0,7716 0,5596 0,8069 0,8879 0,9291 0,6393 0,8049 -0,1145 0,9443 1 0,6774 0,9207 0,8858

INR 0,8906 0,8009 0,7627 0,5979 0,6041 0,7630 0,6207 0,4033 0,8310 0,6346 0,7337 0,7299 0,4725 0,8497 0,6774 1 0,7861 0,8465

BRL 0,9092 0,6767 0,9526 0,5959 0,8858 0,7796 0,5617 0,7412 0,9391 0,8762 0,6759 0,8794 -0,0286 0,9453 0,9207 0,7861 1 0,9585

RUB 0,9541 0,6902 0,9368 0,6607 0,8580 0,8570 0,6386 0,6731 0,9605 0,8311 0,7150 0,8793 0,0837 0,9637 0,8858 0,8465 0,9585 1


USD 1 0,8175 0,5782 0,7388 -0,0818 0,8193 0,6948 0,5986 0,6285 0,4419 0,2777 0,2403 0,6130 0,9760 0,7416 0,8680 0,6224 0,7413

AUD 0,8175 1 0,2938 0,7959 -0,3448 0,7199 0,7487 0,5229 0,2568 0,3821 0,3512 -0,1212 0,7922 0,7472 0,5546 0,8190 0,3581 0,3392

CAD 0,5782 0,2938 1 0,3741 0,6431 0,4739 0,4268 0,5150 0,7919 0,7404 0,1195 0,6948 -0,1427 0,6933 0,8208 0,2215 0,8148 0,8190

CHF 0,7388 0,7959 0,3741 1 -0,1110 0,8910 0,9323 0,2406 0,2270 0,3002 0,6335 -0,1445 0,6623 0,6989 0,5023 0,5538 0,3063 0,4270

CZK -0,0818 -0,3448 0,6431 -0,1110 1 0,0145 -0,0183 0,2446 0,5703 0,5676 -0,0622 0,7733 -0,5993 0,0808 0,4156 -0,3504 0,5151 0,4623

EUR 0,8193 0,7199 0,4739 0,8910 0,0145 1 0,8368 0,3413 0,4880 0,3206 0,6760 0,1116 0,6254 0,7981 0,5676 0,6338 0,5149 0,6839

GBP 0,6948 0,7487 0,4268 0,9323 -0,0183 0,8368 1 0,2266 0,2335 0,3543 0,6234 -0,0975 0,6322 0,6718 0,5083 0,5077 0,3356 0,4597

ZAR 0,5986 0,5229 0,5150 0,2406 0,2446 0,3413 0,2266 1 0,6677 0,7743 -0,1316 0,5476 0,2343 0,6369 0,7701 0,6383 0,6616 0,4841

SGD 0,6285 0,2568 0,7919 0,2270 0,5703 0,4880 0,2335 0,6677 1 0,6338 -0,0415 0,8850 -0,0206 0,7142 0,7321 0,4469 0,8302 0,8876

PLN 0,4419 0,3821 0,7404 0,3002 0,5676 0,3206 0,3543 0,7743 0,6338 1 -0,0207 0,5826 0,0096 0,5395 0,7930 0,3039 0,6757 0,5021

NOK 0,2777 0,3512 0,1195 0,6335 -0,0622 0,6760 0,6234 -0,1316 -0,0415 -0,0207 1 -0,2523 0,3768 0,2699 0,1491 0,0889 0,1922 0,2591

KRW 0,2403 -0,1212 0,6948 -0,1445 0,7733 0,1116 -0,0975 0,5476 0,8850 0,5826 -0,2523 1 -0,3881 0,3611 0,5374 0,0946 0,7155 0,6875

JPY 0,6130 0,7922 -0,1427 0,6623 -0,5993 0,6254 0,6322 0,2343 -0,0206 0,0096 0,3768 -0,3881 1 0,4847 0,1513 0,7878 -0,0100 0,1032

CNY 0,9760 0,7472 0,6933 0,6989 0,0808 0,7981 0,6718 0,6369 0,7142 0,5395 0,2699 0,3611 0,4847 1 0,8342 0,7899 0,7145 0,8140

CPL 0,7416 0,5546 0,8208 0,5023 0,4156 0,5676 0,5083 0,7701 0,7321 0,7930 0,1491 0,5374 0,1513 0,8342 1 0,4931 0,7835 0,7061

INR 0,8680 0,8190 0,2215 0,5538 -0,3504 0,6338 0,5077 0,6383 0,4469 0,3039 0,0889 0,0946 0,7878 0,7899 0,4931 1 0,4113 0,4781

BRL 0,6224 0,3581 0,8148 0,3063 0,5151 0,5149 0,3356 0,6616 0,8302 0,6757 0,1922 0,7155 -0,0100 0,7145 0,7835 0,4113 1 0,8530

RUB 0,7413 0,3392 0,8190 0,4270 0,4623 0,6839 0,4597 0,4841 0,8876 0,5021 0,2591 0,6875 0,1032 0,8140 0,7061 0,4781 0,8530 1


USD 1 0,9015 0,9006 0,8566 -0,0806 0,8698 0,6470 0,7872 0,8255 0,6830 0,5452 0,4919 0,8893 0,9966 0,9395 0,9512 0,7745 0,8531

AUD 0,9015 1 0,8269 0,8732 -0,1414 0,8282 0,7455 0,7340 0,6532 0,7680 0,5394 0,2926 0,8614 0,8879 0,8773 0,8498 0,6973 0,6592

CAD 0,9006 0,8269 1 0,7922 0,1887 0,8138 0,6281 0,7503 0,8546 0,7003 0,4864 0,6156 0,7884 0,9029 0,9083 0,8578 0,7781 0,8265

CHF 0,8566 0,8732 0,7922 1 -0,0585 0,9224 0,7669 0,6465 0,5856 0,5900 0,7677 0,2467 0,9086 0,8353 0,7974 0,7802 0,5563 0,6560

CZK -0,0806 -0,1414 0,1887 -0,0585 1 0,0924 0,0677 0,1025 0,3558 0,2251 -0,0144 0,5399 -0,1038 -0,0553 0,0384 -0,0592 0,2134 0,2307

EUR 0,8698 0,8282 0,8138 0,9224 0,0924 1 0,8239 0,6013 0,6971 0,5893 0,7229 0,3434 0,8542 0,8739 0,8025 0,7780 0,6895 0,8268

GBP 0,6470 0,7455 0,6281 0,7669 0,0677 0,8239 1 0,2742 0,4032 0,4824 0,4622 0,0284 0,6007 0,6607 0,5571 0,5000 0,4661 0,5980

ZAR 0,7872 0,7340 0,7503 0,6465 0,1025 0,6013 0,2742 1 0,8187 0,8335 0,4818 0,6779 0,8011 0,7627 0,8745 0,8855 0,7074 0,6001

SGD 0,8255 0,6532 0,8546 0,5856 0,3558 0,6971 0,4032 0,8187 1 0,7115 0,3479 0,8608 0,6978 0,8406 0,8483 0,8573 0,8456 0,8815

PLN 0,6830 0,7680 0,7003 0,5900 0,2251 0,5893 0,4824 0,8335 0,7115 1 0,3036 0,5304 0,7006 0,6709 0,7817 0,7504 0,6440 0,5028

NOK 0,5452 0,5394 0,4864 0,7677 -0,0144 0,7229 0,4622 0,4818 0,3479 0,3036 1 0,1178 0,7028 0,5165 0,5226 0,4716 0,4146 0,4614

KRW 0,4919 0,2926 0,6156 0,2467 0,5399 0,3434 0,0284 0,6779 0,8608 0,5304 0,1178 1 0,3994 0,5098 0,5874 0,6078 0,6531 0,6363

JPY 0,8893 0,8614 0,7884 0,9086 -0,1038 0,8542 0,6007 0,8011 0,6978 0,7006 0,7028 0,3994 1 0,8656 0,8559 0,9039 0,6226 0,6811

CNY 0,9966 0,8879 0,9029 0,8353 -0,0553 0,8739 0,6607 0,7627 0,8406 0,6709 0,5165 0,5098 0,8656 1 0,9329 0,9426 0,7946 0,8815

CPL 0,9395 0,8773 0,9083 0,7974 0,0384 0,8025 0,5571 0,8745 0,8483 0,7817 0,5226 0,5874 0,8559 0,9329 1 0,9204 0,7894 0,7684

INR 0,9512 0,8498 0,8578 0,7802 -0,0592 0,7780 0,5000 0,8855 0,8573 0,7504 0,4716 0,6078 0,9039 0,9426 0,9204 1 0,7689 0,7928

BRL 0,7745 0,6973 0,7781 0,5563 0,2134 0,6895 0,4661 0,7074 0,8456 0,6440 0,4146 0,6531 0,6226 0,7946 0,7894 0,7689 1 0,8455

RUB 0,8531 0,6592 0,8265 0,6560 0,2307 0,8268 0,5980 0,6001 0,8815 0,5028 0,4614 0,6363 0,6811 0,8815 0,7684 0,7928 0,8455 1


61



USD 1 0,8391 0,9068 0,8310 0,3236 0,8732 0,3347 0,8448 0,9706 0,5570 0,5311 0,9334 0,9001 0,9874 0,9386 0,9446 0,8353 0,9056

AUD 0,8391 1 0,7462 0,7172 0,3848 0,7214 0,4769 0,8111 0,8369 0,8133 0,3791 0,7999 0,7825 0,8350 0,8824 0,8653 0,7685 0,6674

CAD 0,9068 0,7462 1 0,8944 0,4259 0,9239 0,4304 0,7161 0,8941 0,3930 0,6226 0,8598 0,8982 0,8671 0,8275 0,7710 0,7625 0,8938

CHF 0,8310 0,7172 0,8944 1 0,3901 0,9103 0,3222 0,7881 0,7809 0,3932 0,7892 0,7709 0,9627 0,7542 0,7686 0,7243 0,5864 0,7298

CZK 0,3236 0,3848 0,4259 0,3901 1 0,5606 0,5825 0,3139 0,4487 0,4450 0,3364 0,4449 0,3738 0,3367 0,3857 0,3011 0,4598 0,4614

EUR 0,8732 0,7214 0,9239 0,9103 0,5606 1 0,5119 0,7179 0,8895 0,4361 0,6724 0,8448 0,9035 0,8439 0,8214 0,7520 0,7540 0,8970

GBP 0,3347 0,4769 0,4304 0,3222 0,5825 0,5119 1 0,0667 0,4096 0,4160 -0,0707 0,3100 0,2736 0,3867 0,3168 0,2724 0,3647 0,4652

ZAR 0,8448 0,8111 0,7161 0,7881 0,3139 0,7179 0,0667 1 0,8115 0,6752 0,6985 0,8276 0,8766 0,7951 0,8969 0,8825 0,7221 0,6323

SGD 0,9706 0,8369 0,8941 0,7809 0,4487 0,8895 0,4096 0,8115 1 0,5922 0,5097 0,9586 0,8644 0,9765 0,9464 0,9245 0,9058 0,9407

PLN 0,5570 0,8133 0,3930 0,3932 0,4450 0,4361 0,4160 0,6752 0,5922 1 0,1562 0,5793 0,5114 0,5852 0,7123 0,6990 0,6201 0,3723

NOK 0,5311 0,3791 0,6226 0,7892 0,3364 0,6724 -0,0707 0,6985 0,5097 0,1562 1 0,5433 0,7629 0,4246 0,5222 0,4218 0,3912 0,4699

KRW 0,9334 0,7999 0,8598 0,7709 0,4449 0,8448 0,3100 0,8276 0,9586 0,5793 0,5433 1 0,8521 0,9364 0,9439 0,9190 0,8790 0,8866

JPY 0,9001 0,7825 0,8982 0,9627 0,3738 0,9035 0,2736 0,8766 0,8644 0,5114 0,7629 0,8521 1 0,8377 0,8652 0,8338 0,6876 0,7757

CNY 0,9874 0,8350 0,8671 0,7542 0,3367 0,8439 0,3867 0,7951 0,9765 0,5852 0,4246 0,9364 0,8377 1 0,9373 0,9521 0,8614 0,9170

CPL 0,9386 0,8824 0,8275 0,7686 0,3857 0,8214 0,3168 0,8969 0,9464 0,7123 0,5222 0,9439 0,8652 0,9373 1 0,9546 0,8706 0,8119

INR 0,9446 0,8653 0,7710 0,7243 0,3011 0,7520 0,2724 0,8825 0,9245 0,6990 0,4218 0,9190 0,8338 0,9521 0,9546 1 0,8185 0,7855

BRL 0,8353 0,7685 0,7625 0,5864 0,4598 0,7540 0,3647 0,7221 0,9058 0,6201 0,3912 0,8790 0,6876 0,8614 0,8706 0,8185 1 0,8542

RUB 0,9056 0,6674 0,8938 0,7298 0,4614 0,8970 0,4652 0,6323 0,9407 0,3723 0,4699 0,8866 0,7757 0,9170 0,8119 0,7855 0,8542 1


USD 1 0,4684 0,9014 0,7970 0,1211 0,7269 -0,0085 0,6862 0,8744 -0,0623 0,5740 0,9235 0,8472 0,9128 0,8945 0,7185 0,6925 0,9261

AUD 0,4684 1 0,3258 0,3690 0,6088 0,6904 0,4701 0,4515 0,7433 0,6138 0,3647 0,5066 0,3592 0,6022 0,5472 0,6608 0,7669 0,5937

CAD 0,9014 0,3258 1 0,8951 0,0897 0,6690 -0,0828 0,6152 0,6620 -0,1065 0,5916 0,8114 0,9207 0,6874 0,8204 0,4466 0,4877 0,7988

CHF 0,7970 0,3690 0,8951 1 0,2991 0,7989 -0,1053 0,6640 0,6176 -0,0250 0,7975 0,7284 0,9688 0,5799 0,7348 0,4134 0,4010 0,7371

CZK 0,1211 0,6088 0,0897 0,2991 1 0,5998 0,3767 0,1721 0,3585 0,5871 0,2756 0,1422 0,2101 0,2152 0,1832 0,3112 0,2892 0,2994

EUR 0,7269 0,6904 0,6690 0,7989 0,5998 1 0,2816 0,5047 0,8148 0,2267 0,6828 0,6548 0,7260 0,7429 0,6402 0,6313 0,6466 0,8616

GBP -0,0085 0,4701 -0,0828 -0,1053 0,3767 0,2816 1 -0,2777 0,2578 0,3001 -0,2304 -0,0452 -0,1887 0,2229 -0,0882 0,1551 0,2176 0,2115

ZAR 0,6862 0,4515 0,6152 0,6640 0,1721 0,5047 -0,2777 1 0,6107 0,2207 0,7901 0,7581 0,7515 0,5250 0,8051 0,6277 0,5679 0,4892

SGD 0,8744 0,7433 0,6620 0,6176 0,3585 0,8148 0,2578 0,6107 1 0,2031 0,5078 0,8451 0,6503 0,9588 0,8087 0,8837 0,8584 0,9185

PLN -0,0623 0,6138 -0,1065 -0,0250 0,5871 0,2267 0,3001 0,2207 0,2031 1 0,0309 0,0884 -0,0071 0,0555 0,2428 0,2731 0,3879 0,0291

NOK 0,5740 0,3647 0,5916 0,7975 0,2756 0,6828 -0,2304 0,7901 0,5078 0,0309 1 0,5571 0,7788 0,4005 0,5473 0,4057 0,3577 0,4974

KRW 0,9235 0,5066 0,8114 0,7284 0,1422 0,6548 -0,0452 0,7581 0,8451 0,0884 0,5571 1 0,8045 0,8567 0,9372 0,8042 0,7095 0,8137

JPY 0,8472 0,3592 0,9207 0,9688 0,2101 0,7260 -0,1887 0,7515 0,6503 -0,0071 0,7788 0,8045 1 0,6162 0,8201 0,4802 0,4511 0,7292

CNY 0,9128 0,6022 0,6874 0,5799 0,2152 0,7429 0,2229 0,5250 0,9588 0,0555 0,4005 0,8567 0,6162 1 0,7981 0,8595 0,8051 0,9469

CPL 0,8945 0,5472 0,8204 0,7348 0,1832 0,6402 -0,0882 0,8051 0,8087 0,2428 0,5473 0,9372 0,8201 0,7981 1 0,7614 0,7377 0,7731

INR 0,7185 0,6608 0,4466 0,4134 0,3112 0,6313 0,1551 0,6277 0,8837 0,2731 0,4057 0,8042 0,4802 0,8595 0,7614 1 0,8047 0,7233

BRL 0,6925 0,7669 0,4877 0,4010 0,2892 0,6466 0,2176 0,5679 0,8584 0,3879 0,3577 0,7095 0,4511 0,8051 0,7377 0,8047 1 0,7380

RUB 0,9261 0,5937 0,7988 0,7371 0,2994 0,8616 0,2115 0,4892 0,9185 0,0291 0,4974 0,8137 0,7292 0,9469 0,7731 0,7233 0,7380 1


USD 1 -0,1742 0,6674 0,8727 0,0227 0,3503 0,3097 0,3980 0,8523 -0,5168 0,0394 0,9175 0,8876 0,8485 0,8541 -0,2583 0,1140 0,8736

AUD -0,1742 1 0,3299 -0,2409 0,4009 0,7041 0,5125 -0,1248 0,0683 0,7632 0,4930 -0,0818 -0,4167 0,2455 -0,0015 0,8563 0,8612 0,2452

CAD 0,6674 0,3299 1 0,5788 -0,0524 0,5643 0,2606 0,3476 0,4358 -0,0044 0,3215 0,6488 0,5047 0,6598 0,7989 0,2872 0,5754 0,7300

CHF 0,8727 -0,2409 0,5788 1 0,1570 0,3929 0,0957 0,4512 0,7053 -0,4977 0,2299 0,7406 0,9588 0,6227 0,7192 -0,4246 -0,0534 0,7700

CZK 0,0227 0,4009 -0,0524 0,1570 1 0,5868 0,3851 -0,1686 0,3466 0,4029 0,1867 0,0047 0,0130 0,2089 -0,0111 0,2092 0,2795 0,3112

EUR 0,3503 0,7041 0,5643 0,3929 0,5868 1 0,5712 0,0116 0,5546 0,3920 0,6193 0,3345 0,1806 0,6351 0,3618 0,5546 0,7664 0,7458

GBP 0,3097 0,5125 0,2606 0,0957 0,3851 0,5712 1 -0,1634 0,5699 0,2494 0,0720 0,3573 -0,0212 0,6503 0,2322 0,4084 0,5681 0,5410

ZAR 0,3980 -0,1248 0,3476 0,4512 -0,1686 0,0116 -0,1634 1 0,1777 -0,2912 0,4304 0,2283 0,4762 0,1119 0,2701 -0,3524 -0,0589 0,2211

SGD 0,8523 0,0683 0,4358 0,7053 0,3466 0,5546 0,5699 0,1777 1 -0,2824 0,0968 0,7964 0,6724 0,9077 0,6669 -0,0364 0,2817 0,8993

PLN -0,5168 0,7632 -0,0044 -0,4977 0,4029 0,3920 0,2494 -0,2912 -0,2824 1 0,2212 -0,4107 -0,6219 -0,1538 -0,1967 0,7390 0,5785 -0,1370

NOK 0,0394 0,4930 0,3215 0,2299 0,1867 0,6193 0,0720 0,4304 0,0968 0,2212 1 -0,0508 0,0539 0,1424 -0,0555 0,2686 0,4693 0,2894

KRW 0,9175 -0,0818 0,6488 0,7406 0,0047 0,3345 0,3573 0,2283 0,7964 -0,4107 -0,0508 1 0,7475 0,8579 0,8522 -0,1053 0,1810 0,8199

JPY 0,8876 -0,4167 0,5047 0,9588 0,0130 0,1806 -0,0212 0,4762 0,6724 -0,6219 0,0539 0,7475 1 0,5625 0,7302 -0,5495 -0,2102 0,6819

CNY 0,8485 0,2455 0,6598 0,6227 0,2089 0,6351 0,6503 0,1119 0,9077 -0,1538 0,1424 0,8579 0,5625 1 0,7538 0,2060 0,5181 0,9431

CPL 0,8541 -0,0015 0,7989 0,7192 -0,0111 0,3618 0,2322 0,2701 0,6669 -0,1967 -0,0555 0,8522 0,7302 0,7538 1 -0,0179 0,2706 0,7870

INR -0,2583 0,8563 0,2872 -0,4246 0,2092 0,5546 0,4084 -0,3524 -0,0364 0,7390 0,2686 -0,1053 -0,5495 0,2060 -0,0179 1 0,8540 0,1355

BRL 0,1140 0,8612 0,5754 -0,0534 0,2795 0,7664 0,5681 -0,0589 0,2817 0,5785 0,4693 0,1810 -0,2102 0,5181 0,2706 0,8540 1 0,4844

RUB 0,8736 0,2452 0,7300 0,7700 0,3112 0,7458 0,5410 0,2211 0,8993 -0,1370 0,2894 0,8199 0,6819 0,9431 0,7870 0,1355 0,4844 1


USD 1 -0,3204 0,0289 0,7955 -0,0870 0,1356 0,5345 0,3228 0,9298 -0,4949 -0,5408 0,9541 0,7932 0,8471 0,8030 -0,2261 -0,1995 0,8100

AUD -0,3204 1 0,6106 -0,3163 0,1956 0,6219 0,3237 -0,1027 -0,1939 0,7851 0,6732 -0,2410 -0,5137 0,0848 -0,0631 0,8246 0,8927 0,1464

CAD 0,0289 0,6106 1 0,1048 0,3356 0,6084 0,2644 -0,3054 -0,0479 0,6417 0,5206 0,0230 0,0290 0,3902 0,4814 0,7494 0,7878 0,4091

CHF 0,7955 -0,3163 0,1048 1 0,3416 0,3726 0,4053 -0,0375 0,7795 -0,2609 -0,2250 0,6868 0,9380 0,7173 0,7053 -0,2302 -0,2055 0,7835

CZK -0,0870 0,1956 0,3356 0,3416 1 0,6753 0,1906 -0,4535 0,0752 0,4424 0,5784 -0,2371 0,2999 0,2146 0,0246 0,3285 0,2692 0,3157

EUR 0,1356 0,6219 0,6084 0,3726 0,6753 1 0,5673 -0,2835 0,3145 0,6403 0,6827 0,0513 0,1630 0,5599 0,2722 0,7190 0,6881 0,6737

GBP 0,5345 0,3237 0,2644 0,4053 0,1906 0,5673 1 0,1834 0,6397 0,0344 0,1144 0,5156 0,2669 0,7768 0,3796 0,3528 0,3556 0,7005

ZAR 0,3228 -0,1027 -0,3054 -0,0375 -0,4535 -0,2835 0,1834 1 0,3113 -0,2701 -0,4693 0,4761 -0,0319 0,1187 0,1834 -0,2097 -0,2120 0,0461

SGD 0,9298 -0,1939 -0,0479 0,7795 0,0752 0,3145 0,6397 0,3113 1 -0,4014 -0,3638 0,8578 0,7358 0,8674 0,6566 -0,1304 -0,1159 0,8621

PLN -0,4949 0,7851 0,6417 -0,2609 0,4424 0,6403 0,0344 -0,2701 -0,4014 1 0,7875 -0,4733 -0,4086 -0,0992 -0,0743 0,8142 0,7509 0,0113

NOK -0,5408 0,6732 0,5206 -0,2250 0,5784 0,6827 0,1144 -0,4693 -0,3638 0,7875 1 -0,5809 -0,3666 -0,0610 -0,3033 0,6854 0,7159 0,0145

KRW 0,9541 -0,2410 0,0230 0,6868 -0,2371 0,0513 0,5156 0,4761 0,8578 -0,4733 -0,5809 1 0,6642 0,7719 0,7799 -0,2200 -0,1689 0,7238

JPY 0,7932 -0,5137 0,0290 0,9380 0,2999 0,1630 0,2669 -0,0319 0,7358 -0,4086 -0,3666 0,6642 1 0,6431 0,7018 -0,3611 -0,3685 0,6699

CNY 0,8471 0,0848 0,3902 0,7173 0,2146 0,5599 0,7768 0,1187 0,8674 -0,0992 -0,0610 0,7719 0,6431 1 0,7545 0,2387 0,2649 0,9554

CPL 0,8030 -0,0631 0,4814 0,7053 0,0246 0,2722 0,3796 0,1834 0,6566 -0,0743 -0,3033 0,7799 0,7018 0,7545 1 0,0748 0,1026 0,7620

INR -0,2261 0,8246 0,7494 -0,2302 0,3285 0,7190 0,3528 -0,2097 -0,1304 0,8142 0,6854 -0,2200 -0,3611 0,2387 0,0748 1 0,8853 0,2650

BRL -0,1995 0,8927 0,7878 -0,2055 0,2692 0,6881 0,3556 -0,2120 -0,1159 0,7509 0,7159 -0,1689 -0,3685 0,2649 0,1026 0,8853 1 0,2873

RUB 0,8100 0,1464 0,4091 0,7835 0,3157 0,6737 0,7005 0,0461 0,8621 0,0113 0,0145 0,7238 0,6699 0,9554 0,7620 0,2650 0,2873 1


62



USD 1 -0,3177 -0,6016 0,4787 -0,6297 -0,0929 0,8860 0,4992 0,8815 -0,7551 -0,5983 0,9657 0,5222 0,9217 0,6341 0,0303 -0,6068 0,8467

AUD -0,3177 1 0,7123 -0,4094 0,0472 0,2595 -0,0358 0,1084 -0,3426 0,4141 0,5872 -0,1479 -0,5713 -0,1777 0,1812 0,6140 0,7671 -0,1169

CAD -0,6016 0,7123 1 -0,3077 0,4555 0,4297 -0,3684 -0,2819 -0,5575 0,6797 0,8393 -0,5346 -0,3726 -0,3381 0,0486 0,6042 0,8819 -0,2834

CHF 0,4787 -0,4094 -0,3077 1 0,2660 0,6133 0,3386 -0,0861 0,6651 -0,0410 -0,1498 0,3017 0,8982 0,5988 0,2835 -0,1043 -0,2765 0,7287

CZK -0,6297 0,0472 0,4555 0,2660 1 0,6622 -0,6437 -0,4592 -0,2830 0,8543 0,5304 -0,7388 0,1941 -0,4023 -0,2256 -0,0398 0,4957 -0,2307

EUR -0,0929 0,2595 0,4297 0,6133 0,6622 1 -0,0590 -0,2439 0,1527 0,6454 0,5245 -0,1952 0,3984 0,2240 0,3224 0,4439 0,5006 0,4318

GBP 0,8860 -0,0358 -0,3684 0,3386 -0,6437 -0,0590 1 0,5068 0,7012 -0,6714 -0,4189 0,9128 0,3552 0,8540 0,5933 0,2216 -0,3979 0,7619

ZAR 0,4992 0,1084 -0,2819 -0,0861 -0,4592 -0,2439 0,5068 1 0,4852 -0,3520 -0,4236 0,6143 -0,0983 0,3671 0,4086 0,0019 -0,2005 0,3032

SGD 0,8815 -0,3426 -0,5575 0,6651 -0,2830 0,1527 0,7012 0,4852 1 -0,5004 -0,4823 0,7966 0,6875 0,8572 0,6232 -0,1139 -0,5054 0,8708

PLN -0,7551 0,4141 0,6797 -0,0410 0,8543 0,6454 -0,6714 -0,3520 -0,5004 1 0,6640 -0,7759 -0,2152 -0,5068 -0,1678 0,2850 0,7644 -0,3499

NOK -0,5983 0,5872 0,8393 -0,1498 0,5304 0,5245 -0,4189 -0,4236 -0,4823 0,6640 1 -0,5775 -0,1985 -0,3425 -0,0026 0,4116 0,7762 -0,2138

KRW 0,9657 -0,1479 -0,5346 0,3017 -0,7388 -0,1952 0,9128 0,6143 0,7966 -0,7759 -0,5775 1 0,3350 0,8603 0,6264 0,1023 -0,5276 0,7685

JPY 0,5222 -0,5713 -0,3726 0,8982 0,1941 0,3984 0,3552 -0,0983 0,6875 -0,2152 -0,1985 0,3350 1 0,5827 0,2832 -0,2299 -0,4623 0,6689

CNY 0,9217 -0,1777 -0,3381 0,5988 -0,4023 0,2240 0,8540 0,3671 0,8572 -0,5068 -0,3425 0,8603 0,5827 1 0,7722 0,2604 -0,3342 0,9490

CPL 0,6341 0,1812 0,0486 0,2835 -0,2256 0,3224 0,5933 0,4086 0,6232 -0,1678 -0,0026 0,6264 0,2832 0,7722 1 0,5479 0,0217 0,7633

INR 0,0303 0,6140 0,6042 -0,1043 -0,0398 0,4439 0,2216 0,0019 -0,1139 0,2850 0,4116 0,1023 -0,2299 0,2604 0,5479 1 0,5665 0,2721

BRL -0,6068 0,7671 0,8819 -0,2765 0,4957 0,5006 -0,3979 -0,2005 -0,5054 0,7644 0,7762 -0,5276 -0,4623 -0,3342 0,0217 0,5665 1 -0,2588

RUB 0,8467 -0,1169 -0,2834 0,7287 -0,2307 0,4318 0,7619 0,3032 0,8708 -0,3499 -0,2138 0,7685 0,6689 0,9490 0,7633 0,2721 -0,2588 1


USD 1 0,2173 0,1553 -0,4721 -0,7885 -0,2569 0,9154 0,7317 0,6332 -0,8074 -0,4944 0,9443 -0,2733 0,8002 -0,2092 0,8701 -0,3813 0,9133

AUD 0,2173 1 0,5149 -0,3240 -0,2256 -0,1917 0,2630 0,2373 0,2452 -0,1645 0,2033 0,3370 -0,4078 0,2298 0,0901 0,3185 0,5371 0,1698

CAD 0,1553 0,5149 1 -0,4028 -0,1669 -0,0256 0,3101 0,4194 0,0578 -0,1199 0,5058 0,3106 -0,2663 0,1509 -0,2170 0,4976 0,5364 0,2410

CHF -0,4721 -0,3240 -0,4028 1 0,8148 0,8184 -0,6670 -0,8150 0,1631 0,7380 0,2206 -0,6961 0,8995 0,0373 0,7429 -0,5711 0,1936 -0,2122

CZK -0,7885 -0,2256 -0,1669 0,8148 1 0,7334 -0,8807 -0,7986 -0,0827 0,9561 0,5190 -0,8662 0,7126 -0,3182 0,5722 -0,7100 0,4883 -0,5256

EUR -0,2569 -0,1917 -0,0256 0,8184 0,7334 1 -0,4219 -0,4549 0,3890 0,7132 0,3483 -0,4383 0,8166 0,2594 0,5886 -0,2103 0,3936 0,1270

GBP 0,9154 0,2630 0,3101 -0,6670 -0,8807 -0,4219 1 0,8384 0,3714 -0,8752 -0,4242 0,9488 -0,4754 0,5718 -0,4700 0,8332 -0,3707 0,7892

ZAR 0,7317 0,2373 0,4194 -0,8150 -0,7986 -0,4549 0,8384 1 0,2360 -0,7219 -0,3005 0,8755 -0,6260 0,3261 -0,6541 0,8122 -0,2208 0,6196

SGD 0,6332 0,2452 0,0578 0,1631 -0,0827 0,3890 0,3714 0,2360 1 -0,1368 -0,2025 0,4827 0,3297 0,8574 0,3898 0,5290 0,0322 0,7729

PLN -0,8074 -0,1645 -0,1199 0,7380 0,9561 0,7132 -0,8752 -0,7219 -0,1368 1 0,4926 -0,8564 0,5776 -0,3653 0,5237 -0,6691 0,5544 -0,5463

NOK -0,4944 0,2033 0,5058 0,2206 0,5190 0,3483 -0,4242 -0,3005 -0,2025 0,4926 1 -0,4313 0,2445 -0,2139 0,2346 -0,2562 0,6272 -0,2911

KRW 0,9443 0,3370 0,3106 -0,6961 -0,8662 -0,4383 0,9488 0,8755 0,4827 -0,8564 -0,4313 1 -0,5040 0,6343 -0,4223 0,8989 -0,2948 0,8090

JPY -0,2733 -0,4078 -0,2663 0,8995 0,7126 0,8166 -0,4754 -0,6260 0,3297 0,5776 0,2445 -0,5040 1 0,2039 0,6390 -0,3625 0,0636 0,0081

CNY 0,8002 0,2298 0,1509 0,0373 -0,3182 0,2594 0,5718 0,3261 0,8574 -0,3653 -0,2139 0,6343 0,2039 1 0,2971 0,7245 -0,0364 0,8979

CPL -0,2092 0,0901 -0,2170 0,7429 0,5722 0,5886 -0,4700 -0,6541 0,3898 0,5237 0,2346 -0,4223 0,6390 0,2971 1 -0,2580 0,3115 -0,0368

INR 0,8701 0,3185 0,4976 -0,5711 -0,7100 -0,2103 0,8332 0,8122 0,5290 -0,6691 -0,2562 0,8989 -0,3625 0,7245 -0,2580 1 -0,0716 0,8393

BRL -0,3813 0,5371 0,5364 0,1936 0,4883 0,3936 -0,3707 -0,2208 0,0322 0,5544 0,6272 -0,2948 0,0636 -0,0364 0,3115 -0,0716 1 -0,1890

RUB 0,9133 0,1698 0,2410 -0,2122 -0,5256 0,1270 0,7892 0,6196 0,7729 -0,5463 -0,2911 0,8090 0,0081 0,8979 -0,0368 0,8393 -0,1890 1


USD 1 0,2646 0,7795 -0,5366 -0,8226 -0,2867 0,9521 0,8476 0,5907 -0,8799 -0,1486 0,9418 -0,0184 0,7623 0,0931 0,9119 -0,3241 0,9514

AUD 0,2646 1 0,4313 -0,4954 -0,2851 -0,4514 0,2886 0,3085 0,2646 -0,2473 0,1269 0,2965 -0,4889 0,2020 -0,1390 0,1980 0,5467 0,1508

CAD 0,7795 0,4313 1 -0,6520 -0,7381 -0,3676 0,8376 0,8852 0,4217 -0,7878 0,1417 0,8704 -0,1384 0,3893 0,0338 0,8505 -0,0875 0,7317

CHF -0,5366 -0,4954 -0,6520 1 0,7917 0,8209 -0,6527 -0,7650 0,0659 0,6771 -0,0100 -0,6123 0,7570 -0,0492 0,4635 -0,5075 0,0699 -0,3441

CZK -0,8226 -0,2851 -0,7381 0,7917 1 0,6985 -0,8975 -0,8640 -0,1091 0,9566 0,1648 -0,8687 0,3739 -0,3111 0,0717 -0,8065 0,4794 -0,6485

EUR -0,2867 -0,4514 -0,3676 0,8209 0,6985 1 -0,4163 -0,4393 0,3722 0,5977 0,0721 -0,3853 0,7411 0,1976 0,3348 -0,2579 0,1880 -0,0051

GBP 0,9521 0,2886 0,8376 -0,6527 -0,8975 -0,4163 1 0,9108 0,3993 -0,9329 -0,1746 0,9610 -0,1638 0,5598 -0,0136 0,9089 -0,3592 0,8751

ZAR 0,8476 0,3085 0,8852 -0,7650 -0,8640 -0,4393 0,9108 1 0,3276 -0,8487 -0,0315 0,9210 -0,2801 0,3954 -0,1083 0,8912 -0,2252 0,7791

SGD 0,5907 0,2646 0,4217 0,0659 -0,1091 0,3722 0,3993 0,3276 1 -0,2205 0,0402 0,4593 0,4354 0,8606 0,3643 0,5194 0,1816 0,7132

PLN -0,8799 -0,2473 -0,7878 0,6771 0,9566 0,5977 -0,9329 -0,8487 -0,2205 1 0,1390 -0,9274 0,1959 -0,4115 -0,0587 -0,8784 0,4869 -0,7382

NOK -0,1486 0,1269 0,1417 -0,0100 0,1648 0,0721 -0,1746 -0,0315 0,0402 0,1390 1 -0,1032 0,0760 -0,1245 0,1452 -0,0647 0,2019 -0,1084

KRW 0,9418 0,2965 0,8704 -0,6123 -0,8687 -0,3853 0,9610 0,9210 0,4593 -0,9274 -0,1032 1 -0,1016 0,5583 0,1295 0,9750 -0,3082 0,8759

JPY -0,0184 -0,4889 -0,1384 0,7570 0,3739 0,7411 -0,1638 -0,2801 0,4354 0,1959 0,0760 -0,1016 1 0,3045 0,6523 0,0363 -0,2191 0,1687

CNY 0,7623 0,2020 0,3893 -0,0492 -0,3111 0,1976 0,5598 0,3954 0,8606 -0,4115 -0,1245 0,5583 0,3045 1 0,2087 0,5643 -0,0267 0,8267

CPL 0,0931 -0,1390 0,0338 0,4635 0,0717 0,3348 -0,0136 -0,1083 0,3643 -0,0587 0,1452 0,1295 0,6523 0,2087 1 0,2614 -0,2135 0,1590

INR 0,9119 0,1980 0,8505 -0,5075 -0,8065 -0,2579 0,9089 0,8912 0,5194 -0,8784 -0,0647 0,9750 0,0363 0,5643 0,2614 1 -0,3342 0,8830

BRL -0,3241 0,5467 -0,0875 0,0699 0,4794 0,1880 -0,3592 -0,2252 0,1816 0,4869 0,2019 -0,3082 -0,2191 -0,0267 -0,2135 -0,3342 1 -0,2527

RUB 0,9514 0,1508 0,7317 -0,3441 -0,6485 -0,0051 0,8751 0,7791 0,7132 -0,7382 -0,1084 0,8759 0,1687 0,8267 0,1590 0,8830 -0,2527 1


USD 1 -0,1476 0,7593 -0,0891 -0,3079 0,2002 0,5783 0,6660 0,7647 -0,3043 0,0639 0,5432 0,4690 0,6619 0,1087 0,6077 0,1176 0,9095

AUD -0,1476 1 0,3036 -0,5062 -0,2383 -0,4290 0,3535 0,2238 -0,2473 -0,2662 0,3764 0,3440 -0,5615 -0,4163 0,0197 0,1814 0,0797 -0,1063

CAD 0,7593 0,3036 1 -0,4836 -0,6961 -0,2377 0,8892 0,8627 0,3024 -0,6912 0,2384 0,8266 0,0746 0,0996 0,2362 0,8099 -0,1984 0,6388

CHF -0,0891 -0,5062 -0,4836 1 0,7269 0,8236 -0,6071 -0,6716 0,4158 0,5986 -0,3203 -0,5908 0,7541 0,4762 0,1518 -0,4661 0,0705 0,0341

CZK -0,3079 -0,2383 -0,6961 0,7269 1 0,7169 -0,7819 -0,7427 0,2987 0,9539 -0,2893 -0,8117 0,2518 0,4575 -0,3970 -0,8102 0,5155 -0,1170

EUR 0,2002 -0,4290 -0,2377 0,8236 0,7169 1 -0,3544 -0,3319 0,6447 0,6559 -0,3154 -0,4212 0,6758 0,6668 -0,0864 -0,3190 0,2343 0,4202

GBP 0,5783 0,3535 0,8892 -0,6071 -0,7819 -0,3544 1 0,9016 0,0204 -0,7852 0,1289 0,9337 -0,1400 -0,1871 0,2328 0,8814 -0,3250 0,5400

ZAR 0,6660 0,2238 0,8627 -0,6716 -0,7427 -0,3319 0,9016 1 0,1184 -0,6685 0,2256 0,8692 -0,1553 -0,0313 0,0785 0,8360 -0,1305 0,6107

SGD 0,7647 -0,2473 0,3024 0,4158 0,2987 0,6447 0,0204 0,1184 1 0,2680 -0,0572 -0,0049 0,7041 0,9304 -0,0007 0,0907 0,3693 0,7583

PLN -0,3043 -0,2662 -0,6912 0,5986 0,9539 0,6559 -0,7852 -0,6685 0,2680 1 -0,2384 -0,8414 0,1453 0,4628 -0,5222 -0,8398 0,5749 -0,1257

NOK 0,0639 0,3764 0,2384 -0,3203 -0,2893 -0,3154 0,1289 0,2256 -0,0572 -0,2384 1 0,2115 -0,2212 -0,1215 0,2072 0,2018 0,0778 -0,0066

KRW 0,5432 0,3440 0,8266 -0,5908 -0,8117 -0,4212 0,9337 0,8692 -0,0049 -0,8414 0,2115 1 -0,1208 -0,2269 0,4132 0,9613 -0,2880 0,4973

JPY 0,4690 -0,5615 0,0746 0,7541 0,2518 0,6758 -0,1400 -0,1553 0,7041 0,1453 -0,2212 -0,1208 1 0,6468 0,3951 0,0540 -0,1128 0,4389

CNY 0,6619 -0,4163 0,0996 0,4762 0,4575 0,6668 -0,1871 -0,0313 0,9304 0,4628 -0,1215 -0,2269 0,6468 1 -0,2089 -0,1370 0,5197 0,6547

CPL 0,1087 0,0197 0,2362 0,1518 -0,3970 -0,0864 0,2328 0,0785 -0,0007 -0,5222 0,2072 0,4132 0,3951 -0,2089 1 0,5373 -0,4896 0,0514

INR 0,6077 0,1814 0,8099 -0,4661 -0,8102 -0,3190 0,8814 0,8360 0,0907 -0,8398 0,2018 0,9613 0,0540 -0,1370 0,5373 1 -0,3403 0,5506

BRL 0,1176 0,0797 -0,1984 0,0705 0,5155 0,2343 -0,3250 -0,1305 0,3693 0,5749 0,0778 -0,2880 -0,1128 0,5197 -0,4896 -0,3403 1 0,2319

RUB 0,9095 -0,1063 0,6388 0,0341 -0,1170 0,4202 0,5400 0,6107 0,7583 -0,1257 -0,0066 0,4973 0,4389 0,6547 0,0514 0,5506 0,2319 1


63



USD 1 -0,7418 0,7782 0,9213 0,6475 0,8843 0,2922 0,0111 0,9881 -0,1510 -0,7172 -0,3021 0,9731 0,9899 -0,3602 0,6890 -0,5256 0,9667

AUD -0,7418 1 -0,3839 -0,6998 -0,4637 -0,5688 -0,1465 0,2229 -0,7057 0,0221 0,6538 0,5200 -0,7262 -0,7628 0,4098 -0,3475 0,5649 -0,7300

CAD 0,7782 -0,3839 1 0,6291 0,2879 0,6276 0,5652 0,4165 0,7396 -0,3313 -0,3836 0,1543 0,7019 0,7160 0,0255 0,7842 -0,3800 0,7335

CHF 0,9213 -0,6998 0,6291 1 0,7195 0,9558 0,1115 -0,1684 0,9543 -0,1364 -0,8029 -0,3488 0,9689 0,9242 -0,3293 0,5925 -0,6297 0,8516

CZK 0,6475 -0,4637 0,2879 0,7195 1 0,7385 -0,1497 -0,3111 0,7136 0,5193 -0,6120 -0,5966 0,6630 0,7280 -0,7186 0,0539 -0,1932 0,6372

EUR 0,8843 -0,5688 0,6276 0,9558 0,7385 1 0,0463 -0,0526 0,9309 -0,0865 -0,7324 -0,3096 0,9369 0,8874 -0,3352 0,5858 -0,5863 0,8057

GBP 0,2922 -0,1465 0,5652 0,1115 -0,1497 0,0463 1 0,3747 0,2090 -0,3606 -0,0552 0,4336 0,1825 0,2037 0,2348 0,5703 -0,1551 0,3807

ZAR 0,0111 0,2229 0,4165 -0,1684 -0,3111 -0,0526 0,3747 1 -0,0448 -0,2198 0,3077 0,6482 -0,1005 -0,0685 0,2690 0,4235 0,2030 -0,0362

SGD 0,9881 -0,7057 0,7396 0,9543 0,7136 0,9309 0,2090 -0,0448 1 -0,1033 -0,7492 -0,3360 0,9827 0,9877 -0,3933 0,6443 -0,5355 0,9407

PLN -0,1510 0,0221 -0,3313 -0,1364 0,5193 -0,0865 -0,3606 -0,2198 -0,1033 1 0,0460 -0,5160 -0,1969 -0,0295 -0,6438 -0,6590 0,4283 -0,0969

NOK -0,7172 0,6538 -0,3836 -0,8029 -0,6120 -0,7324 -0,0552 0,3077 -0,7492 0,0460 1 0,3893 -0,7455 -0,7415 0,4065 -0,3500 0,5627 -0,6473

KRW -0,3021 0,5200 0,1543 -0,3488 -0,5966 -0,3096 0,4336 0,6482 -0,3360 -0,5160 0,3893 1 -0,3445 -0,4098 0,6990 0,3997 0,2464 -0,3289

JPY 0,9731 -0,7262 0,7019 0,9689 0,6630 0,9369 0,1825 -0,1005 0,9827 -0,1969 -0,7455 -0,3445 1 0,9645 -0,3130 0,6682 -0,6323 0,9266

CNY 0,9899 -0,7628 0,7160 0,9242 0,7280 0,8874 0,2037 -0,0685 0,9877 -0,0295 -0,7415 -0,4098 0,9645 1 -0,4607 0,5875 -0,4899 0,9585

CPL -0,3602 0,4098 0,0255 -0,3293 -0,7186 -0,3352 0,2348 0,2690 -0,3933 -0,6438 0,4065 0,6990 -0,3130 -0,4607 1 0,3014 -0,0404 -0,3789

INR 0,6890 -0,3475 0,7842 0,5925 0,0539 0,5858 0,5703 0,4235 0,6443 -0,6590 -0,3500 0,3997 0,6682 0,5875 0,3014 1 -0,4457 0,6578

BRL -0,5256 0,5649 -0,3800 -0,6297 -0,1932 -0,5863 -0,1551 0,2030 -0,5355 0,4283 0,5627 0,2464 -0,6323 -0,4899 -0,0404 -0,4457 1 -0,4654

RUB 0,9667 -0,7300 0,7335 0,8516 0,6372 0,8057 0,3807 -0,0362 0,9407 -0,0969 -0,6473 -0,3289 0,9266 0,9585 -0,3789 0,6578 -0,4654 1


USD 1 -0,3147 0,9440 0,9653 0,5436 0,9410 0,4434 0,5479 0,9949 -0,7429 0,3389 -0,0797 0,9789 0,9993 0,5092 0,9530 -0,2761 0,1730

AUD -0,3147 1 -0,1562 -0,1913 -0,1118 -0,0885 -0,1862 0,2589 -0,2759 0,0230 0,4946 0,3875 -0,3437 -0,3182 0,3404 -0,2515 0,6031 -0,5741

CAD 0,9440 -0,1562 1 0,9160 0,4842 0,9045 0,4768 0,6770 0,9423 -0,7066 0,4470 -0,0262 0,9046 0,9440 0,5874 0,9026 -0,1642 0,0626

CHF 0,9653 -0,1913 0,9160 1 0,5472 0,9818 0,3601 0,5528 0,9795 -0,7828 0,3726 0,0301 0,9674 0,9627 0,5776 0,9427 -0,2865 0,0473

CZK 0,5436 -0,1118 0,4842 0,5472 1 0,5801 0,3807 0,2768 0,5599 -0,0049 -0,0162 -0,0935 0,4969 0,5587 -0,0396 0,4102 -0,1474 0,4968

EUR 0,9410 -0,0885 0,9045 0,9818 0,5801 1 0,3158 0,6135 0,9603 -0,7680 0,4232 0,0522 0,9413 0,9386 0,6058 0,9220 -0,2524 0,0118

GBP 0,4434 -0,1862 0,4768 0,3601 0,3807 0,3158 1 0,1445 0,4201 -0,0775 0,2296 -0,2425 0,3348 0,4461 0,1626 0,3855 0,0073 0,3573

ZAR 0,5479 0,2589 0,6770 0,5528 0,2768 0,6135 0,1445 1 0,5512 -0,4817 0,6342 0,2865 0,4744 0,5522 0,6198 0,5469 0,3015 -0,3192

SGD 0,9949 -0,2759 0,9423 0,9795 0,5599 0,9603 0,4201 0,5512 1 -0,7439 0,3285 -0,0351 0,9849 0,9939 0,5125 0,9581 -0,2871 0,1557

PLN -0,7429 0,0230 -0,7066 -0,7828 -0,0049 -0,7680 -0,0775 -0,4817 -0,7439 1 -0,5905 -0,0796 -0,7632 -0,7298 -0,7710 -0,7815 0,1569 0,4071

NOK 0,3389 0,4946 0,4470 0,3726 -0,0162 0,4232 0,2296 0,6342 0,3285 -0,5905 1 0,1435 0,2530 0,3316 0,8049 0,3686 0,4485 -0,5997

KRW -0,0797 0,3875 -0,0262 0,0301 -0,0935 0,0522 -0,2425 0,2865 -0,0351 -0,0796 0,1435 1 -0,0574 -0,0832 0,3167 0,0828 0,3815 -0,3778

JPY 0,9789 -0,3437 0,9046 0,9674 0,4969 0,9413 0,3348 0,4744 0,9849 -0,7632 0,2530 -0,0574 1 0,9758 0,4759 0,9565 -0,3825 0,1557

CNY 0,9993 -0,3182 0,9440 0,9627 0,5587 0,9386 0,4461 0,5522 0,9939 -0,7298 0,3316 -0,0832 0,9758 1 0,4916 0,9457 -0,2654 0,1788

CPL 0,5092 0,3404 0,5874 0,5776 -0,0396 0,6058 0,1626 0,6198 0,5125 -0,7710 0,8049 0,3167 0,4759 0,4916 1 0,6126 0,1519 -0,5188

INR 0,9530 -0,2515 0,9026 0,9427 0,4102 0,9220 0,3855 0,5469 0,9581 -0,7815 0,3686 0,0828 0,9565 0,9457 0,6126 1 -0,2520 0,0943

BRL -0,2761 0,6031 -0,1642 -0,2865 -0,1474 -0,2524 0,0073 0,3015 -0,2871 0,1569 0,4485 0,3815 -0,3825 -0,2654 0,1519 -0,2520 1 -0,4072

RUB 0,1730 -0,5741 0,0626 0,0473 0,4968 0,0118 0,3573 -0,3192 0,1557 0,4071 -0,5997 -0,3778 0,1557 0,1788 -0,5188 0,0943 -0,4072 1


USD 1 0,0643 0,8552 0,9414 0,2848 0,9040 0,3006 0,3357 0,9888 -0,7688 0,4587 0,0764 0,9680 0,9999 0,6727 0,9629 -0,2221 -0,0935

AUD 0,0643 1 0,4243 0,2836 0,3159 0,3744 0,2553 0,8455 0,1565 -0,4187 0,5839 0,6706 0,0102 0,0673 0,6507 0,1204 0,7350 -0,5946

CAD 0,8552 0,4243 1 0,8858 0,2785 0,8731 0,4465 0,6586 0,8833 -0,7985 0,5901 0,2956 0,8050 0,8572 0,8042 0,8549 0,0978 -0,2924

CHF 0,9414 0,2836 0,8858 1 0,3755 0,9771 0,2907 0,4886 0,9723 -0,8355 0,4986 0,2435 0,9362 0,9427 0,7505 0,9246 -0,1040 -0,2575

CZK 0,2848 0,3159 0,2785 0,3755 1 0,4427 0,3708 0,2316 0,3364 -0,0073 0,0857 0,0845 0,2537 0,2840 0,2081 0,2234 -0,0388 0,2837

EUR 0,9040 0,3744 0,8731 0,9771 0,4427 1 0,2667 0,5460 0,9428 -0,8169 0,5540 0,2842 0,8950 0,9047 0,7901 0,8984 -0,0541 -0,2936

GBP 0,3006 0,2553 0,4465 0,2907 0,3708 0,2667 1 0,2660 0,3068 -0,1207 0,2857 -0,0392 0,1976 0,3001 0,3175 0,2993 0,2391 0,1714

ZAR 0,3357 0,8455 0,6586 0,4886 0,2316 0,5460 0,2660 1 0,4072 -0,6417 0,6313 0,6396 0,2669 0,3394 0,7711 0,3598 0,5857 -0,6021

SGD 0,9888 0,1565 0,8833 0,9723 0,3364 0,9428 0,3068 0,4072 1 -0,7928 0,4578 0,1647 0,9727 0,9892 0,7002 0,9664 -0,1827 -0,1351

PLN -0,7688 -0,4187 -0,7985 -0,8355 -0,0073 -0,8169 -0,1207 -0,6417 -0,7928 1 -0,6245 -0,3354 -0,7587 -0,7717 -0,8124 -0,7571 -0,1270 0,6006

NOK 0,4587 0,5839 0,5901 0,4986 0,0857 0,5540 0,2857 0,6313 0,4578 -0,6245 1 0,3535 0,3214 0,4601 0,8533 0,4585 0,5229 -0,6612

KRW 0,0764 0,6706 0,2956 0,2435 0,0845 0,2842 -0,0392 0,6396 0,1647 -0,3354 0,3535 1 0,0589 0,0785 0,4919 0,1703 0,5728 -0,5281

JPY 0,9680 0,0102 0,8050 0,9362 0,2537 0,8950 0,1976 0,2669 0,9727 -0,7587 0,3214 0,0589 1 0,9677 0,5791 0,9533 -0,3223 -0,0744

CNY 0,9999 0,0673 0,8572 0,9427 0,2840 0,9047 0,3001 0,3394 0,9892 -0,7717 0,4601 0,0785 0,9677 1 0,6751 0,9619 -0,2209 -0,0980

CPL 0,6727 0,6507 0,8042 0,7505 0,2081 0,7901 0,3175 0,7711 0,7002 -0,8124 0,8533 0,4919 0,5791 0,6751 1 0,6798 0,4263 -0,6257

INR 0,9629 0,1204 0,8549 0,9246 0,2234 0,8984 0,2993 0,3598 0,9664 -0,7571 0,4585 0,1703 0,9533 0,9619 0,6798 1 -0,1242 -0,1225

BRL -0,2221 0,7350 0,0978 -0,1040 -0,0388 -0,0541 0,2391 0,5857 -0,1827 -0,1270 0,5229 0,5728 -0,3223 -0,2209 0,4263 -0,1242 1 -0,4965

RUB -0,0935 -0,5946 -0,2924 -0,2575 0,2837 -0,2936 0,1714 -0,6021 -0,1351 0,6006 -0,6612 -0,5281 -0,0744 -0,0980 -0,6257 -0,1225 -0,4965 1


USD 1 -0,1842 0,5119 0,7725 0,0843 0,7384 0,3729 -0,1820 0,9687 -0,1606 0,5271 0,2732 0,8699 0,9998 0,5157 0,9489 -0,1385 0,2619

AUD -0,1842 1 0,6094 0,3197 0,3688 0,3772 0,1318 0,9534 -0,0197 -0,5793 0,5001 0,5521 -0,1882 -0,1799 0,6564 -0,1653 0,8993 -0,6646

CAD 0,5119 0,6094 1 0,7151 0,2289 0,7260 0,5002 0,5914 0,6194 -0,4784 0,7305 0,5819 0,4005 0,5153 0,8240 0,5614 0,6138 -0,2942

CHF 0,7725 0,3197 0,7151 1 0,2906 0,9538 0,2934 0,2938 0,8733 -0,4755 0,6543 0,5648 0,7656 0,7753 0,7645 0,7618 0,2735 -0,1642

CZK 0,0843 0,3688 0,2289 0,2906 1 0,4002 0,3738 0,3286 0,1843 0,2751 0,1018 0,2340 0,0095 0,0815 0,2383 0,0557 0,2786 0,2328

EUR 0,7384 0,3772 0,7260 0,9538 0,4002 1 0,3038 0,3515 0,8478 -0,4370 0,6639 0,5700 0,7163 0,7398 0,7875 0,7374 0,2641 -0,1431

GBP 0,3729 0,1318 0,5002 0,2934 0,3738 0,3038 1 0,1089 0,3949 0,1830 0,2938 0,1863 0,1139 0,3719 0,3677 0,4297 0,2577 0,3281

ZAR -0,1820 0,9534 0,5914 0,2938 0,3286 0,3515 0,1089 1 -0,0205 -0,5946 0,5269 0,5517 -0,1986 -0,1763 0,6541 -0,1653 0,8552 -0,6747

SGD 0,9687 -0,0197 0,6194 0,8733 0,1843 0,8478 0,3949 -0,0205 1 -0,2288 0,5529 0,4409 0,8823 0,9693 0,6058 0,9572 -0,0152 0,1843

PLN -0,1606 -0,5793 -0,4784 -0,4755 0,2751 -0,4370 0,1830 -0,5946 -0,2288 1 -0,6600 -0,3858 -0,2172 -0,1673 -0,6750 -0,1241 -0,5631 0,8034

NOK 0,5271 0,5001 0,7305 0,6543 0,1018 0,6639 0,2938 0,5269 0,5529 -0,6600 1 0,4101 0,3399 0,5324 0,8699 0,4333 0,5413 -0,4817

KRW 0,2732 0,5521 0,5819 0,5648 0,2340 0,5700 0,1863 0,5517 0,4409 -0,3858 0,4101 1 0,2261 0,2786 0,6166 0,3640 0,4703 -0,2811

JPY 0,8699 -0,1882 0,4005 0,7656 0,0095 0,7163 0,1139 -0,1986 0,8823 -0,2172 0,3399 0,2261 1 0,8675 0,3837 0,8695 -0,1798 0,1621

CNY 0,9998 -0,1799 0,5153 0,7753 0,0815 0,7398 0,3719 -0,1763 0,9693 -0,1673 0,5324 0,2786 0,8675 1 0,5215 0,9482 -0,1335 0,2553

CPL 0,5157 0,6564 0,8240 0,7645 0,2383 0,7875 0,3677 0,6541 0,6058 -0,6750 0,8699 0,6166 0,3837 0,5215 1 0,4793 0,6432 -0,4888

INR 0,9489 -0,1653 0,5614 0,7618 0,0557 0,7374 0,4297 -0,1653 0,9572 -0,1241 0,4333 0,3640 0,8695 0,9482 0,4793 1 -0,1366 0,3062

BRL -0,1385 0,8993 0,6138 0,2735 0,2786 0,2641 0,2577 0,8552 -0,0152 -0,5631 0,5413 0,4703 -0,1798 -0,1335 0,6432 -0,1366 1 -0,6387

RUB 0,2619 -0,6646 -0,2942 -0,1642 0,2328 -0,1431 0,3281 -0,6747 0,1843 0,8034 -0,4817 -0,2811 0,1621 0,2553 -0,4888 0,3062 -0,6387 1


64



USD 1 -0,6473 0,5928 0,9082 0,0982 0,9017 0,6476 -0,4374 0,9804 -0,2183 0,3841 0,2917 0,8805 1,0000 0,5985 0,9574 -0,5618 0,6031

AUD -0,6473 1 0,0761 -0,3710 0,3685 -0,3378 -0,0650 0,8390 -0,5227 0,2930 0,1982 0,2272 -0,6663 -0,6470 0,0941 -0,5556 0,9395 -0,1607

CAD 0,5928 0,0761 1 0,7194 0,3012 0,7161 0,7865 0,2352 0,6851 -0,0159 0,5072 0,5239 0,4624 0,5926 0,6934 0,6803 0,1936 0,5087

CHF 0,9082 -0,3710 0,7194 1 0,2921 0,9720 0,7253 -0,2403 0,9510 -0,0628 0,5054 0,3772 0,8412 0,9078 0,7039 0,9189 -0,3068 0,7449

CZK 0,0982 0,3685 0,3012 0,2921 1 0,4116 0,4907 0,4935 0,1460 0,4853 0,1556 0,2502 -0,0965 0,0978 0,3911 0,0316 0,3267 0,3951

EUR 0,9017 -0,3378 0,7161 0,9720 0,4116 1 0,7845 -0,1671 0,9355 -0,0627 0,5107 0,4060 0,7666 0,9014 0,7390 0,8937 -0,2830 0,7408

GBP 0,6476 -0,0650 0,7865 0,7253 0,4907 0,7845 1 0,1876 0,6942 -0,0088 0,2672 0,4258 0,4447 0,6466 0,6953 0,6775 0,0252 0,5218

ZAR -0,4374 0,8390 0,2352 -0,2403 0,4935 -0,1671 0,1876 1 -0,3315 0,1516 0,1473 0,3724 -0,5802 -0,4356 0,2035 -0,3831 0,8075 -0,1197

SGD 0,9804 -0,5227 0,6851 0,9510 0,1460 0,9355 0,6942 -0,3315 1 -0,1632 0,4468 0,4153 0,8870 0,9807 0,6789 0,9776 -0,4445 0,6801

PLN -0,2183 0,2930 -0,0159 -0,0628 0,4853 -0,0627 -0,0088 0,1516 -0,1632 1 -0,2601 0,1115 -0,1426 -0,2191 -0,0551 -0,1970 0,1946 0,2773

NOK 0,3841 0,1982 0,5072 0,5054 0,1556 0,5107 0,2672 0,1473 0,4468 -0,2601 1 0,2333 0,2980 0,3849 0,6642 0,3875 0,2732 0,1710

KRW 0,2917 0,2272 0,5239 0,3772 0,2502 0,4060 0,4258 0,3724 0,4153 0,1115 0,2333 1 0,1953 0,2946 0,5379 0,4086 0,1824 0,5246

JPY 0,8805 -0,6663 0,4624 0,8412 -0,0965 0,7666 0,4447 -0,5802 0,8870 -0,1426 0,2980 0,1953 1 0,8797 0,4626 0,8993 -0,5666 0,5540

CNY 1,0000 -0,6470 0,5926 0,9078 0,0978 0,9014 0,6466 -0,4356 0,9807 -0,2191 0,3849 0,2946 0,8797 1 0,5988 0,9572 -0,5625 0,6034

CPL 0,5985 0,0941 0,6934 0,7039 0,3911 0,7390 0,6953 0,2035 0,6789 -0,0551 0,6642 0,5379 0,4626 0,5988 1 0,6188 0,1673 0,4483

INR 0,9574 -0,5556 0,6803 0,9189 0,0316 0,8937 0,6775 -0,3831 0,9776 -0,1970 0,3875 0,4086 0,8993 0,9572 0,6188 1 -0,4693 0,6705

BRL -0,5618 0,9395 0,1936 -0,3068 0,3267 -0,2830 0,0252 0,8075 -0,4445 0,1946 0,2732 0,1824 -0,5666 -0,5625 0,1673 -0,4693 1 -0,2358

RUB 0,6031 -0,1607 0,5087 0,7449 0,3951 0,7408 0,5218 -0,1197 0,6801 0,2773 0,1710 0,5246 0,5540 0,6034 0,4483 0,6705 -0,2358 1


USD 1 -0,4541 0,3671 0,8272 0,4749 0,7368 0,7124 0,1272 0,9550 -0,1432 0,1555 0,4279 0,7783 0,9999 0,5490 0,8617 -0,4584 0,6595

AUD -0,4541 1 0,4981 -0,1923 -0,4052 -0,4560 -0,3892 0,5693 -0,1919 0,4842 0,5237 0,4824 -0,0259 -0,4540 0,2874 -0,0081 0,8460 0,2218

CAD 0,3671 0,4981 1 0,3453 -0,1688 0,0070 0,1541 0,6880 0,5512 0,2905 0,3597 0,8201 0,4816 0,3678 0,5624 0,7141 0,3645 0,6550

CHF 0,8272 -0,1923 0,3453 1 0,6922 0,9045 0,8273 0,3222 0,8693 -0,0087 0,3970 0,3902 0,7544 0,8260 0,6699 0,7634 -0,1042 0,7541

CZK 0,4749 -0,4052 -0,1688 0,6922 1 0,8590 0,7979 0,0898 0,4027 0,0602 -0,0337 -0,2435 0,3442 0,4713 0,2727 0,1993 -0,0997 0,2299

EUR 0,7368 -0,4560 0,0070 0,9045 0,8590 1 0,8980 0,0513 0,6904 -0,1260 0,1850 0,0199 0,5469 0,7345 0,4487 0,5130 -0,2272 0,4890

GBP 0,7124 -0,3892 0,1541 0,8273 0,7979 0,8980 1 0,1389 0,6651 -0,0727 0,0040 0,0430 0,4865 0,7086 0,4741 0,5355 -0,1732 0,4592

ZAR 0,1272 0,5693 0,6880 0,3222 0,0898 0,0513 0,1389 1 0,3324 0,3215 0,3298 0,5786 0,3696 0,1282 0,4832 0,4172 0,5240 0,5258

SGD 0,9550 -0,1919 0,5512 0,8693 0,4027 0,6904 0,6651 0,3324 1 -0,0317 0,3489 0,6328 0,8660 0,9557 0,7049 0,9465 -0,2437 0,8140

PLN -0,1432 0,4842 0,2905 -0,0087 0,0602 -0,1260 -0,0727 0,3215 -0,0317 1 0,3276 0,2196 0,1160 -0,1440 0,3777 -0,0019 0,4733 -0,0184

NOK 0,1555 0,5237 0,3597 0,3970 -0,0337 0,1850 0,0040 0,3298 0,3489 0,3276 1 0,5860 0,4368 0,1568 0,5265 0,3774 0,4042 0,5135

KRW 0,4279 0,4824 0,8201 0,3902 -0,2435 0,0199 0,0430 0,5786 0,6328 0,2196 0,5860 1 0,6225 0,4309 0,6768 0,7624 0,2240 0,7362

JPY 0,7783 -0,0259 0,4816 0,7544 0,3442 0,5469 0,4865 0,3696 0,8660 0,1160 0,4368 0,6225 1 0,7795 0,6713 0,7964 -0,1272 0,7311

CNY 0,9999 -0,4540 0,3678 0,8260 0,4713 0,7345 0,7086 0,1282 0,9557 -0,1440 0,1568 0,4309 0,7795 1 0,5487 0,8621 -0,4604 0,6601

CPL 0,5490 0,2874 0,5624 0,6699 0,2727 0,4487 0,4741 0,4832 0,7049 0,3777 0,5265 0,6768 0,6713 0,5487 1 0,7060 0,2340 0,6906

INR 0,8617 -0,0081 0,7141 0,7634 0,1993 0,5130 0,5355 0,4172 0,9465 -0,0019 0,3774 0,7624 0,7964 0,8621 0,7060 1 -0,1290 0,8673

BRL -0,4584 0,8460 0,3645 -0,1042 -0,0997 -0,2272 -0,1732 0,5240 -0,2437 0,4733 0,4042 0,2240 -0,1272 -0,4604 0,2340 -0,1290 1 0,1146

RUB 0,6595 0,2218 0,6550 0,7541 0,2299 0,4890 0,4592 0,5258 0,8140 -0,0184 0,5135 0,7362 0,7311 0,6601 0,6906 0,8673 0,1146 1


USD 1 0,3691 0,7693 0,5646 -0,2170 -0,1547 0,4280 0,7402 0,9333 -0,4542 -0,0124 0,5989 0,8663 0,9998 0,7038 0,8379 0,6378 0,6969

AUD 0,3691 1 0,7966 0,1153 -0,7134 -0,6251 -0,4080 0,7455 0,6515 -0,2893 0,5727 0,8999 0,4771 0,3761 0,6553 0,7849 0,7933 0,8247

CAD 0,7693 0,7966 1 0,1990 -0,6883 -0,6467 -0,1402 0,9059 0,9122 -0,5119 0,1752 0,8819 0,7163 0,7737 0,7120 0,9548 0,8645 0,8436

CHF 0,5646 0,1153 0,1990 1 0,3953 0,5241 0,7191 0,3492 0,4787 0,0663 0,3378 0,1821 0,5709 0,5666 0,5510 0,3562 0,2859 0,3956

CZK -0,2170 -0,7134 -0,6883 0,3953 1 0,9432 0,6641 -0,5215 -0,4498 0,5754 -0,1104 -0,6609 -0,3042 -0,2248 -0,2914 -0,5649 -0,6029 -0,4782

EUR -0,1547 -0,6251 -0,6467 0,5241 0,9432 1 0,7339 -0,5020 -0,3750 0,5560 0,0993 -0,5885 -0,1998 -0,1624 -0,1490 -0,4994 -0,5126 -0,4054

GBP 0,4280 -0,4080 -0,1402 0,7191 0,6641 0,7339 1 -0,0837 0,1799 0,1758 -0,0824 -0,2494 0,2356 0,4219 0,2371 0,0037 -0,1207 -0,0594

ZAR 0,7402 0,7455 0,9059 0,3492 -0,5215 -0,5020 -0,0837 1 0,8772 -0,4495 0,2220 0,8175 0,7429 0,7459 0,7083 0,8918 0,8213 0,8374

SGD 0,9333 0,6515 0,9122 0,4787 -0,4498 -0,3750 0,1799 0,8772 1 -0,5434 0,1744 0,7920 0,8853 0,9364 0,7916 0,9492 0,8395 0,8567

PLN -0,4542 -0,2893 -0,5119 0,0663 0,5754 0,5560 0,1758 -0,4495 -0,5434 1 0,1680 -0,2966 -0,5130 -0,4608 -0,1418 -0,4187 -0,6126 -0,3506

NOK -0,0124 0,5727 0,1752 0,3378 -0,1104 0,0993 -0,0824 0,2220 0,1744 0,1680 1 0,4383 0,1880 -0,0120 0,4166 0,2559 0,3308 0,4331

KRW 0,5989 0,8999 0,8819 0,1821 -0,6609 -0,5885 -0,2494 0,8175 0,7920 -0,2966 0,4383 1 0,6076 0,6035 0,7251 0,9158 0,7529 0,8805

JPY 0,8663 0,4771 0,7163 0,5709 -0,3042 -0,1998 0,2356 0,7429 0,8853 -0,5130 0,1880 0,6076 1 0,8702 0,7098 0,7674 0,6751 0,7163

CNY 0,9998 0,3761 0,7737 0,5666 -0,2248 -0,1624 0,4219 0,7459 0,9364 -0,4608 -0,0120 0,6035 0,8702 1 0,7051 0,8413 0,6443 0,7008

CPL 0,7038 0,6553 0,7120 0,5510 -0,2914 -0,1490 0,2371 0,7083 0,7916 -0,1418 0,4166 0,7251 0,7098 0,7051 1 0,7851 0,7027 0,7527

INR 0,8379 0,7849 0,9548 0,3562 -0,5649 -0,4994 0,0037 0,8918 0,9492 -0,4187 0,2559 0,9158 0,7674 0,8413 0,7851 1 0,8203 0,9099

BRL 0,6378 0,7933 0,8645 0,2859 -0,6029 -0,5126 -0,1207 0,8213 0,8395 -0,6126 0,3308 0,7529 0,6751 0,6443 0,7027 0,8203 1 0,8012

RUB 0,6969 0,8247 0,8436 0,3956 -0,4782 -0,4054 -0,0594 0,8374 0,8567 -0,3506 0,4331 0,8805 0,7163 0,7008 0,7527 0,9099 0,8012 1


USD 1 0,5748 0,9068 0,2895 -0,5894 -0,3731 0,3289 0,7674 0,9139 -0,4950 -0,0702 0,7352 0,7450 0,9940 0,6126 0,9092 0,8064 0,7916

AUD 0,5748 1 0,7788 0,1762 -0,6766 -0,6327 -0,1035 0,7853 0,7125 -0,3409 -0,2371 0,7553 0,4072 0,5951 0,6341 0,7746 0,6375 0,5029

CAD 0,9068 0,7788 1 0,1288 -0,7155 -0,5478 0,0501 0,8556 0,8851 -0,4403 -0,1470 0,8357 0,5971 0,9069 0,5818 0,9658 0,8071 0,7920

CHF 0,2895 0,1762 0,1288 1 -0,1799 -0,2449 0,4635 0,4154 0,4639 -0,5143 -0,3969 -0,0990 0,6661 0,3414 0,4957 0,0880 0,4656 -0,0992

CZK -0,5894 -0,6766 -0,7155 -0,1799 1 0,8969 0,3188 -0,7257 -0,7422 0,6932 0,6212 -0,5157 -0,6051 -0,6439 -0,4788 -0,6657 -0,5722 -0,3241

EUR -0,3731 -0,6327 -0,5478 -0,2449 0,8969 1 0,4438 -0,7087 -0,6440 0,7183 0,8335 -0,3204 -0,5859 -0,4473 -0,4071 -0,4646 -0,4792 -0,1005

GBP 0,3289 -0,1035 0,0501 0,4635 0,3188 0,4438 1 0,0244 0,2116 -0,0183 0,4122 0,0058 0,2758 0,3006 0,3176 0,0836 0,2457 0,2403

ZAR 0,7674 0,7853 0,8556 0,4154 -0,7257 -0,7087 0,0244 1 0,9006 -0,5949 -0,4238 0,6288 0,7460 0,8025 0,6942 0,7962 0,8146 0,4892

SGD 0,9139 0,7125 0,8851 0,4639 -0,7422 -0,6440 0,2116 0,9006 1 -0,7129 -0,3792 0,6462 0,8646 0,9440 0,7199 0,8522 0,8825 0,6076

PLN -0,4950 -0,3409 -0,4403 -0,5143 0,6932 0,7183 -0,0183 -0,5949 -0,7129 1 0,7164 -0,0637 -0,7599 -0,5704 -0,3569 -0,3525 -0,6481 -0,0767

NOK -0,0702 -0,2371 -0,1470 -0,3969 0,6212 0,8335 0,4122 -0,4238 -0,3792 0,7164 1 0,1556 -0,5283 -0,1624 -0,2296 -0,0413 -0,2736 0,2810

KRW 0,7352 0,7553 0,8357 -0,0990 -0,5157 -0,3204 0,0058 0,6288 0,6462 -0,0637 0,1556 1 0,3065 0,7085 0,4954 0,9076 0,5155 0,7927

JPY 0,7450 0,4072 0,5971 0,6661 -0,6051 -0,5859 0,2758 0,7460 0,8646 -0,7599 -0,5283 0,3065 1 0,7921 0,6576 0,5456 0,6938 0,3035

CNY 0,9940 0,5951 0,9069 0,3414 -0,6439 -0,4473 0,3006 0,8025 0,9440 -0,5704 -0,1624 0,7085 0,7921 1 0,6339 0,9016 0,8247 0,7408

CPL 0,6126 0,6341 0,5818 0,4957 -0,4788 -0,4071 0,3176 0,6942 0,7199 -0,3569 -0,2296 0,4954 0,6576 0,6339 1 0,5746 0,6382 0,3296

INR 0,9092 0,7746 0,9658 0,0880 -0,6657 -0,4646 0,0836 0,7962 0,8522 -0,3525 -0,0413 0,9076 0,5456 0,9016 0,5746 1 0,7410 0,8303

BRL 0,8064 0,6375 0,8071 0,4656 -0,5722 -0,4792 0,2457 0,8146 0,8825 -0,6481 -0,2736 0,5155 0,6938 0,8247 0,6382 0,7410 1 0,5910

RUB 0,7916 0,5029 0,7920 -0,0992 -0,3241 -0,1005 0,2403 0,4892 0,6076 -0,0767 0,2810 0,7927 0,3035 0,7408 0,3296 0,8303 0,5910 1


65



USD 1 -0,0322 0,9288 0,0435 0,0510 0,4027 0,7705 0,5160 0,7960 0,0601 0,6084 0,7843 0,4706 0,9853 0,4179 0,9247 0,8062 0,8932

AUD -0,0322 1 0,2071 0,2876 -0,5275 -0,4846 -0,1965 0,6023 0,3551 -0,3988 -0,2996 0,0893 0,1280 0,0593 0,5020 0,1421 0,2896 -0,1502

CAD 0,9288 0,2071 1 -0,0449 -0,0654 0,2671 0,6073 0,6194 0,7886 0,0424 0,5430 0,8192 0,3370 0,9204 0,4096 0,9532 0,8527 0,8693

CHF 0,0435 0,2876 -0,0449 1 -0,3749 -0,4094 0,1924 0,5145 0,4014 -0,6143 -0,4082 -0,3313 0,6478 0,1456 0,5995 -0,1256 0,3275 -0,2286

CZK 0,0510 -0,5275 -0,0654 -0,3749 1 0,7737 0,3752 -0,4966 -0,3296 0,8096 0,5745 0,2822 -0,3679 -0,0668 -0,3663 0,0502 -0,2756 0,2824

EUR 0,4027 -0,4846 0,2671 -0,4094 0,7737 1 0,5969 -0,3872 -0,1444 0,8186 0,8950 0,5858 -0,3541 0,2791 -0,2012 0,3861 -0,0492 0,6013

GBP 0,7705 -0,1965 0,6073 0,1924 0,3752 0,5969 1 0,2539 0,5488 0,1974 0,6525 0,5721 0,3660 0,7367 0,3759 0,6165 0,5260 0,6916

ZAR 0,5160 0,6023 0,6194 0,5145 -0,4966 -0,3872 0,2539 1 0,8242 -0,5273 -0,1245 0,2549 0,6434 0,6076 0,7495 0,5109 0,7895 0,2764

SGD 0,7960 0,3551 0,7886 0,4014 -0,3296 -0,1444 0,5488 0,8242 1 -0,4634 0,0816 0,4672 0,7913 0,8735 0,6854 0,7306 0,8966 0,5138

PLN 0,0601 -0,3988 0,0424 -0,6143 0,8096 0,8186 0,1974 -0,5273 -0,4634 1 0,7319 0,4535 -0,6638 -0,0889 -0,4669 0,1520 -0,3156 0,4071

NOK 0,6084 -0,2996 0,5430 -0,4082 0,5745 0,8950 0,6525 -0,1245 0,0816 0,7319 1 0,7977 -0,2860 0,4834 -0,0534 0,6303 0,2236 0,8203

KRW 0,7843 0,0893 0,8192 -0,3313 0,2822 0,5858 0,5721 0,2549 0,4672 0,4535 0,7977 1 -0,0339 0,7153 0,1498 0,9018 0,5459 0,8950

JPY 0,4706 0,1280 0,3370 0,6478 -0,3679 -0,3541 0,3660 0,6434 0,7913 -0,6638 -0,2860 -0,0339 1 0,5782 0,6006 0,2676 0,5856 0,0949

CNY 0,9853 0,0593 0,9204 0,1456 -0,0668 0,2791 0,7367 0,6076 0,8735 -0,0889 0,4834 0,7153 0,5782 1 0,4972 0,9028 0,8457 0,8158

CPL 0,4179 0,5020 0,4096 0,5995 -0,3663 -0,2012 0,3759 0,7495 0,6854 -0,4669 -0,0534 0,1498 0,6006 0,4972 1 0,3216 0,6407 0,1456

INR 0,9247 0,1421 0,9532 -0,1256 0,0502 0,3861 0,6165 0,5109 0,7306 0,1520 0,6303 0,9018 0,2676 0,9028 0,3216 1 0,7752 0,8958

BRL 0,8062 0,2896 0,8527 0,3275 -0,2756 -0,0492 0,5260 0,7895 0,8966 -0,3156 0,2236 0,5459 0,5856 0,8457 0,6407 0,7752 1 0,6317

RUB 0,8932 -0,1502 0,8693 -0,2286 0,2824 0,6013 0,6916 0,2764 0,5138 0,4071 0,8203 0,8950 0,0949 0,8158 0,1456 0,8958 0,6317 1


USD 1 0,3565 0,9633 0,1786 0,4593 0,8521 0,9453 0,8041 0,9586 0,5290 0,8690 0,8914 0,7129 0,9944 0,7631 0,9619 0,9672 0,9052

AUD 0,3565 1 0,4198 0,2049 0,0523 0,3040 0,3191 0,6604 0,4480 0,3794 0,3332 0,5209 0,2546 0,3695 0,6115 0,4683 0,4376 0,1817

CAD 0,9633 0,4198 1 0,0642 0,3826 0,8172 0,8823 0,7666 0,9106 0,5437 0,9049 0,9148 0,5606 0,9573 0,6852 0,9564 0,9384 0,9306

CHF 0,1786 0,2049 0,0642 1 -0,1239 -0,0365 0,2458 0,4345 0,3155 -0,2277 -0,0854 -0,0585 0,6256 0,2186 0,4374 0,0613 0,2925 -0,0328

CZK 0,4593 0,0523 0,3826 -0,1239 1 0,7781 0,5671 0,3660 0,3475 0,8276 0,5583 0,5374 0,2812 0,3993 0,2413 0,5160 0,3859 0,4649

EUR 0,8521 0,3040 0,8172 -0,0365 0,7781 1 0,8420 0,6887 0,7336 0,8072 0,8890 0,8753 0,4737 0,8108 0,5604 0,9091 0,7808 0,8320

GBP 0,9453 0,3191 0,8823 0,2458 0,5671 0,8420 1 0,7812 0,9123 0,5614 0,8115 0,8193 0,7439 0,9323 0,7548 0,8900 0,9204 0,8354

ZAR 0,8041 0,6604 0,7666 0,4345 0,3660 0,6887 0,7812 1 0,8376 0,4978 0,6723 0,7350 0,7287 0,8052 0,8508 0,8148 0,8498 0,6037

SGD 0,9586 0,4480 0,9106 0,3155 0,3475 0,7336 0,9123 0,8376 1 0,3886 0,7461 0,8195 0,8262 0,9749 0,8296 0,8959 0,9546 0,7906

PLN 0,5290 0,3794 0,5437 -0,2277 0,8276 0,8072 0,5614 0,4978 0,3886 1 0,7173 0,7374 0,1086 0,4627 0,3267 0,6605 0,4918 0,5708

NOK 0,8690 0,3332 0,9049 -0,0854 0,5583 0,8890 0,8115 0,6723 0,7461 0,7173 1 0,9244 0,3604 0,8285 0,5283 0,9215 0,8193 0,9457

KRW 0,8914 0,5209 0,9148 -0,0585 0,5374 0,8753 0,8193 0,7350 0,8195 0,7374 0,9244 1 0,4406 0,8660 0,6365 0,9577 0,8606 0,8757

JPY 0,7129 0,2546 0,5606 0,6256 0,2812 0,4737 0,7439 0,7287 0,8262 0,1086 0,3604 0,4406 1 0,7451 0,7672 0,5802 0,7304 0,4279

CNY 0,9944 0,3695 0,9573 0,2186 0,3993 0,8108 0,9323 0,8052 0,9749 0,4627 0,8285 0,8660 0,7451 1 0,7743 0,9440 0,9659 0,8785

CPL 0,7631 0,6115 0,6852 0,4374 0,2413 0,5604 0,7548 0,8508 0,8296 0,3267 0,5283 0,6365 0,7672 0,7743 1 0,7214 0,7969 0,5210

INR 0,9619 0,4683 0,9564 0,0613 0,5160 0,9091 0,8900 0,8148 0,8959 0,6605 0,9215 0,9577 0,5802 0,9440 0,7214 1 0,9314 0,8952

BRL 0,9672 0,4376 0,9384 0,2925 0,3859 0,7808 0,9204 0,8498 0,9546 0,4918 0,8193 0,8606 0,7304 0,9659 0,7969 0,9314 1 0,8486

RUB 0,9052 0,1817 0,9306 -0,0328 0,4649 0,8320 0,8354 0,6037 0,7906 0,5708 0,9457 0,8757 0,4279 0,8785 0,5210 0,8952 0,8486 1


USD 1 0,0973 0,9589 0,0129 0,4137 0,7881 0,9737 0,8271 0,9474 0,6342 0,6775 0,9245 0,9360 0,9926 0,8239 0,9725 0,8957 0,7563

AUD 0,0973 1 0,1802 0,4980 0,0312 0,1265 0,0778 0,4536 0,3470 0,3014 0,1404 0,3562 0,2276 0,1659 0,4599 0,1788 0,2999 -0,0847

CAD 0,9589 0,1802 1 0,0477 0,3309 0,7157 0,9333 0,8210 0,9358 0,5613 0,7050 0,9057 0,8621 0,9659 0,7773 0,9227 0,9035 0,7886

CHF 0,0129 0,4980 0,0477 1 0,1872 0,1847 -0,0133 0,1326 0,2484 0,1110 0,4271 0,1656 0,1412 0,0951 0,1324 -0,0153 0,3342 0,2922

CZK 0,4137 0,0312 0,3309 0,1872 1 0,8104 0,5163 0,3530 0,4444 0,8312 0,6070 0,5326 0,4638 0,3996 0,2606 0,4480 0,4484 0,4411

EUR 0,7881 0,1265 0,7157 0,1847 0,8104 1 0,8227 0,7022 0,7755 0,8333 0,7757 0,8103 0,7743 0,7802 0,6053 0,8195 0,7693 0,6768

GBP 0,9737 0,0778 0,9333 -0,0133 0,5163 0,8227 1 0,7895 0,9261 0,6984 0,7088 0,9166 0,9116 0,9609 0,7991 0,9452 0,8582 0,7644

ZAR 0,8271 0,4536 0,8210 0,1326 0,3530 0,7022 0,7895 1 0,8500 0,6557 0,6174 0,8645 0,8399 0,8266 0,8601 0,8899 0,8182 0,4934

SGD 0,9474 0,3470 0,9358 0,2484 0,4444 0,7755 0,9261 0,8500 1 0,6782 0,7073 0,9636 0,9436 0,9696 0,8592 0,9255 0,9331 0,7379

PLN 0,6342 0,3014 0,5613 0,1110 0,8312 0,8333 0,6984 0,6557 0,6782 1 0,6116 0,7830 0,6892 0,6228 0,5684 0,6933 0,6342 0,4261

NOK 0,6775 0,1404 0,7050 0,4271 0,6070 0,7757 0,7088 0,6174 0,7073 0,6116 1 0,7061 0,6043 0,6861 0,4778 0,6427 0,8000 0,8559

KRW 0,9245 0,3562 0,9057 0,1656 0,5326 0,8103 0,9166 0,8645 0,9636 0,7830 0,7061 1 0,9159 0,9369 0,8299 0,9349 0,9160 0,6746

JPY 0,9360 0,2276 0,8621 0,1412 0,4638 0,7743 0,9116 0,8399 0,9436 0,6892 0,6043 0,9159 1 0,9364 0,8539 0,9363 0,8401 0,6365

CNY 0,9926 0,1659 0,9659 0,0951 0,3996 0,7802 0,9609 0,8266 0,9696 0,6228 0,6861 0,9369 0,9364 1 0,8273 0,9618 0,9160 0,7662

CPL 0,8239 0,4599 0,7773 0,1324 0,2606 0,6053 0,7991 0,8601 0,8592 0,5684 0,4778 0,8299 0,8539 0,8273 1 0,8465 0,7826 0,4648

INR 0,9725 0,1788 0,9227 -0,0153 0,4480 0,8195 0,9452 0,8899 0,9255 0,6933 0,6427 0,9349 0,9363 0,9618 0,8465 1 0,8734 0,6478

BRL 0,8957 0,2999 0,9035 0,3342 0,4484 0,7693 0,8582 0,8182 0,9331 0,6342 0,8000 0,9160 0,8401 0,9160 0,7826 0,8734 1 0,7845

RUB 0,7563 -0,0847 0,7886 0,2922 0,4411 0,6768 0,7644 0,4934 0,7379 0,4261 0,8559 0,6746 0,6365 0,7662 0,4648 0,6478 0,7845 1


USD 1 0,3539 0,8267 -0,1167 0,0329 0,4699 0,9140 0,5676 0,6478 0,1597 -0,0060 0,6521 0,7245 0,9173 0,7617 0,8266 0,2981 -0,1872

AUD 0,3539 1 0,6115 0,5570 0,2694 0,4645 0,3449 0,3395 0,7888 0,0597 0,6598 0,7642 0,5289 0,5349 0,6337 0,2953 0,6135 0,3443

CAD 0,8267 0,6115 1 0,0433 -0,0184 0,3453 0,7580 0,6438 0,7085 0,1783 0,1537 0,7587 0,5755 0,7940 0,7887 0,7572 0,5483 0,2005

CHF -0,1167 0,5570 0,0433 1 0,4757 0,3809 -0,0265 -0,2537 0,6070 -0,2733 0,8286 0,3931 0,4492 0,2081 0,1316 -0,2317 0,3583 0,2888

CZK 0,0329 0,2694 -0,0184 0,4757 1 0,8179 0,2232 -0,0474 0,3721 0,3171 0,5270 0,4060 0,3427 0,1522 0,0419 0,0783 0,2637 0,0972

EUR 0,4699 0,4645 0,3453 0,3809 0,8179 1 0,5810 0,2920 0,6026 0,3349 0,5075 0,6212 0,6123 0,5299 0,4418 0,4662 0,3850 0,0054

GBP 0,9140 0,3449 0,7580 -0,0265 0,2232 0,5810 1 0,5317 0,6634 0,2839 0,0182 0,6855 0,6865 0,8330 0,7524 0,8133 0,3608 -0,1361

ZAR 0,5676 0,3395 0,6438 -0,2537 -0,0474 0,2920 0,5317 1 0,2628 0,6741 -0,1435 0,5357 0,0843 0,3240 0,6790 0,8703 0,6710 0,3155

SGD 0,6478 0,7888 0,7085 0,6070 0,3721 0,6026 0,6634 0,2628 1 -0,0654 0,6304 0,8758 0,8614 0,8367 0,7181 0,4477 0,5427 0,1001

PLN 0,1597 0,0597 0,1783 -0,2733 0,3171 0,3349 0,2839 0,6741 -0,0654 1 -0,2924 0,3091 -0,2444 -0,1065 0,2677 0,6007 0,5397 0,3506

NOK -0,0060 0,6598 0,1537 0,8286 0,5270 0,5075 0,0182 -0,1435 0,6304 -0,2924 1 0,4676 0,5042 0,3128 0,1709 -0,1546 0,3089 0,1826

KRW 0,6521 0,7642 0,7587 0,3931 0,4060 0,6212 0,6855 0,5357 0,8758 0,3091 0,4676 1 0,6543 0,7110 0,7768 0,6657 0,7454 0,2560

JPY 0,7245 0,5289 0,5755 0,4492 0,3427 0,6123 0,6865 0,0843 0,8614 -0,2444 0,5042 0,6543 1 0,8989 0,5481 0,3799 0,1591 -0,2528

CNY 0,9173 0,5349 0,7940 0,2081 0,1522 0,5299 0,8330 0,3240 0,8367 -0,1065 0,3128 0,7110 0,8989 1 0,7075 0,6006 0,2665 -0,1834

CPL 0,7617 0,6337 0,7887 0,1316 0,0419 0,4418 0,7524 0,6790 0,7181 0,2677 0,1709 0,7768 0,5481 0,7075 1 0,7849 0,6521 0,1673

INR 0,8266 0,2953 0,7572 -0,2317 0,0783 0,4662 0,8133 0,8703 0,4477 0,6007 -0,1546 0,6657 0,3799 0,6006 0,7849 1 0,5815 0,1079

BRL 0,2981 0,6135 0,5483 0,3583 0,2637 0,3850 0,3608 0,6710 0,5427 0,5397 0,3089 0,7454 0,1591 0,2665 0,6521 0,5815 1 0,6120

RUB -0,1872 0,3443 0,2005 0,2888 0,0972 0,0054 -0,1361 0,3155 0,1001 0,3506 0,1826 0,2560 -0,2528 -0,1834 0,1673 0,1079 0,6120 1


66



USD 1 0,4908 0,7044 0,1606 -0,4226 0,3315 0,9228 -0,4798 0,7087 -0,6758 0,3558 0,5270 0,8713 0,9602 0,0233 -0,2630 -0,3938 -0,3986

AUD 0,4908 1 0,5806 0,5804 -0,0103 0,5794 0,5053 -0,2433 0,7853 -0,3872 0,7265 0,7714 0,6299 0,6172 0,3275 -0,2753 0,0899 0,0366

CAD 0,7044 0,5806 1 0,2062 -0,1252 0,2546 0,6816 0,1294 0,6857 -0,1664 0,2847 0,7567 0,5042 0,6061 0,5003 0,2561 0,1914 0,1792

CHF 0,1606 0,5804 0,2062 1 0,5375 0,8032 0,3143 -0,1006 0,7318 -0,1102 0,7809 0,5956 0,4865 0,3202 0,4387 -0,0048 0,3378 0,1370

CZK -0,4226 -0,0103 -0,1252 0,5375 1 0,5029 -0,3225 0,4594 0,1199 0,5685 0,3178 0,1297 -0,2173 -0,3701 0,4157 0,5137 0,6338 0,4016

EUR 0,3315 0,5794 0,2546 0,8032 0,5029 1 0,3818 -0,2469 0,6787 -0,2398 0,8490 0,5098 0,5881 0,4784 0,1602 -0,1403 0,1236 0,0276

GBP 0,9228 0,5053 0,6816 0,3143 -0,3225 0,3818 1 -0,4388 0,7562 -0,5941 0,3775 0,6050 0,8412 0,9002 0,1516 -0,2080 -0,2551 -0,2747

ZAR -0,4798 -0,2433 0,1294 -0,1006 0,4594 -0,2469 -0,4388 1 -0,2436 0,8826 -0,3221 0,0841 -0,6618 -0,6263 0,5162 0,8815 0,8021 0,7329

SGD 0,7087 0,7853 0,6857 0,7318 0,1199 0,6787 0,7562 -0,2436 1 -0,4264 0,7425 0,8515 0,8269 0,7787 0,4838 -0,0658 0,1042 -0,0781

PLN -0,6758 -0,3872 -0,1664 -0,1102 0,5685 -0,2398 -0,5941 0,8826 -0,4264 1 -0,4138 -0,1102 -0,7957 -0,7904 0,3762 0,8025 0,7789 0,7144

NOK 0,3558 0,7265 0,2847 0,7809 0,3178 0,8490 0,3775 -0,3221 0,7425 -0,4138 1 0,5679 0,6507 0,5352 0,2066 -0,2642 0,0580 -0,1161

KRW 0,5270 0,7714 0,7567 0,5956 0,1297 0,5098 0,6050 0,0841 0,8515 -0,1102 0,5679 1 0,5201 0,5412 0,6681 0,1749 0,4197 0,2858

JPY 0,8713 0,6299 0,5042 0,4865 -0,2173 0,5881 0,8412 -0,6618 0,8269 -0,7957 0,6507 0,5201 1 0,9567 -0,0002 -0,4641 -0,4237 -0,4901

CNY 0,9602 0,6172 0,6061 0,3202 -0,3701 0,4784 0,9002 -0,6263 0,7787 -0,7904 0,5352 0,5412 0,9567 1 -0,0235 -0,4408 -0,4456 -0,4656

CPL 0,0233 0,3275 0,5003 0,4387 0,4157 0,1602 0,1516 0,5162 0,4838 0,3762 0,2066 0,6681 -0,0002 -0,0235 1 0,6241 0,7160 0,5449

INR -0,2630 -0,2753 0,2561 -0,0048 0,5137 -0,1403 -0,2080 0,8815 -0,0658 0,8025 -0,2642 0,1749 -0,4641 -0,4408 0,6241 1 0,7631 0,6071

BRL -0,3938 0,0899 0,1914 0,3378 0,6338 0,1236 -0,2551 0,8021 0,1042 0,7789 0,0580 0,4197 -0,4237 -0,4456 0,7160 0,7631 1 0,7755

RUB -0,3986 0,0366 0,1792 0,1370 0,4016 0,0276 -0,2747 0,7329 -0,0781 0,7144 -0,1161 0,2858 -0,4901 -0,4656 0,5449 0,6071 0,7755 1


67

8.3 Appendix 21-22 – Improvements, 2011 Q4

Appendix 21 – Improvements, 2011 Q4

Weight (w

n )Annual volatility (σ

n )w

n σn

USD

AUD

GBP

SGD

NO

KCPL

INR

BRLRU

B

USD

53%17%

9%U

SD1

0,35390,9140

0,6478-0,0060

0,76170,8266

0,2981-0,1872

AUD

28%13%

4%AU

D0,3539

10,3449

0,78880,6598

0,63370,2953

0,61350,3443

GBP

9%13%

1%G

BP0,9140

0,34491

0,66340,0182

0,75240,8133

0,3608-0,1361

SGD

-11%12%

-1%SG

D0,6478

0,78880,6634

10,6304

0,71810,4477

0,54270,1001

NO

K-6%

8%0%

NO

K-0,0060

0,65980,0182

0,63041

0,1709-0,1546

0,30890,1826

CPL14%

16%2%

CPL0,7617

0,63370,7524

0,71810,1709

10,7849

0,65210,1673

INR

-7%15%

-1%IN

R0,8266

0,29530,8133

0,4477-0,1546

0,78491

0,58150,1079

BRL8%

14%1%

BRL0,2981

0,61350,3608

0,54270,3089

0,65210,5815

10,6120

RUB

11%13%

2%RU

B-0,1872

0,3443-0,1361

0,10010,1826

0,16730,1079

0,61201

100%16%

Portfolio Variance2%

Std. Portfolio12%

USD

53%211971350,6

AUD

28%111868351,1

Black&Scholes

GBP

9%37046908,32

Strike Price396298806

D10,334758031

Call23173171,3

SGD

-11%-45204402,52

Spot Price396298806

D20,236247623

Put12182547,49

NO

K-6%

-22352734,92

volatility0,124606905

CPL14%

55519242,06

Rf0,045

INR

-7%-28571627,24

Time

0,625BRL

8%30708225,75

N(D1)

0,6255RU

B11%

45313492,9

N(D2)

0,5832100%

396298806

If calculated as 4 smaller baskets w

ith different T's

Black&Scholes

3 months

7 400 192,56

Strike Price396298806

D10,423439137

Call28568846,44

6 months

10 076 577,06

Spot Price396298806

D20,298832232

Put11130701,03

9 months

11 299 095,93


12 months

11 130 701,03

Rf0,045

TOTAL

39 906 566,58

Time

1

N(D1)

0,6628Total exposed

1585195224

N(D2)

0,6179Prem

ium %

0,025174544


68

Appendix 22 – Improvements, 2011 Q4

Weight (w

n )Annual volatility (σ

n )w

n σn

CADCHF

CZKEU

RZAR

PLNKRW

JPYCN

Y

CAD4%

17%1%

CAD1

0,0433-0,0184

0,34530,6438

0,17830,7587

0,57550,7940

CHF-62%

13%-8%

CHF0,0433

10,4757

0,3809-0,2537

-0,27330,3931

0,44920,2081

CZK6%

13%1%

CZK-0,0184

0,47571

0,8179-0,0474

0,31710,4060

0,34270,1522

EUR

5%12%

1%EU

R0,3453

0,38090,8179

10,2920

0,33490,6212

0,61230,5299

ZAR38%

8%3%

ZAR0,6438

-0,2537-0,0474

0,29201

0,67410,5357

0,08430,3240

PLN8%

16%1%

PLN0,1783

-0,27330,3171

0,33490,6741

10,3091

-0,2444-0,1065

KRW12%

15%2%

KRW0,7587

0,39310,4060

0,62120,5357

0,30911

0,65430,7110

JPY15%

14%2%

JPY0,5755

0,44920,3427

0,61230,0843

-0,24440,6543

10,8989

CNY

75%13%

10%CN

Y0,7940

0,20810,1522

0,52990,3240

-0,10650,7110

0,89891

100%12%

Portfolio Variance3%

Std. Portfolio16%

CAD4%

10998030,2

CHF-62%

-175772419

Black&Scholes

CZK6%

16061011,41

Strike Price281347179,4

D10,283973277

Call16451491,36

EUR

5%13073394,5

Spot Price281347179,4

D20,156175613

Put8648841,034

ZAR38%

105560751,6


PLN8%

23416407,06

Rf0,045

KRW12%

34373732,44

Time

0,625JPY

15%43561444,84

N(D1)

0,6255CN

Y75%

210074826,3

N(D2)

0,5832100%

281347179,4

If calculated as 4 smaller baskets w

ith different T's

Black&Scholes

3 months

7 442 128,95

Strike Price281347179,4

D10,35920094

Call24418307,04

6 months

9 316 776,59

Spot Price281347179,4

D20,197548261

Put12038322,67

9 months

11 210 756,47


12 months

12 038 322,67

Rf0,045

TOTAL

40 007 984,68

Time

1

N(D1)

0,6406Total exposed

1,13E+09

N(D2)

0,5793Prem

ium %

0,03555

Date post:	24-Mar-2022
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