Report prepared for International Financial Risk Institute

(IFRI) Roundtable, 29-30 September 2005

“Understanding and Managing Correlation Risk and

Liquidity Risk”

By

Viral V. Acharya1 and Stephen Schaefer2

First Draft: 19th September 2005

This Draft: 1st November 20053

1 Viral V. Acharya, Associate Professor of Finance, London Business School, and Research Affiliate of Center for Economic Policy Research (CEPR). Contact: London Business School, Regent’s Park, London NW1 4SA, Tel: +44(0)20 7262 5050, e-mail: vacharya@london.edu 2 Stephen Schaefer, Professor of Finance, London Business School. Contact: London Business School, Regent’s Park, London NW1 4SA, Tel: +44(0)207262 5050, e-mail: sschaefer@london.edu 3 We are grateful to members of the IFRI for their feedback and comments on earlier versions of this report. All errors remain our own.

Table of Contents

I. Executive Summary (Page 3)

II. Survey: What You Said (Page 9)

III. Correlation Risk (Page 14)

a. Tables and Figures (Page 39)

b. References (Page 50)

IV. Liquidity Risk and its Management for Banks and

Financial Institutions (Page 51)

a. Tables and Figures (Page 76 )

b. References (Page 86)

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I. Executive Summary This report focuses on the issues of correlation risk and liquidity risk, and their

management. Below, we summarize our robust conclusions regarding these two

seemingly different but most likely inter-connected dimensions of risk. Section II

presents a summary of survey questions on these topics answered by risk officers.

Section III discusses correlation risk and the difficulties of quantifying it. It also

touches upon the importance of long-run portfolio choices in risk measurement.

Section IV presents the analysis of liquidity risk and its management, and argues that

asset risk, funding liquidity risk, market liquidity risk, and correlation risk are highly

intertwined.

Robust Conclusions on Correlation Risk and Its

Management

1. While correlation between different asset classes changes over time, there

is little evidence so far that these changes are predictable to any

significant extent. The correlation between national equity markets and

between stocks and bonds has changed substantially over time. For equity

markets correlation appears to be more stable than volatility and it may be

worthwhile breaking down forecasts of covariance into volatility and

correlation components. Existing time series prediction models for correlation

are too imprecise to have much practical value. Structural models of

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correlation have the potential – perhaps not yet realised – to provide useful

intuition on the causes of correlation change.

2. The debate on “contagion” is important to risk managers because contagion

represents a more fundamental breakdown of risk assessment models than

“interdependence”. There are two main explanations for the apparent increase

in correlation between markets in times of crisis. The first is “contagion”, a

change in the structure of dependence and the second is “interdependence”,

the result of an increase in the volatility of common factors. Contagion means

a breakdown in existing risk models since, with contagion, some markets

acquire sensitivity to risk factors to which previously they had no exposure. In

other words, with contagion, the model changes. With interdependence the

structure remains the same but the volatility of common factors increases. The

existing literature fails to find support for contagion. If the volatility of

common factors increases in a crisis, linear hedges should still be effective.

3. Measuring the correlation of unusually large (“crisis”) returns is fraught

with statistical difficulties. Estimates of correlation that are based on “large”

observations are subject to significant bias. Moreover the direction of the bias

depends on whether the observations are large in absolute size or large in one

direction (positive or negative). In the first case and for variables that have a

joint normal distribution, the correlation of large changes is biased and high.

In the second case – again for normally distributed variables – the bias goes in

the opposite direction. Any investigation of “crisis” correlation needs to take

these biases carefully into account.

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4. Correlation is asymmetric in up and down markets although, once again,

there are statistical problems in assessing the extent of this asymmetry for

large changes. There is evidence from several markets that correlation is

higher correlation in down markets. Further research is emerging on this issue

but, if substantiated, asymmetry has important consequences for risk

assessment since the shape of the distribution of portfolio returns is affected.

5. The behaviour of correlation measures that are imputed from derivative

pricing models may be strongly influenced by limitations of the models

themselves. Great care needs to be taken not to over-interpret correlation

measures obtained by calibrating derivative models to prices. The process of

calibration results in even poor models fitting the data very well. Since most

parameters in derivative models, apart from volatility and correlation, are

typically given, any deficiencies in the model will show up in implied

volatilities and correlations. The Credit derivatives sector represents one area

whether this seems particularly likely to occur.

6. Long run estimates of risk are unlikely to be of useful if based on an

assumption of fixed portfolio positions. To assess risk in the long run,

banks need to think through how their portfolios are likely to change as

their financial position changes. This may be thought of as a different form

of “scenario analysis”. The dynamic character of portfolio policy has a strong

effect on the risks that an institution bears in the long run. Some recent work

in dynamic banking models suggests one approach to this problem.

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Robust Conclusions on Liquidity risk and its Management

1. Funding liquidity risk is primarily a concern during systemic shocks for those

banks and financial institutions that do not have access to deposit insurance or

alternate government support arrangements (which produce “flight to quality”

of deposits). Liquidity risk is a concern for most institutions during

idiosyncratic shocks when government support is unlikely and it is difficult

to isolate illiquidity from insolvency.

2. Liquidity shocks are generally preceded by asset shocks of some nature,

especially when they are market-wide in nature. Risk managers should

recognize this correlation while projecting their stress-test scenarios for

liquidity risk management.

3. Market liquidity and funding liquidity, though different concepts per se,

feed on each other and cause sudden drying up of liquidity when asset

shocks are large. Market liquidity risk is highly non-linear in asset risk: It

arises primarily when asset prices fall sufficiently to push intermediaries

sufficiently close to their funding constraints. Lower market liquidity, in turn,

further aggravates the funding position of intermediaries due to increase in

hair-cuts and margin requirements, as well as deterioration of collateral values.

4. Market liquidity risk, funding liquidity risk, and correlation risk, are thus

all inter-related, with their source generally lying in large asset shocks:

Asset prices exhibit two regimes: first, a normal regime in which prices reflect

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fundamentals and illiquidity is low, and second, an illiquidity regime in which

prices reflect market-wide liquidity (for example, arbitrage capital available

with intermediaries). In the normal regime, correlations across securities, as

implied by models that do not consider liquidity effects, correspond to

statistical correlation in underlying risks. In the illiquidity regime, implied

correlations capture the impact of liquidity on prices and need not correspond

to true underlying correlations.

5. Hedging of correlation risk during times of market-wide illiquidity is

likely to be misleading if based on delta-hedging (using the underlying)

from models that do not allow for liquidity effects. Since liquidity risk is

non-linear in asset risk, hedging should either be based on models that capture

this non-linear relationship (such models are few!), or based on hedging

liquidity risk directly. Correlation risk hedging thus itself exhibits two

regimes: normal regime when correlation risk is hedged using the underlying

risks, and illiquidity regime when it is hedged (at least partly) by managing

liquidity risk.

6. Capital is not necessarily liquidity during stress times unless capital is

employed to ensure short-term and price-insensitive liquidity buffers.

These buffers could be in the form of state-contingent liquidity options, as

issued by the Federal Reserve in the United States specifically to address the

Y2K problem, and in the form of standby lines of credit from other banks and

financial institutions, preferably those that will benefit from flight to quality

effects or government support. Next, buffers could also be arranged in the

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form of (relatively) state-incontingent high quality collateral, such as strong

OECD bonds, against which secured borrowing can be affected. State-

contingent liquidity arrangement is superior in stress times to state-

incontingent arrangements since a unit of capital employed for both raises

greater liquidity through state-contingent arrangements.

7. Stress scenarios of liquidity risk are perhaps a useful way of managing

this risk, given its high level of non-linearity in asset risk. The underlying

relationship with asset risk must however be kept in background, if not

directly modelled (as is currently the case). Finally, it is possible that this

form of risk management itself prevents free mobility of capital from a set of

financial intermediaries and markets they participate in, to other intermediaries

and markets, in itself causing liquidity risk to an extent.

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II. Survey: What You Said

A. Questions

The questions asked of the risk officers and members of IFRI were as follows.

1. Correlation: Do you consider changes in the degree of correlation between

markets as a major risk management issue? If so, (i) do you consider this to be

a problem only in times of market stress or do you think that there is a trend

towards higher correlation as markets become more integrated? Has your firm

carried out formal analysis in this area? If so, with what results? What changes

to its risk management procedures has your firm adopted (or is planning to

adopt) to address this problem?

2. Scope of Risk Management: Does your firm include in your formal risk

management processes the risk that derives from changes in the value of major

intangible assets and liabilities? Typical examples here might include, e.g., the

value of an M&A operation, a credit card division, pension liabilities, an

undrawn line of credit etc. If so, what challenges have you faced in

implementing this approach? If not, why have you decided not to extend the

scope of risk management in this way?

3. Time Horizon in Risk Assessment. Over what horizons do you assess the risk

of your firm? When you make these assessments over longer periods, do you

take into account the relation between the amount of risk that your firm takes

between the assessment date and the horizon and changes in the level of

capital over that time? If you do take this into account, how do you attempt to

capture the relation between changes in the level of risk taken by the firm up

to the horizon and changes in the level of capital?

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4. Liquidity Risk.

Does your firm consider changes in funding liquidity to be a major risk factor?

If so, how would you characterise the most important aspects of funding

liquidity risk? Do you have a view on the mechanism that creates liquidity

crises? Do you think that financial regulation, in particular, capital adequacy

regulation, makes liquidity crises more or less likely?

5. Liquidity Management. Does your firm’s risk assessment system take liquidity

risk into account explicitly and, if so, how? In particular, is liquidity risk

accounted for at the level of individual contracts, a trading desk or at the level

of the enterprise? Does your firm have a policy for the management of

liquidity risk? If so, please describe both the policy and how the management

of liquidity is co-ordinated across the firm?

6. Static versus Dynamic Hedges. In those cases where managing the risk of a

position requires dynamic adjustment over time (probably the majority of

cases) how important are the problems created by: (i) hedging costs, (ii) model

risk, and (iii) changes in liquidity. If your answer depends on the context,

please give examples.

B. Responses

We received around ten sets of answers to these questions. We summarize

below what we considered as the most salient responses to these questions. Since the

rest of the report focuses on correlation risk, liquidity risk, and their management, we

have restricted our summary of the survey to these topics.

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1. Correlation: There is overall consensus that changes in correlation are a matter of

concern for risk management. Several features of correlation risk were mentioned:

• Increasing globalisation of markets has produced a trend in correlation (increasing

over time across markets and products), creating a challenge for risk management

of newer products such as Collateralized Debt Obligations (CDOs).

• Correlation increases reduce benefits of diversification.

• Correlations seem to be higher in times of market stress. At least some responses

mention the cause for this as the significant withdrawal of capital and liquidity

from specific capital markets.

2. Correlation risk management: There is mixed feedback on whether there is

institutional response to correlation changes:

• Most responses mentioned the use of correlations (high as well as low) from stress

periods (market crash, flight to quality events) in stress tests, and some mentioned

deploying this for economic capital calculations as well. The stress tests are

primarily employed for the trading book correlations, but some also mention the

banking (credit) book correlations.

• There is mention in some cases of the risk of “over-modelling” correlation,

especially the fact that statistical correlations may be intrinsically different from

implied model-based correlations: the latter may simply reflect a model’s

calibration bias when it does not account for shifts in statistical correlations. The

lack of clarity on what is the real correlation risk was cited by some as the reason

for not engaging in an elaborate institutional response to it.

• It is recognized that an important problem in managing correlation risk is one of

deciding relevant time horizon for assessing impact of correlation change. Though

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one year is typically the risk horizon, this is problematic for positions that evolve

dynamically and at different paces (e.g., new and growing credit portfolios).

• There were also some banks and institutions which said that correlation changes

were not a major risk-management issue because they relate mainly to market

risks and the latter form only small part of overall risk (in particular, market risk is

small relative to the total size of credit risk).

3. Liquidity risk: There is consensus that funding liquidity-risk is important but

there are opposite views on when it matters:

• View # 1: only in times of market-wide (country or global) crisis of confidence

• View # 2: only at times of crisis affecting own institution

• View #3: both market-wide as well as idiosyncratic crisis, especially if the

institution is in a banking sector with very few players.

Most institutions seem to consider that in times of crisis, capital and liquidity are not

the same in the sense of ability to access short-term funding. Also, liquidity risk was

mentioned to be a bigger concern for institutions relying more on short-term and

capital-market funding.

The responses did not think financial regulations (e.g., capital adequacy rules)

constitute or contribute to major sources of liquidity risk, but did point out that lender-

of-last-resort activities could restore confidence among consumers and market

investors during times of stress.

4. Management of liquidity risk: A distinction was pointed out between the

management of:

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• Impact of changes in market liquidity in traded instruments (“market liquidity”),

and

• Access to short-term funding (“funding liquidity”)

The management of market liquidity is generally performed at the level of

individual trading desks, whereas the management of funding liquidity risk is

performed at the firm level.

Like correlation risk, management of funding liquidity risk also features stress

scenarios and contingency plans.

• The approach to managing funding liquidity appears in almost all cases to be

carried out using projections of inflows / outflows and net liquidity needs. These

methods – as we understand them – do not seem to address in a modelled or

statistical fashion the uncertainty in future liquidity needs / access.

Finally, both internal and external funding of liquidity needs is considered important,

with the following important differences:

• The issue about the source of funding is not just about availability but also about

price. In particular, cash and bilateral commitments for secured borrowing are

generally price insensitive, and thus, preferred to unsecured wholesale funding at

time of liquidity needs.

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III. Correlation Risk. In their questionnaire responses, IFRI members raise a number of important

issues connected with correlation. Changes in correlation were seen as difficult to

predict while increasing globalisation has resulted in a secular trend towards

higher correlation. Correlation was higher at times of market stress and the

correlation measures in some derivatives models (e.g., CDO tranches) were not

necessarily closely connected with statistical measures of the correlation of the

underlying assets. In stress tests most tests suggested using high and low values

of correlation to represent periods of market stress.

The views that these responses represent raise questions that are closely

connected with the burgeoning academic literature on correlation that has

developed over the past 10-15 years. While the literature provides a definitive

answer in very few cases, it is nonetheless helpful in clarifying some issues,

providing empirical evidence on others and highlighting the statistical problems

that arise in attempting to identify differences between correlation in normal

times and in crises.

The objective in this section of the paper is to draw out the implications of this

work for dealing with correlation in a risk management setting.

Much of the literature deals with one of four topics. First, there is substantial

evidence that the correlation between stock returns in different countries, and

between stocks and bonds is quite different in different periods. Thus several

authors have attempted to explain how correlation changes over time. For

example, using daily data, Li (2002) shows that the correlation between bonds

and stocks in the US fell from around 0.5 in the late 1990’s to around zero by

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2001/2002. (See Figure III.1) Rolling estimates using monthly data exhibit a

similar pattern (see Figure III.2 and Figure III.3 below) and other countries

exhibit comparable, if slightly less dramatic changes. Other papers attempt to

predict these changes or explain them using valuation models.

The second topic centres on the claim that the co-movement of prices in different

sectors or markets often appears to become more pronounced in financial crises.

There is, however, considerable debate about the explanation for this behaviour

and, indeed, whether the phenomenon is real or merely a statistical artefact.

Whether or not correlation really is different in a crisis and what gives rise to this

change are important questions with significant implications for risk

management.

The first explanation is known as “contagion”, where, particularly in crises,

shocks to prices in one market are transmitted to other markets in a way that does

not occur in normal times. The propagation of these shocks continues and

intensifies the crisis. The main alternative explanation is that different markets

may simply depend on a given number of underlying common variables and the

increase in the apparent synchronicity of movement in several markets is not due

to some change in the structure of dependence but is simply the result of larger

shocks to these common variables.

A third point of view is that the apparent increase in correlation is a statistical

artefact. In other words, according to this view, correlation is constant and the

higher correlation that is measured is the result of the way the sample of data

points – e.g., “returns in a crisis” – is selected. Even if higher correlation is not

explained entirely in this way, it raises important issues about the way statistical

tests of correlation differences are conducted.

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The third topic concerns the fine structure of correlation and, in particular,

“asymmetry”, i.e., whether correlation is different in, for example, bull versus

bear markets and in periods of growth versus recessions. A number of studies

have investigated this question and find, inter-alia, that correlation does indeed

tend to increase in bear markets and decrease in bull markets. This effect appears

both within markets (e.g., within the US equity market) and across markets (e.g.,

between the equity markets of different countries).

The fourth issue has to do with measures of correlation that are related to

derivative prices. The issue here is that the correlation parameter in a derivatives

model (e.g., for the prices pf CDO tranches) may be only loosely connected with

statistical measures. We discuss this issue and its relation to the other dimensions

of correlation towards the end of this section.

We have referred above to the possibility that some changes in correlation may

be simply statistical artefacts. More broadly, it is often quite difficult to measure

correlation reliably and, for this reason, it is useful to take a long run perspective

rather than trying to focus on what has happened, or appears to have happened,

over the past few days or weeks. Thus academic studies that extend over long

periods, even if these do not include the very recent past, are nonetheless

valuable.

Evolution of Correlation over time

We begin with the work that is devoted to measuring, understanding and even

predicting correlation. This effort has been directed both to the correlation of

16

assets within a country, e.g., between equities (within markets) and between

stocks and bonds (between asset classes) and across countries.

Among the earliest studies is by Kaplanis (1988) who studies international equity

return indices and finds that correlations have somewhat greater intertemporal

stability than covariances4. She also finds evidence of mean reversion in

correlations, i.e., a tendency for correlations to return over time to some long run

average level. Longin and Solnik (1995) also investigate the stability of

correlation in international equity returns and confirm Kaplanis’s findings that

correlations, while not constant, were more stable than covariances. Figure III.2

below shows their estimates of the average correlation of US equity returns with

those of seven other US markets. This falls from an early peak of around 0.55 in

the mid-1960s to a low point of around 0.3 in the mid-1960s and then rises to

around 0.7 in 1990.

The result that correlations display somewhat greater stability than covariances

represents some modest good news. Risk measures ultimately depend on

covariances rather than correlations alone and the result says that at least some of

the changes in covariances are the result of changes volatility rather than

correlation. It suggests that, it may well be worthwhile decomposing covariance

into volatility and correlation and predicting these separately with correlation

exhibiting less short run variation than correlation.

The study of international equity returns by Erb, Harvey and Viskanta (1994)

[EHV] investigates two aspects of the time pattern of correlation. The first is the

4 There is, of course, a vast literature on equity “betas” that is relevant here. Because a conventional equity beta is simply the correlation between the return on the equity in question and the return on the market multiplied by the ratio of the two standard deviations, studies of beta stability over time are implicitly studies of correlation.

17

connection between correlation and the business cycle.5 Here they find that the

correlation between equity returns in the US and other G-7 countries is highest

when both countries are contracting. They also find that, even within the US, the

equity-bond correlation is higher in downturns. Second, they investigate

predictability using a number of predictor variables that include lagged

correlation, lagged domestic and foreign equity returns and the domestic and

foreign interest rate term spread. The last of these variables is included because,

as Campbell (1993) shows, the term spread has significant predictive power for

economic growth.

EHV find that lagged correlation has significant explanatory power, i.e., that,

consistent with Kaplanis (1988), there is evidence of mean reversion in

correlation. They also find that the lagged domestic (US) equity return is

significant and enters with a negative sign for short horizons and a positive sign

for long horizons.

Figure III.3 below, reproduced from EHV, shows the actual and fitted values of

correlation between US equities and those of the other G-7 countries. These

calculations use data up to December 1993 and the chart also shows out-of-

sample predictions of correlations (the dotted lines) for the period up to 1998. In

most cases, excepting Japan, the correlation in December 1993 – the date the

forecasts are made – was relatively high compared with previous 15 years and the

effect of mean reversion is therefore to produce forecasts of declining correlation

for the following 5 years.

Two points should be noted here. First, as Kaplanis, EHV and others have found,

there is some mean reversion is correlations and this should be taken into account

5 Asymmetry in correlation is discussed more extensively below.

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in making predictions of future correlation. The second is a caution. Whenever

we estimate correlation from actual data there will be some imprecision that

comes from sampling error, i.e., from the fact that we do not have an unlimited

amount of data. Thus a high estimate of correlation is, on average likely to

contain a positive estimation error and a low value a negative error. Since average

errors are zero, there will be a natural tendency for high estimates of correlation

to be followed by lower values and low estimates by higher values. The fact that

correlation – even if measured with error – is a number that always lies between

minus one will exacerbate this pattern. Thus the presence of sampling error alone

will tend to give the appearance of mean reversion in correlation.

The model that EHV use to predict changes in correlation over time is essentially

ad-hoc: apart from the lagged value of correlation, their choice of predictor

variables, such as the term spread, has no theoretical basis. More recently, a

number of authors have attempted to address the problem of predicting

correlation using a valuation model of the assets in question. The object of this

work is to link the correlation between returns on different assets, say, to the

correlation between the fundamental factors that determine their prices.

A recent example of such an attempt is Li (2002) who uses a model of returns on

equities and bonds, based on macroeconomic variables, to estimate the theoretical

correlation between bonds and stocks. The macro-variables he uses are: the real

interest rate, expected inflation and unexpected inflation. According to Li,

uncertainty about long-term expected inflation plays a key role and increases in

the uncertainty about long-term expected inflation increases the co movement

between bonds and stocks. He goes on:

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The effect of unexpected inflation is ambiguous and depends on how dividends and the real interest rate respond to unexpected inflation shocks. Empirical analysis generally confirms these predictions. Among the macroeconomic factors considered here, the uncertainty about long-term expected inflation plays a dominant role in affecting the major trends of how stock and bond returns co-move. The effect of unexpected inflation and the real interest rate is significant to a lesser degree. (Li (2002), p. 27).

A potential problem with Li’s analysis is that, while the model is internally

consistent, the limited set of (macro) variables he chooses may simply not do a

good job of explaining the prices of stocks and bonds. In this case we cannot

expect the model to do a good job of explaining their correlation. A second

problem, one that applies not only to Li’s work but other similar analyses (e.g.,

Shiller and Beltratti (1992) and Addona and Kind (2005)), is that the exogenous

shocks to the model are all homoscedastic and this means that all (conditional)

moments, including the correlation, are constant. Using a model in which

correlation is constant to explain changes in correlation is clearly not ideal. On

the other hand models with heteroscedastic shocks are intractable with closed-

form pricing results generally unavailable and without a closed-form solution,

Li’s approach is very difficult to implement.

With homoscedastic models, however, it is possible to investigate changes in

correlation only by changing the parameters; these, of course, are supposed to be

fixed. Thus Li investigates the effect of changing the volatility of the macro-

economic inputs to his model and finds that the volatility of long-term expected

inflation has the strongest effect. However, this change (in the volatility of long-

term expected inflation) must be interpreted as a “one off” surprise event: the

model itself assumes that such changes will not occur in the future and so prices

will also not reflect the possibility of such a change.

Despite these difficulties, the idea of explaining correlation in a structural model

of the type employed by Li is interesting because, although it may not offer great

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accuracy, in contrast to ad hoc forecasting models, it at least provides some

insight into the main drivers of changes in correlation.

Crises and Correlation

A common feature of many of the financial crises of the last few decades is that

problems that appear in one market appear frequently to spread, or least to

manifest themselves in other markets. Examples here would include the stock

market crash of October 1987 and the 1997 Asian crisis. Indeed, these events are

also often described in terms of correlation and it is claimed that the correlation

between markets and between assets is ‘higher in a crisis’.

In the next section we discuss two explanations of this phenomenon. The first is

“contagion” – defined in more detail below – that captures the idea that the

structure of the relation between markets is different in a crisis. The alternative

view is “interdependence”: here the structure does not change but that the world

is, perhaps briefly, riskier. The distinction between these views and the

implications for risk management are described below.

First, however, it is important to deal with some statistical issues. In financial

markets we often identify a crisis by the size of price movements. This would

certainly be true of, say, the 1987 stock market crash. However, if we calculate

the correlation between the returns in two markets based on a sample that chosen

on the basis of the size of the returns, then it turns out that the estimate of

correlation is biased.

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To see why, suppose we generate two zero mean random variables with a joint

normal distribution and a correlation coefficient of 0.5. There are two cases we

need to deal with and they lead to biases in the opposite direction.

First, suppose that, we choose only those observations where the absolute size of

one of these variables (variable 1, for example) exceeds a given number of

standard deviations (the “cut-off”). What is the (now conditional) correlation

between these ‘large’ observations on variable 1 and the corresponding

observations on variable 2?

Figure III.5 (Ronn, Sayrak and Tompaidis (2001)) gives the answer and shows

that, when the underlying ‘true’ correlation is positive, the conditional correlation

increases as the cut-off increases. Figure III.6 shows how the bias varies with the

sign and size of the underlying correlation when the conditional correlation is

computed using the largest 50% of the observations on variable 1. What this

result shows is that, if markets have an underlying correlation that is positive,

estimates of the correlation calculated using only those periods when one market

experiences large changes, will be biased and high.

Figure III.7 and Figure III.8 provide some insight into this result. Figure III.7

shows a scatter plot of two random variables, each with zero mean and unit

standard deviation. The variables are simulated drawings from a joint normal

distribution with a constant correlation of 0.5. The figure shows 10,000 points

and the sample correlation is 0.51. Figure III.8 shows a sample from the data in

Figure III.7 chosen according to whether the absolute value of the first variable

(x_1) is greater than two. Essentially, this is the same as Figure III.7 but with the

data in centre of the scatter plot “cut out”. The distribution of x_1 is, of course,

now not normal and the correlation in this case is much higher (0.81).

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The reason for the high correlation, however, has nothing to do with a close

association between pairs of points. What the sampling procedure has done, as is

clear from the Figure, is two produce a sample of two groups of observations. In

one, where the majority of points lie in the first quadrant, both variables have a

positive mean. In the other, where most points are in the third quadrant, both

means are negative. The high correlation in this case comes from the difference in

the mean values of these two sub-samples and this difference is created entirely

by the way the sample is constructed.

If the underlying correlation were negative the sub-samples would lie in the

second and fourth quadrants and the correlation would be strongly negative. In

neither case, however, is the measured correlation a good measure of the

correlation that generates the data: each pair of points – the large returns as well

as the small ones – is drawn from the same joint distribution where the

correlation is a constant.

The second case is where the sign of the returns is taken into account, i.e., where

we look at a sample of either large positive returns or large negative returns.

Where we make the choice based on the value of one of the variables the data

will be exactly as in one of the two groups in Figure III.8. In this se the bias is

actually negative and, if the underlying data is jointly normal, the correlation

within one of these groups goes to zero. This result is critical in understanding the

important results obtained by Longin and Solnik (2001) on the difference

between the correlation of large negative versus large positive returns. We return

to this point in the section on asymmetric correlation below.

These results are important because both international economists and risk

managers would like to know whether correlation really is different in crisis.

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What the results in Figure III.5 and Figure III.6 show is that, when we define a

crisis in terms of the size of returns, we must be careful to adjust for the bias that

will arise when we calculate correlation for just these large changes.

Contagion

The term economists have coined to describe crisis interconnectedness is

“contagion”. There is no universally accepted precise definition but a well known

paper by Forbes and Rigobon (2002 [FB] defines contagion as

… a significant increase in cross-market linkages after a shock to one country (or group of countries). (Forbes and Rigobon (2002, p2223)).

The term “cross-market linkages” refers to the idea that, after a “crisis” shock to

one country (or group of countries), other countries acquire sensitivity to this

shock that is not present in non-crisis periods. In other words, under FB’s

definition, the structure of dependence is different in a crisis.

The distinction between contagion and the case where volatility simply increases

is illustrated in the following simple model of the linkages between three

markets6. Suppose the returns on three asset markets during a non-crisis period

are defined as:

. (0.1) 1 2 3{ , , }x x x

All returns are assumed to have zero means. The returns could be on currencies,

national equity markets etc. The following simple index model is used to

summarise the dynamics of the three processes during a non-crisis period

(“tranquillity”):

6 This discussion is adapted from Dungey, Fry, González-Hermosillo and Martin (2003).

24

, 1, 2,3.it i t i i tx w u iλ δ= + = (0.2)

Here, the variable wt represents common shocks that impact each of the three

asset returns with loadings λi. In general we may think of wt as representing

market fundamentals, e.g., a “world factor”, that determines the average level of

asset returns across international markets during “normal”, that is, tranquil, times.

The terms uit in equation (0.2) are three idiosyncratic factors that are unique to a

specific asset market; i.e., the u’s for different countries are not correlated. The

contribution of the idiosyncratic shocks to the volatility of asset markets is

determined by the loadings δi.

In this set-up the three markets are interdependent as a result of their common

dependence on the factor, wt. On the other hand there is no spillover from the

idiosyncratic shock in one market, uit, to another.

Contagion occurs when an idiosyncratic shock in one market affects the return in

another market; in other words when the idiosyncratic shock is no longer

idiosyncratic. For example, if the idiosyncratic shock in market one is transmitted

to market two, the structure of the factor model changes to:

1 1 1 1,

2 2 2 2, 1,

3 3 3 3,

t t t

t t t

t t t

x w u

tx w u ux w u

λ δ

λ δ γ

λ δ

= +

= + +

= +

(0.3)

Tests for contagion amount to testing for the significance of the parameter γ (> 0)

that measures the impact on market two of market one’s idiosyncratic shock. If γ

25

is non-zero in crisis times then this increases the covariance between returns in

markets 1 and 2 from (λ1 λ2) to (λ1 λ2+δ1 γ)7.

The presence of contagion is, however, not necessary to give rise to an increase in

covariance during a “crisis”. The reason is that crises are typically accompanied,

and in some cases defined by in an increase in volatility. This in turn may

increase correlation without a change in the structure of dependence – the

appearance of a non-zero γ in equation (0.3) – that is the key characteristic of

contagion.

Without contagion equation (0.3) becomes:

1 1 1 1,

2 2 2 2,

3 3 3 3,

t t t

t t t

t t t

x w ux w ux w u

λ δ

λ δ

λ δ

= +

= +

= +

(0.4)

The correlation between, say, markets one and two is:

1, 2, 1 22 2 2 2

1, 2, 1 1 2

1 22 2 2 2

1 1 2 2

cov( , ) var( )( ) ( ) var( ) var( )

/ var( ) / var( )

t t t

t t t t

t t

x x wx x w w

w w

λ λσ σ λ δ λ δ

λ λλ δ λ δ

=+ +

=+ +

2

(0.5)

If a crisis is characterised by an increase in the volatility of the common shock,

wt, then, as this increases relative to the volatility of the idiosyncratic shock, ui,

the correlation also increases.

It is important to be clear that in both these cases– either as a result of contagion

or from an increase in the volatility of wt – the increase in correlation is “real” as

distinct from a statistical artefact of the type illustrated in, for example, Figure

III.7 and Figure III.8.

7 For simplicity the shocks wt and ui, t are assumed to be iid with unit variance.

26

In an important article Forbes and Rigobon (2002) [FB] point out that, because of

the potential for an increase in the volatility of the common shock to increase

correlation, simply observing an increase in correlation in a crisis does not

necessarily imply contagion (in the sense of a non-zero value of γ in equation

(0.3)). Correlation could simply have increased because the volatility of the

common shock, wt, in the crisis has increased. FB analyse the cross-country

equity correlation in the 1997 Asian crisis, the 1994 Mexican Peso and the 1987

US stock market crash and find that, while the correlation between countries

increases in a crisis, there is little evidence of contagion8. Rather, they conclude

that correlation increases in these cases because the volatility of the common

shock is higher not because the structure of dependence changes.

From the perspective of international economists and international securities

markets regulators, the distinction between contagion and interdependence is

important. While the IMF or IOSCO may have little hope of influencing the

overall level of volatility, a change in the structure of dependence in a crisis it

may be due to some activity on the part of market participants – e.g., the actions

of foreign investors or hedge funds etc. – that regulators might be able to

influence. Thus the importance to regulators of establishing whether contagion

plays a role in financial crises is clear.

To banks and other institutions, however, understanding precisely why

correlation increases in a crisis may be somewhat less important. On one hand, in

both cases portfolio risk actually increases and the benefits of diversification

across markets diminish. On the other, the strategy for reducing risk is different

8 To carry out these tests Forbes and Rigobon adjust for the statistical biases in correlation that are described above.

27

in the two cases. Without contagion then the sensitivity of markets to common

shocks is unchanged – although their volatility has increased – and so, although

an institution may wish to reduce its positions as a result of the increased risk,

their risk models remain valid except for a change in volatility. With contagion,

however, the risk model itself is no longer correct because risk factors appear for

some markets (e.g., market two in equation (0.3)) where previously they were

absent. Thus the contagion debate, mainly focussed on policy issues in the

literature, is also important to risk managers.

Asymmetric Correlation

Are financial risks the same in downturns and upturns? This is a question that has

attracted attention over many years and, for example, there is substantial evidence

that equity volatility is higher in downturns. One possible explanation is the so-

called leverage effect: a decline in a firm’s equity price increases its leverage and,

therefore, its equity volatility. Alternatively, higher volatility may increase the

expected return and thus lead to a fall in prices.

More recently, interest in asymmetric risk has extended from volatility to

correlation where, for a wide range of assets, there is a well-documented

tendency for correlation to be larger on the downside than the upside. The

possible existence of asymmetric correlation is important and would have

implications for, not only risk measurement, but also the effectiveness of hedging

and the benefits of diversification.

Ang and Chen (2002) study the correlations between stock portfolios and the US

market and find strongly asymmetric correlations. Longin and Solnik (2001)

28

[LS], in an important study of international equity returns, calculate the

correlation between pairs of national equity markets for returns that exceed a

given threshold level in both markets (“exceedances”). They also calculate the

theoretical correlation for these returns under a joint normal distribution. Figure

III.9 shows their results for the US and UK markets. The (roughly symmetric)

dotted line shows the theoretical correlation for returns that exceed the threshold

level given on the horizontal axis. Notice that these correlations decline as the

(absolute) level of the exceedance threshold increases. In other words, under a

bivariate normal distribution the correlation calculated from only those

observations where both variables exceed a given threshold level, declines as the

size of the threshold increases.

In Figure III.8 – described earlier – the points selected are those for which the

absolute size of x_1 exceeds 2, i.e., a sample that consists of both large positive

observations and large negative observations. LS study samples that consist of

large positive observations or large negative observations. For example, Figure

III 10 shows the sample for large positive returns derived from the simulated data

in Figure III.8. The feature of the data that produced large correlations in Figure

III.8 – the difference in means for the two subsets created by the selection

procedure – is now absent and the correlation for this particular simulation is only

0.21 (vs. 0.81 previously).

The dotted lines in Figure III.9 show the conditional correlation, calculated by

LS, for each level of exceedance: this is the relevant benchmark against which

empirical estimates of conditional correlation should be compared. Since the

bivariate normal distribution is symmetric, the benchmark conditional

correlations are also symmetric in the threshold exceedances.

29

The results they obtain are therefore striking. The solid line in Figure III.9 shows

the empirical estimates of correlation for cases where, for negative exceedances,

the value of both US and UK returns is more negative than the threshold and, for

positive exceedances, is more positive than the threshold. In contrast to the

benchmark values – which are symmetric – the empirical estimates of correlation

are highly asymmetric, with the correlation for negative exceedances much larger

than the benchmark. For positive exceedances the correlations are broadly in line

with the benchmarks. Results for US-Germany, US-Japan and US-France are

very similar.

In assessing the practical importance, and indeed reliability of these results, it

should be recognised that, for large exceedances, the amount of data may be very

small. Table III.I shows calculations of correlation based on LS’s analysis. The

data used are monthly returns on the S&P 500 and the FT All-Share Index for the

dates studied by LS, i.e., from 01/1959 to December 1996, a total of 455 months9.

For each threshold value the table shows, the number of observations where

returns in both markets exceed the threshold (i.e., fall below it for negative

thresholds and above it for positive thresholds), the corresponding conventional

correlation and an estimate of the standard error of the conventional correlation.

For example, the first row of the table shows the case where monthly returns in

both the US and UK equity markets that are lower than 10%. Here, in the roughly

35 years covered by the data, we see that there are just three months where

returns in both markets are lower than 10%. The correlation in this case is just

below one (1.00 to two decimal places) but a correlation computed from three

points is meaningless. LS use a more sophisticated approach based on extreme

30

value theory and their estimate of correlation in this case is 0.68. On the other

hand, even the most sophisticated statistical tools cannot make up for a lack of

data

The correlation estimates in Error! Reference source not found. show roughly

the same asymmetric pattern of correlation that LS find: high correlation for

negative returns and low correlation for positive returns. However, in interpreting

these results we must remember that the data for minus 5% for example, also

includes the data for minus 10%. In other words the estimates of correlation on

each side of zero are correlated and, as result, there is a danger that we over-

interpret the relation between results for similar thresholds.

Longin and Solnik remains an important study of the relation between correlation

in up and down markets. However, perhaps what it illustrates most clearly is,

once again, the difficulty in reaching reliable conclusions about events that occur

only very infrequently.

Correlation and Derivatives Models

To this point most of our discussion has focussed on correlation as a measure of

the co-movement of asset prices or rates that are actually observed. However,

another aspect of correlation, and one of great concern to practitioners at certain

times is the risk that stems from movements in correlation as a parameter in a

derivative pricing model.

Many derivatives depend on the correlation between two or more variables. One

example is the well-known “quanto” contract. For example, a quanto forward

9 Longin and Solnik use other equity indices but this is unlikely to influence the results.

31

contract on the DAX pays a number of US dollars equal to the difference between

the level of the DAX (a Euro-denominated price) and the (Euro-denominated)

strike price. The value of this contract will depend on the correlation between the

DAX (in Euros) and the Euro-US$ FX rate.

A second example is the relation between the implied volatility on options on

individual stocks and the implied volatility on a stock index. As the average

correlation between individual stocks changes, the relation between the index

ISD and individual stock ISDs will also change.

A third and very important example is the default correlation parameter in the

valuation of certain credit derivates. As the correlation between the default of the

different credits underlying a CDO, for example, changes, so does the relative

pricing of the different CDO tranches.

In models used to value such contracts, the meaning of correlation is precisely the

same as in our earlier discussion. In another sense, however, it is not the same

and this is because changes in the correlation parameter in a derivatives pricing

model may easily result from imperfections in the model rather than a change in

the actual correlation between the variables concerned.

An analogy with a simpler and more familiar problem may be helpful. It is well

known that option implied volatility (ISD) in many, if not most markets is

inconsistent with the Black-Scholes model. In particular, we often observe

different ISDs for different strike prices (the “smile”) while the Black-Scholes

model predicts that the ISD should be the same for all strikes.

There is no shortage of explanations for the smile but to this point, no one

explanation is commonly accepted. One possibility is that the smile is indeed

32

connected to volatility and reflects differences between the actual distribution of

the price of the underlying asset and the distribution assumed in the Black-

Scholes model. In this case, changes in the smile would indeed reflect changes in

the anticipated volatility of the price of the underlying asset.

However, it is also possible that the ISD smile has little to do with volatility. The

ISD is calculated as the number that needs to be pt into an option pricing model

(say, Black-Scholes) to match the market price. In this sense it is similar to the

residual in a regression: it takes up the slack between the model and the data.

Since the other parameters of the model are typically determined exogenously,

any deviation between the Black-Scholes and market prices will show up as a

deviation between actual volatility and the ISD. What the smile tells us is that, all

else equal, options with a low exercise price typically have a (relatively) high

price and, therefore, ISD. For example, there may be a strong demand for deep

out of-the-money puts by investors who are concerned about a crash and banks,

in their turn, may charge a price premium for supplying these options (because

they cannot easily hedge them). In this case ISDs on deep out of-the-money puts

will be high but not as a result of a change in the volatility of the underlying

asset.

A similar effect may well affect implied correlation measures. For example, the

value of collateralised debt obligations will vary strongly with the likelihood that,

in the event of default of one entity, others also default. Different models

parameterise this “default correlation” in different ways (e.g., via the correlation

of firm values in structural models or via copulas). In practice, however – just as

in the case of option ISDs – the correlation parameter or parameters will be

33

backed out of prices and any deficiencies in the model will show up as deviations

between implied and “objective” measures of correlation.

These problems will also be more significant in markets that are relatively illiquid

where prices may deviate from fundamental values as a result of, for example,

imbalances in supply and demand. Once again, because the models are invariably

calibrated to actual prices, any idiosyncrasies in pricing will compound the effect

of model inadequacy to produce anomalous behaviour in correlation.

Thus there is an important difference between analyses of, on one hand, changing

correlation in data such as equity and bond returns and, on the other, changing

implied correlation in, say, models of CDO valuation. The former may be beset

with statistical pitfalls, as we have seen, but at least we are able to observe the

relevant data. With implied volatility and implied correlation, what we observe is

likely to be only partly related to the volatility or correlation of interest. The

remainder is a measure of the imperfection of the model. Distinguishing between

the two is a challenging task.

Long Term Risk Assessment

A major shortcoming of most, if not all practical risk assessment systems is that

the portfolio position is invariably assumed to remain fixed over time. In other

words, it is assumed that at each future date up to a given horizon, the risk of the

portfolio is generated by a portfolio position that is the same as the position

today.

For portfolios that naturally have a very horizon, e.g., some arbitrage positions,

such an assumption may be adequate. In some other cases there may be reasons

34

that make it impossible to change a position and so, once again, the assumption of

an unchanged portfolio may be adequate. In the great majority of cases, however,

unless the horizon dates refers to the very short term, assuming that the portfolio

position does not change is a major distortion of reality.

For many financial institutions – and their regulators – longer-term measures of

risk would be highly desirable. In contrast, an assumption of fixed portfolio

positions over long horizons robs such calculations of much of their value.

To make progress some way must be found to model an institution’s portfolio

behaviour over time. This problem may seem highly intractable and indeed, to the

extent that an institution’s portfolio decisions are opportunistic, the problem may

indeed be intractable. However, not all portfolio decisions are opportunistic and

recent work in the banking area suggests a possible way forward.

A Model of Bank Portfolio Behaviour

In the analysis of bank capital adequacy rules, the calculation of the probability of

failure, or the cost of providing deposit insurance is similarly compromised by

the assumption of a fixed portfolio position. Nonetheless, early models assumed

not only that the bank’s portfolio remained fixed but also that the bank behaved

in a myopic manner, in other words, planning its portfolio as it expected to

survive for just one period. More recent models take into account that the bank

will likely survive for several periods and relax both the myopia and the fixed

portfolio assumptions.

In Pelizzon and Schaefer (2004) [LS], a bank’s dynamic portfolio policy reflects

two conflicting incentives and, over time, the consequences of managing its

35

portfolio dynamically – in a way that reflects these incentives – has a significant

impact on its risk. The first of these incentives is that banks try to exploit deposit

insurance. In effect the bank has a put option on the deposit insurance fund and

maximises the value of this put by increasing the risk of its portfolio. The second

incentive arises when the bank has a franchise value that it (i.e., its shareholders)

will lose if the bank fails. This second incentive induces the bank to moderate its

risk so as to reduce the likelihood of losing its franchise value.

Overall the bank’s optimal portfolio policy in PS is “U”-shaped and is illustrated

in the left hand panel of Figure III.11. This shows the fraction of the portfolio in

the risky asset (w) as a function of the ratio of the asset value to deposits, A/D

(i.e., one plus the capital ratio). When the bank is relatively well capitalised it

optimally holds a risky portfolio, i.e., w ≈ 1, without running a significant risk of

failure. However, if the bank makes losses and its capital falls the bank will

reduce the risk of its asset portfolio in order to stave off default. (This part of the

portfolio strategy is similar to portfolio insurance). If, despite this, things turn out

badly and the bank’s capital erodes still further there comes a point – just to the

left of the bottom of the “U” – when it makes sense for the bank to “go for broke”

and increase the risk of its portfolio in order to try to get away from the default

boundary.

The right hand panel of Figure III.11 shows the consequences of this dynamic

strategy in terms of the distribution of the asset value. The distribution in the

figure is measured at a point in time about half way between audit dates. Even

though, in this simple model, the return on the risky asset is assumed to be

normally distributed, the return on the portfolio is far from normal. If the bank

were to maintain constant portfolio proportions, the distribution of the portfolio

36

return would be normal. The substantial difference between the distribution in

Figure III.11 – and, therefore, the banks risk – and its risk under a normal

distribution comes about entirely as a result of the dynamic portfolio policy. In

fact, in this example, the bank will actually default less often than under a

portfolio policy with a fixed portfolio, but the average value of the loss given

default will be higher.

Risk Assessment

The insight that the model provides is that risk is influenced in a systematic way

by the dynamics of portfolio policy. As just mentioned, the affect of the dynamic

strategy is actually to reduce the frequency of default relative to the static case

but to increase the conditional loss. The impact of portfolio dynamics on risk is

well understood in the context of derivative pricing but receives far too little

attention at the level of institutional risk assessment.

The model presented is theoretical: it makes no pretence to be “realistic”. The

“U” shaped strategy may be reasonable for a given bank or it may not. The two

main important points from this analysis, however, are these.

First, it is likely that a bank’s portfolio policy will depend on its capital position

(which is, in turn, the result of previous portfolio decisions). Any attempt by a

bank to think about the risk it runs in the longer run will necessitate some way of

capturing the policy he bank will follow in bad times as well as good.

Second, over longer horizons the dependence of portfolio policy at any point in

time on the level of capital can have a profound influence on the distribution of

asset value and, therefore, bank risk. As just mentioned, to work out the practical

37

consequences of this observation, a bank needs to think about its appetite for risk

in different scenarios. If the bank does well, will the bank be prepared to take on

more risk or less risk? And, if the bank were in real trouble, what would it

(realistically) do then? In thinking about these questions it is important to subject

the answer to a reasonableness test. For example, a bank that believes that, as its

capital position declines it will always become more prudent, may well be saying

that it has a probability of default of precisely zero.

38

Table III.I

The table shows calculations of correlation based on the analysis by Longin & Solnik (2001). The data used are monthly returns on the S&P 500 and the FT All-Share Index from 01/1959 to December 1996, a total of 455 months. For each threshold value the table shows, the number of observations where returns in both markets

exceed the threshold (i.e., fall below it for negative thresholds and above it for positive thresholds), the corresponding conventional correlation and an estimate of

the standard error of the conventional correlation.

Threshold # Observations Correlation SE (Corr)1 -10% 3 1.00 0.582 -8% 9 0.96 0.333 -5% 20 0.73 0.224 -3% 36 0.72 0.175 0% 100 0.55 0.106 3% 67 0.41 0.127 5% 22 0.24 0.218 8% 4 0.63 0.509 10% 1 --- ---

39

Figure III.1 Source:

Non-Overlapping Stock-Bond Correlations Using Daily Data, 1980-2001. The figure shows the non-overlapping monthly stock-bond correlations of G7 countries. Monthly correlations are calculated using daily stock and bond returns within each month. All graphs are smoothed by Hodrick-Prescott filter with a smoothing parameter of 14400. Daily stock and bond returns are available only from or after January 1980.

40

Figure III.2 Source: Longin and Solnik (1995)

41

Figure III.3 Source: Erb, Harvey and Viskanta (1994)

42

Figure III.4 Stock Market Indices during the 1987 US Stock Market Crash (Source, Forbes and Rigobon, 2002)

43

Figure III.5 Source: Ronn, Sayrak and Pompaidis (2001)

Figure III.6 Source: Ronn, Sayrak and Pompaidis (2001)

44

Figure III.7 Scatter plot of bivariate normal variables with correlation of 0.5

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

X_1

x_2

corr = 0.51

45

Figure III.8 Scatter plot of bivariate normal variables with correlation of 0.5 for observations where absolute value of x_1 > 2. The correlation between x_1 and x_2 for these observations is 0.81

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

X_1

x_2

corr = 0.81

46

Figure III.9 Source: Longin and Solnik (2001)

47

Figure III 10

Example of sample selection in Longin & Solnik: scatter plot of subset data from Figure III.9 for which both x_1 and x_2 exceed 2.

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

X_1

x_2

corr = 0.21

48

Figure III.11 Optimal portfolio strategies and the distribution of asset value

(Source: Pelizzon and Schaefer, 2004)

This Figure plots the optimal strategies conditional on time to audit and the distribution of asset value at different times. We consider an audit frequency of one year.

49

References

Artzner, P., F. Delbaen, J. M. Eber, and D. Heath. 1999. Coherent measures of risk. Mathematical Finance 9 (November): 203-228

Erb, Claude , Campbell R. Harvey and Tadas Viskanta, (1994) “Forecasting International Equity Correlations”, Financial Analysts Journal November/December 32-45

Evi C. Kaplanis, (1988) “Stability and Forecasting of the Comovement Measures of International Stock Market Returns”, Journal of International Money and Fiannce,7, 63-75.

Forbes, Kristin and Roberto Rigobon, (2002) No Contagion only Interdependence: Measuring Stock Market Comovements, Journal of Finance, vol. LVII (5, October), pgs. 2223-2261.

Harvey, Campbell, (1993), "The Term Structure Forecasts Economic Growth," Financial Analysts Journal May/June: 6-8

Li, Lingfeng (2002), “Macroeconomic Factors and the Correlation of Stock and Bond Returns”, Working Paper, Department of Economics, Yale University (http://ssrn.com/abstract_id=363641).

Longin, Francois and Bruno Solnik, (1995), “Is the correlation in international equity returns constant: 160-1990?”, Journal of International Money and Finance, Vol. 14, No, 1, pp. 3-26.

Pelizzon, Loriana and Stephen Schaefer (2004), Do Bank Risk Management and Regulatory Policy Reduce Risk in Banking? Working paper, London Business School

Ronn, Ehud I., Akin Sayrak and Stathis Tompaidis (2001) The Impact of Large Changes in Asset Prices on Intra-Market Correlations in the Domestic and International Markets, Working Paper, Department of Finance, University of Texas at Austin

Shiller, Robert J., and Andrea E. Beltratti (1992), “Stock Prices and Bond Yields”, Journal of Monetary Economics, 30, 25-46.

50

IV. Liquidity Risk and its Management for Banks and

Financial Institutions

There has been a surge in the recent academic literature on issues concerning

liquidity and liquidity risk. While practitioners would perhaps question the late arrival

of these topics into academic focus, academics have traditionally preferred to look at

the world through the lens of complete and frictionless markets. The limitations of

this traditional approach have however become glaringly transparent over the last

decade or two in the wake of events where the ability to trade securities and the ability

to access capital-market financing dried up considerably. The most striking of these

events include the stock market crash of 1987 in the United States, the Russian default

in 1998, the Long Term Capital Management episode that followed, and, most

recently, the aftermath of GM and Ford downgrade. It is thus timely and fitting to

examine the implications of liquidity, liquidity risk, and their management, from the

standpoint of banks and financial institutions.

A central difficulty with discussing issues relating to liquidity is the lack of

consensus on what it means. Liquidity is clearly multi-faceted and perhaps also a

somewhat loosely employed economic concept. To capital market participants,

liquidity generally refers to transaction costs arising from bid-ask spreads, price

impacts, and (limited) market depth for trading in securities. By token, liquidity risk

for this segment of market participants generally refers to unpredictable variations in

transaction costs. We shall henceforth refer to this notion of liquidity and liquidity

risk as pertaining to “market liquidity.” In contrast, and often times in addition, risk

managers at banks and financial institutions are concerned about liquidity on the

funding side. This pertains to the ease with which cash shortfalls of the enterprise can

51

be funded through various sources of financing – internal or external – that the

enterprise has access to. We shall refer to this as “funding liquidity” and its

unpredictable fluctuations over time as funding liquidity risk.

In this report, we focus primarily on understanding why banks and financial

institutions should be concerned about funding liquidity risk, and which form(s) of

funding liquidity risk – systematic (economy-wide) or idiosyncratic – should they be

concerned more about. Next, we argue that collateral requirements for securities

trading and hair-cuts on collateral value of securities imply that there is an important

linkage between market liquidity and funding liquidity. This linkage, in turn, implies

that market liquidity risk, funding liquidity risk, and correlation risk (in price changes

of traded securities) are all inter-related and may even reflect the same underlying

uncertainty. In particular, liquidity shocks while highly episodic tend to be preceded

by or associated with asset return shocks.

Finally, we discuss different mechanisms to manage such liquidity risk and

their relative merits: The relationships between different dimensions of liquidity risk,

and the seemingly unrelated correlation and asset return risks, have important

implications for risk managers and the hedging strategies their institutions employ.

Somewhat interestingly, the choice of specific techniques to manage liquidity risk

may itself have subtle and important feedback effects on the nature of liquidity risk

that banks and financial institutions face. We conclude with some conjectures about

the role played by the episodic nature of liquidity risk on the recent trend of shorter

but deeper economic cycles.

52

A. Funding Liquidity Risk: What Should Banks and Financial Institutions Be

Concerned About?

“With market risk and credit risk, you could lose a fortune. With [funding]

liquidity risk, you could lose the bank!” – Bruce McLean Forrest, UBS Group

Treasury.

Put simply, funding liquidity risk is the risk that an institution will have to

meet uncertain cash requirements in future arising from its day-to-day business

activities. Depending on the nature of the institution’s cash flow exposures – retail

versus wholesale, commercial bank versus investment bank versus universal bank –

the specific reasons for cash requirements will vary. However, in all cases, the ability

to manage funding liquidity risk depends crucially on the correlation between the

outflow of funds and the inflow of (or the ability to access) funds. Understanding the

nature of this correlation thus sheds light on what kinds of funding liquidity risks

should banks and institutions be concerned about.

There are two primary sources of funding liquidity risk: cash outflows that

arise during periods of systematic asset or liquidity shocks, and those that arise due to

idiosyncratic or institution-specific shocks. Systematic asset shocks arise during

recessions (e.g., the Great Depression), oil-price shocks (e.g., of mid 70’s), stock-

market crashes (e.g., in the United States in 1987), and real-estate crashes (e.g., in

Japan in late 1980’s). Systematic liquidity shocks such as the stock market crash in

1987 and the Long Term Capital Management episode in 1998 often coincide or are

preceded by asset-market shocks. However, it is safe to assume that there is a shock to

cash flows in these periods due to market illiquidity (wider bid-ask spreads, greater

53

hair-cuts on collateral, and complete inability to trade some instruments) – shocks that

are not attributable purely to asset shocks.

In contrast, idiosyncratic or institution-specific shocks may arise due to fraud,

disclosure of accumulated losses or accounting irregularities, legal settlements,

significant model risk, poor risk management, and the resulting loss of reputation in

capital markets, and perhaps to a smaller extent, due to idiosyncratic asset shocks

(more relevant for regional or community banks). Even if such shocks are not

accompanied by market-wide liquidity shocks, a disorderly liquidation of assets could

produce end outcomes for the affected institution that could resemble those in times

of market-wide shocks.

The key question to ask is: What happens to the institution’s funding sources

in the wake of a systematic or idiosyncratic liquidity shock? The answer to this

question depends crucially on the modern-day financial regulatory environment and

also on the nature of the bank – commercial or not. Specifically, a recent study by

Evan Gatev and Philip Strahan (Journal of Finance, 2005, forthcoming) shows that

during times of systematic liquidity shocks, there is a “flight to quality” of deposits to

commercial banks. The authors measure systematic liquidity shocks by a widening of

the (non-financial) commercial-paper to treasury-bill spread (the so-called “paper-bill

spread”). The paper-bill spread is considered a good proxy for times when liquidity

(and default) risk rises, as evidenced during the Penn Central default in 1970, LTCM

episode in 1998, and recently, the Enron bankruptcy in 2002.10

The authors find that when the paper-bill spread widens, commercial banks in

the United States experience an increase in deposit inflow. Furthermore, as Figure

IV.2 shows, when the paper-bill spread widens, commercial banks experience a

10 See Covitz and Downing (2002) and also Figure IV.1.

54

growth in assets, a growth in their commercial and industrial lending, and even a

growth in their liquidity buffers: a 25 basis points (bps) increase in the paper-bill

spread causes assets of commercial banks to grow at 0.4% weekly rate and their

liquidity buffers to grow at 0.17%. Finally, these banks are able to issue subordinated

debt and large negotiable certificates of deposit (CD) at lower rates, a 25 bps increase

in paper-bill spread corresponding to a 6 bps reduction in their CD rate. Several

additional aspects of this evidence are noteworthy: (1) These effects are observed only

for commercial banks and not for finance companies; (2) These effects do not depend

on the safety, that is, default risk, of the commercial banks; and (3) Only the levels of

deposit liabilities of commercial banks increase and not those of the non-deposit

liabilities.

These facts put together suggest that the regulatory deposit insurance is an

important (even if partial) hedge that commercial banks have against systematic

liquidity shocks. While United States stands out in its somewhat large deposit

insurance coverage, the size of deposit insurance is non-trivial in most other

economies as well. What is also interesting to note is that such effects were not

prevalent in the period prior to the introduction of deposit insurance in the United

States. For example, during the Great Depression of 1929-1933, there was a wide-

scale of conversion of deposits into currency, resulting in one of the sharpest

monetary and lending contraction (and, in fact, paving way for establishment of

federal deposit insurance in the United States).

In addition to deposit insurance, central bank intervention and guarantees are

more likely to be brought into play during market-wide crises. Hoggarth, Reidhill and

Sinclair (Bank of England Working Paper, 2004) study resolution policies adopted in

33 banking crises over the world during 1977-2002. They document that when faced

55

with individual bank failures regulatory authorities have usually sought a private

sector resolution where the failed institution is generally sold to one of the surviving

ones, and its losses are typically passed onto existing shareholders, managers and

sometimes uninsured creditors, but almost always not to taxpayers. However,

government involvement has been an important feature of the resolution process

during systemic crises: At early stages, liquidity support from central banks and

blanket government guarantees have been granted, usually at a cost to the fiscal

budget; bank liquidations have been very rare and creditors have rarely made losses.

To summarize, central bank or government intervention makes systemic

liquidity crises a smaller liquidity risk concern for banks and financial institutions.

Due to explicit deposit insurance, commercial banks have a partial regulatory hedge

against systematic liquidity risk. This also constitutes a strategic advantage for

commercial banks and perhaps explains their significant role in providing commercial

paper back-ups relative to other institutions. However, for institutions other than

commercial banks, and even for commercial banks when liquidity needs are of an

intra-day basis (for example, due to collateral requirements or margin calls on traded

securities), other forms of funding become crucial to avoiding a liquidity crisis.

In addition to deposits, banks and financial institutions can rely on external

forms of financing such as equity, subordinated debt, unsecured inter-bank credit,

secured debt against collateral, and undrawn lines of credit, and on internal financing

in the form of cash and retained earnings.

In times of systematic liquidity or default risk, public markets such as equities

and subordinated debt tend to dry up the first. Even if these markets are available, the

increased risk premium in times of stress and the resulting dilution cost implies that

56

these markets are typically not used.11 In contrast, the unsecured inter-bank market

has generally been found to be robust during systematic stress. In a case study

surrounding the Long Term Capital Management episode in Autumn 1998, Furfine

(BIS Working Paper, 1999) found that although there were large flight to quality and

liquidity effects in treasury markets, individual fed-funds transactions between banks

exhibited substantial robustness. Figures IV.3 and IV.4 illustrate that the volume of

inter-bank lending jumped up 20% during July and August 1998 compared to months

before, there was not much change in the level of inter-bank lending rate, and all

institutions, risky as well as relatively safe ones, borrowed in this market. While it is

not yet clear what lent the robustness to this inter-bank market – the nature of

relationships between banks and/or anticipated regulatory intervention – it

nonetheless makes the case more compelling for systematic liquidity stress being not

as significant a concern for banks and financial institutions as idiosyncratic or

institution-specific stress.

The price-sensitive funding sources – equity, subordinated debt, and

unsecured inter-bank credit – are however not as readily available to solvent

institutions which have experienced idiosyncratic liquidity shocks. The very fact that

the shock is idiosyncratic renders financing of the institution difficult: Central bank

support is unlikely in case of an isolated liquidity problem (unless the institution is

too-big-to-fail), there is a loss of reputation in making losses when other institutions

have done well (there is no one to “share the blame with”), the opaqueness of typical

bank balance-sheet aggravates the matter by blurring the boundary between

insolvency and illiquidity, and the institution’s management as well as risk-

management practices come into question. Some cases in point here are Continental

11 Several academic studies, e.g., Choe, Masulis and Nanda (1993), have shown that the

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Illinois’s collapse in 1989, the Barings disaster in 1995, and to an extent the distress

of Long Term Capital Management in 1998 in spite of its pre-existing complex web

of relationships for borrowing against collateral at small hair-cuts.

In essence, price-sensitive funding sources are rendered either unviable or too

expensive during idiosyncratic liquidity shocks to institutions. Although, retained

earnings and undrawn lines of credit represent price-insensitive sources of funding,

these have to be arranged in advance and may not constitute a liquidity buffer that is

large enough in the wake of a significant liquidity shock. The material adversity

clauses (MACs) in the lines of credit are more likely to invoked if the liquidity needs

of the affected institution are easier to attribute to internal (idiosyncratic) problems

rather than external (systematic) ones. The institution would thus typically have to

resort to at least some form of intermediate financing, such as secured borrowing

against collateral. The extent of such borrowing that can be undertaken depends upon

the market value of the collateral and the size of hair-cuts being charged by

counterparties (typically, 2-5% for highly liquid assets like OECD government bonds,

10-25% for highly-rated industrials, and 25-50% for illiquid assets like major-index

equities, but generally higher during liquidity crises). The variation in hair-cuts over

time, and, in turn, in collateral values, creates a role for market liquidity in

determining the institution’s funding liquidity risk.

B. Market Liquidity Risk, Funding Liquidity Risk and Correlation Risk

Asset shocks often precede and give rise to liquidity needs. However, in

absence of liquidity shocks, a solvent institution can generally tap into various

price-impacts from equity issuances are greater in recessions than in expansions.

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funding sources and weather these shocks. Thus, liquidity shocks to markets that are

accessed by institutions for funding lend a critical dimension to funding liquidity risk.

Recent evidence shows that asset shocks and liquidity shocks tend to be highly

correlated, in the aggregate as well as at the level of individual securities. In

particular, Acharya and Pedersen (Journal of Financial Economics, 2005) show that

there are three covariances or betas that are relevant in asset-pricing from a liquidity

standpoint: the covariance of security’s illiquidity with market-wide illiquidity; the

covariance of security’s return or price changes with market-wide illiquidity; and, the

covariance of security’s illiquidity with market-wide return. Figure IV.5 from

Acharya and Pedersen (2005) plots the time-series of innovations in stock-market

illiquidity computed using the daily price-impact measure of Amihud (2002) over the

period 1964-2000, a measure that has been shown by Amihud (2002) to be related to

other measures of liquidity such as the bid-ask spread.

Strikingly, liquidity shocks are highly episodic. That is, innovations in market

illiquidity are generally small but quite high during the few periods that anecdotally

were characterized by liquidity crisis, for instance, in 5/1970 (Penn Central

commercial paper crisis), 11/1973 (oil crisis), 10/1987 (stock market crash), 8/1990

(Iraqi invasion of Kuwait), 4-12/1997 (Asian crisis), and 6–10/1998 (Russian default

and Long-Term Capital Management crisis). Many of these coincide with negative

asset value shocks, highlighting the correlation of market-wide illiquidity with

negative shocks to market-wide returns.12 The relative size of illiquidity peaks to

average illiquidity also illustrates that when illiquidity does rise, it tends to dry up

suddenly, inducing a non-linear or regime-switching relationship between liquidity

12 For other studies documenting the importance of some of these covariances, see, Chordia, Roll and Subrahmanyam (2000) for commonality in liquidity across securities, Pastor and Stambaugh (2003) for covariance of security returns with market liquidity, and Chordia, Sarkar and Subrahmanyam (2005) for commonality in liquidity across stocks and bonds.

59

shocks and asset return shocks, an observation whose likely roots will be explored

further in the discussion that follows.

Furthermore, Acharya and Pedersen (2005) find that securities that do exhibit

substantial liquidity covariances or betas in the above sense are also more illiquid on

average. To emphasize, illiquid securities (such as equities) tend to become more

illiquid during market-wide asset and liquidity shocks. This is also true for individual

stocks within the broad class of equities.

The importance of this result stems from three observations: First, asset shocks

and liquidity shocks occur together accentuating the overall impact of funding

liquidity risk; second, when funding liquidity risk rises, the market value of certain

forms of collateral may fall as well; and, third, when funding liquidity risk rises, hair-

cuts on collateral may rise too since funding liquidity risk arises when there is market

liquidity risk too. For instance, hair-cuts on AAA-rated commercial mortgages jump

up from 2% in normal times to 10% during stress times limiting their usefulness as

collateral for secured funding. In another instance highlighting the correlation of

market and funding liquidity risks, as many as 12 NYSE specialist firms had no

buying power whatsoever on October 19, 1987 during the stock-market crash due to

lack of capital for posting margins on additional transactions.

To summarize, the real funding liquidity risk is that if it coincides with market

liquidity risk and asset return risk (and we argued above that it often will) then it

could render an institution and its collateral illiquid when the cash inflows from flight

to quality are not sufficient to overcome its heightened funding needs, especially on

an intra-day basis. If a specific institution suffers more adversely than others due to

differential risk exposure or due to a compounding of asset shocks with managerial

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and risk-management issues, then the institution may not benefit from flight to quality

effects, and the effect of funding liquidity risk may be more pernicious.

In order to understand the implications of this discussion further, it is useful to

step back and ask the question: What causes market liquidity to be lower during times

of large asset shocks? The explanation has perhaps been best expounded in a recent

paper by Brunnermeier and Pedersen (2005) who start from the premise that due to

the presence of hair-cuts, trading requires capital. Asset shocks reduce the amount of

capital available with capital-market intermediaries (specialist firms and hedge-funds,

who are unlikely to benefit from flight to quality, and universal banks, which may

partially benefit from flight to quality). This, in turn, lowers the ability of their trading

desks to provide liquidity in the form of narrow bid-ask spreads, smaller price-

impacts, and greater depth. As liquidity in the market worsens, the funding ability of

intermediaries, whose revenues, wholly or partly, consist of market-making revenues,

worsens too. This worsening of funding ability in turn limits their liquidity-provision

role even further, giving rise to a downward spiral, and a sudden drop in both the

funding liquidity of intermediaries and the market liquidity they provide. To

summarize, if asset shock is large enough that the capital position of a sufficiently

large number of intermediaries is rendered constrained, then a sudden dry up of both

funding and market liquidity may arise.

The presence of such a link between funding and market liquidity risks implies

that prices in capital markets exhibit two “regimes”. In the normal regime,

intermediaries are well-capitalized and liquidity effects are minimal: prices of assets

reflect fundamentals and no (or little) liquidity effect. Thus, the correlations across

asset prices in these times are also driven primarily by correlation in fundamentals of

the underlying entities or risks. In the illiquidity regime, intermediaries are close to

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their financing or capital constraints and prices now reflect the “shadow” cost of

capital to these intermediaries, i.e., the cost they suffer from issuing an additional unit

of funding capital to undertake a transaction. In economic parlance, there is “cash-in-

the-market” pricing (Allen and Gale, Journal of Finance, 1998) and the total capital of

market participants in a particular security market affects the price of that security.

Since this liquidity effect (the illiquidity discount) is related to intermediaries’ capital

rather than to fundamentals of the security, it affects prices of securities traded by

these intermediaries across the board, inducing a correlation in securities’ market

prices that is over and above the one induced by fundamentals.

C. Example: Effect of GM and Ford downgrades on credit markets13

It is useful to consider a recent example that is consistent with correlations

being induced across security prices due to such liquidity effects. On May 5 2005,

Standard and Poors downgraded General Motors (GM and GMAC) and Ford (and

FMC) to “junk” category and maintained a negative outlook. While the downgrades

were anticipated to a large extent by the market, the precise timing was uncertain.

What was striking during the downgrade was that not only the prices of the securities

of GM and Ford, and more broadly of the automobile sector, but also in other markets

and sectors, for example, the credit-default swaps (CDS) for financial institutions and

the mezzanine and equity tranches of collateralized debt obligations (CDOs), moved

considerably. In particular, these prices moved considerably in the short-run and

exhibited at least a partial reversal within a few weeks (Figure IV.6).

13 Parts of this section on the effects of GM and Ford downgrade on CDS and CDO markets have been prepared with the help of Ronald Johannes of Bank of England. All errors and attribution of facts represented remain our responsibility, and not of Ronald Johannes.

62

Consider the widening of the CDS premia for financial institutions, reflecting

a price correlation of this sector with the auto-sector during this episode. One possible

explanation is that the downgrades resulted in huge losses to some of the hedge funds

(through their correlation exposures as explained below), and the markets were

uncertain about the size of exposure that financial institutions had as prime brokers to

these funds. A plausible alternative explanation consists of recognizing the inventory

risk that intermediaries faced in the period following the downgrade announcement.

Institutional investors and funds that had held onto GM and Ford securities (a

miniscule amount of global financial securities but not a small fraction of dollar-

denominated and Eurozone corporate debt) were forced to liquidate bonds of GM and

Ford due to regulatory restrictions or charter restrictions that prevented them from

investing in junk-rated securities. Even the high-yield investors often face restrictions

on the maximum exposure to an individual name’s credit, rendering it difficult for the

market to absorb the large supply of GM and Ford debt. Market-clearing conditions

thus required that financial intermediaries, and to an extent, high-yield desks, ended

up with a huge supply of such securities. Since default risk is greater and the collateral

value (especially when adjusted for hair-cuts) is smaller for junk-rated securities,

financial intermediaries ended up with significantly risky inventory.

The same set of financial intermediaries make markets in other securities

including the CDS on financial institutions. The inventory risk of intermediaries, and

the extant funding pressure, thus caused a widening of prices across the board

including those in the CDS market, as prices moved from the normal regime to the

illiquidity regime. Even marking these positions to market was rendered difficult due

to the illiquidity resulting from unreliable or out-of-date quotes posted on otherwise

reliable price feeds such as those from MarkIt Partners. As Figure IV.6 illustrates, the

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rise in CDS prices of financial institutions at least partly reversed in the next few

weeks, reflecting that the liquidity impact of GM and Ford downgrades on this market

was temporary, consistent with the academic literature (e.g., Pastor and Stambaugh,

2003) that in fact uses price reversals to measure market illiquidity.

Next let us consider the effect on the CDO market, specifically on the

mezzanine and equity tranches of CDS indexes. A large number of hedge funds and

leveraged short-term traders had a positive correlation exposure due to being short

mezzanine tranches of CDOs (long mezzanine protection) and long the junior or

equity tranches (short junior protection). The mezzanine tranche could essentially be

viewed as a delta-hedge of the equity tranche position. This trade benefits from an

increase in correlation of default risk of constituent names of the CDO, but leaves

exposure to idiosyncratic default risk of individual names. The GM and Ford

downgrades generated losses on these positions and a large number of these players

moved out of equity tranches into mezzanine tranches. The liquidity effects and the

relative pricing of equity to mezzanine (both spreads widened in absolute terms)

implied that the unwinding of positive correlation trades occurred at significant price

impacts or fire-sale discounts. This price pressure pushed further down the mark-to-

market valuation of positive correlation trades producing a significant swing in

relative prices of different CDO tranches. As seen in Figure IV.6, again this effect

was temporary and largely reversed itself within a few weeks. In effect, a part of the

swing in implied correlations from CDO pricing models occurred due to illiquidity in

the market for CDO tranches affecting prices of these tranches.

This discussion points to a rather important implication of the regime-

switching liquidity view of prices and correlations. Measuring and interpreting

correlation risk through implied correlations from models that do not capture such

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regime switches can be highly misleading. Specifically, it is well-known that such

implied correlations fluctuate widely, especially during market-wide shocks.

Attributing them to shifts in fundamentals, and coming up with hedging strategies

based on models that do not capture the inherent rationale for their fluctuations, can

pose a significant “model risk” for banks and financial institutions.

While it is difficult as of yet to build simple models that capture liquidity

effects and perhaps even more difficult to calibrate the small body of such models that

exist, it is in order to point out that managing the funding liquidity risk (and, in turn,

hedging against market liquidity risk) may be necessary and effective in managing the

correlation risk across securities. Hedges based on traditional models which employ

underlying securities may not work well during times of market-wide shocks: Indeed,

as Tucker (2005) points out, this is a general point that is observed in markets in

different guises. During the stock market crash of 1987, Leland, O’Briend and

Rubinstein, who had sold large quantities of portfolio insurance on retail portfolios,

attempted to hedge their short put positions by selling equity, based on delta

calculations from the Black-Scholes model. The Black-Scholes model is a model of

normal regime when markets are close to being frictionless. In the illiquidity regime,

delta based on the Black-Scholes model is incorrect since it ignores the price-impact

of the dynamic delta hedge on the underlying stock market. This is much the same as

the delta hedge of a long equity tranche in the form of a short mezzanine tranche

being inaccurate when trades in these tranches move the prices of these very tranches.

Tucker (2005) makes the risk management implication of this in a rather

succinct manner: “Is the Street and/or the fund community short volatility or gamma

or vega in a big way in any particular market (where they are the primary players)?”

The knowledge of the inherent positions of peers in markets where institutional

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investors are dynamically managing short options positions is the key in many such

other settings: In 1994 and 2003, the dynamic hedging of the negative convexity of

US mortgage-backed securities amplified the rise in dollar bond yields (here, the

financial sector is structurally short prepayment options), and another case in point is

the Constant Proportion Portfolio Insurance (CPPI) sold by hedge funds, where to

preserve the nominal principal, the “guarantor” sells units, in say, a fund of funds as

its value falls.

To summarize, delta hedges based on normal regime models entail significant

“model risk” in illiquidity times, and, in fact, amplify the price fluctuations. A specific

case of this was the failure of credit derivative pricing models to account for price-

impacts resulting from the recent GM and Ford downgrades, making it notoriously

difficult to calibrate correlation parameters: naturally, the implied correlations from

normal regime models fluctuated wildly during the illiquidity regime to “fit” the

liquidity-affected prices. In such times, liquid and quality instruments may be better

than dynamic underlying hedges to weather illiquidity-induced price shocks. We

discuss this and the overall issue of liquidity risk management next.

D. Management of Funding Liquidity Risk

Since liquidity risk is considered as one of the most critical risks by many

banks and financial institutions, its management is often termed as arranging for “life

insurance.” Given the earlier discussion on the crucial role played by government

guarantees, it should be expected that the extent of such arrangement would vary

across commercial, investment and universal banks, and financial intermediaries. In

countries with deposit insurance, banks domiciled in those countries would benefit

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from the flight to quality of deposits. However, in other countries, and for banks

whose financing is more wholesale rather than retail, it is important to assess the

fraction of deposits that are “core” (sticky) versus those that are likely to get

withdrawn or move to other havens during stress times. Typically, such stickiness can

be assessed based on past withdrawal patterns of deposits. Similarly, banks can

arrange lines of credit with other banks and financial institutions. In a stress situation,

counterparties benefiting from government guarantees are more likely to be able to

honour draw-downs on the arranged lines of credit. Hence, preferably these lines of

credit should be arranged with institutions such as commercial banks with retail

deposits, and those that are domiciled in deposit-insurance providing countries.

In all cases, however, it is the quality and liquidity of securities that is a must

during liquidity stress times: Are the deposits sticky and unlikely to migrate during

times of stress? Are the standby lines of credit likely to be available, that is, will the

counterparty bank on which lines of credit are drawn be healthy? Will the security

holdings have the required value and liquidity for collateral-based borrowing? These

include securities such as good quality OECD government bonds which have tiny

hair-cuts and good tradeability during stress times, and, of course, cash.

Unfortunately, not much academic literature exists on how banks and financial

institutions manage liquidity. In an exception, Aspachs, Nier and Tiesset (Bank of

England Working Paper, 2005) examine the effect of macroeconomic conditions

(GDP growth rate of a country) and anticipated government support (based on Fitch

support ratings) on holdings of liquid assets – cash, reverse repos, bills, and

commercial paper – for 57 UK-resident banks. The measures for liquid holdings are

liquid assets to total assets, and also liquid assets to total deposits. Their two

important findings are as follows. First, greater anticipation of lender-of-last-resort

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support from the regulator of the country where the bank is domiciled reduces the

liquidity holdings of banks. This is consistent with the view that internal liquidity and

lender-of-last-resort provision are substitutes, as argued by Repullo (Working Paper,

2003).14

Second, and somewhat more interestingly, liquidity holdings of banks are

countercyclical. During economic upturns, measured by high GDP growth rates, bank

liquidity buffers are low, whereas during downturns, these buffers grow: all else being

equal, a reduction in GDP growth rate by 1% raises the liquidity holdings by around

8%. Put another way, banks appear to hoard liquidity in downturns and run down

these buffers in good times. While a part of this effect may be mechanically

attributable to lower demand for credit in downturns, and the lower attractiveness of

credit in such times, it is also plausible that the increase in liquidity holdings in

downturns represent a precautionary motive of banks wishing to hedge against

liquidity risk. While this evidence is preliminary and not fully conclusive, the effects

on liquidity holdings are stronger for smaller banks that may face greater liquidity risk

than larger banks due to limited access to capital markets.

Another important dimension of liquidity risk management is the role played

by bank capital. Is capital a buffer against liquidity risk? The answer to this is yes to

some extent, but largely no. On average, capital does increase the liquidity creation

ability of large banks and financial institutions. In an important recent contribution,

Berger and Bouwman (Working Paper, 2005) classify the balance sheet and off-

balance sheet activities of banks into Illiquid, Semi-liquid, and Liquid assets and

liabilities (Table IV.1). Next, they define measures of liquidity creation of the bank by

taking a weighted difference between assets and liabilities (weight of +1/2 for illiquid

14 In another interesting piece of evidence that is consistent with this, Gonzalez-Eiras (2003)

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category, 0 for semi-liquid, and -1/2 for liquid ones), as illustrated in Table IV.2.

While this procedure is somewhat ad-hoc, it represents a novel and to an extent

complete classification of bank activities into liquidity buckets since they take

account of undrawn lines of credit extended by banks to borrowers and also those

arranged by banks for their own use.

Berger and Bouwman relate the extent of bank capital (bank’s lagged equity

capital ratio) to the bank’s measures of bank’s liquidity creation in a year. In essence,

they ask the question of how much illiquidity does a unit of bank capital enable the

bank to hold in its portfolio? For large banks, they find that a unit of capital enables

the bank to hold 2.5 units of illiquidity. The authors suggest that capital reduces the

risk of failure for the institution by creating a buffer against liquidity risk, and, this in

turn, enables the bank to invest more in illiquid assets.

While this liquidity risk-absorption role of capital (on average) is important, it

is unclear whether capital by itself can serve as a buffer in times of an actual liquidity

shock. It is clear that capital reduces default risk in absence of liquidity risk by

lowering the chance of insolvency. However, when liquidity risk actually arises,

capital sources such as equity and subordinated debt may not be available in the first

place. The relevant funding sources in such a situation are bilateral funds and easy-to-

collateralize securities. Given that funding liquidity risk and market liquidity risk have

a feedback relationship as described before, bilateral funds may also be hard to obtain.

Capital can partly dampen the liquidity risk spiral by reducing asymmetric

information about the solvency of the affected institution, nevertheless it cannot

perform the (essentially) unconditional liquidity role that high quality instruments can

perform. This distinction between capital and liquidity in times of liquidity crisis is

documents that the introduction of repurchase agreements in 1996 facilitated better lender-of-

69

important, and implies that liquidity risk may in fact command a role for economic

capital by itself, over and above other risks to banks.

This distinction is particularly striking for large banks and institutions: they

are typically well-capitalized, far above the regulatory minimum requirements, and

yet, are not always sure if this capital will translate into liquidity when needed. One

attractive use of capital is to employ it to create state-contingent liquidity. Ideally,

what banks and financial institutions would like in order to manage liquidity risk is to

purchase securities that pay off in states where liquidity risk is high. While such

liquidity-contingent securities are not yet traded in the market, there are some

substitutes that may be attractive.

Recently, during the (anticipated) Y2K crisis, many banks and institutions in

the United States purchased the “liquidity (Y2K) options” from the Federal Reserve

Bank of New York in the first nine months of the year 1999. As Sundaresan and

Wang (2004) discuss, in addition to extending the maturity of government bond

repurchase contracts (repos) and expanding the set of collateral securities (to include

mortgage-backed securities), the Fed introduced liquidity options. The first option

issued by the U.S. central bank was the Special Liquidity Facility (SLF), which was

voted and passed by the Federal Reserve Board on July 20, 1999, more than five

months ahead of the Millennium Date Change. Under the SLF, the depository

institutions were allowed to borrow from the Federal Reserve discount window at an

interest rate that is 150 basis points above the prevailing federal funds target rate from

October 1, 1999 to April 7, 2000. Therefore, depository institutions were given call

options for credit on July 20, 1999. The strike of the option was set at 150 basis points

above the prevailing federal funds target rate, and it could be exercised during the

last-resort provision and this led to a reduction in internal bank liquidity by 6.7% on average.

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period from October 1, 1999 to April 7, 2000. By issuing such options, the central

bank committed itself to provide banks an alternative source of liquidity for handling

potentially large withdrawals (demand for liquidity) of deposits or currencies.

The second important policy initiative using option contracts was to commit to

conducting a series of auctions known as the Standby Financing Facility (SFF). These

options gave the holders the right, but not the obligation, to execute overnight repo

transactions with the New York Fed at a pre-set strike price, a financing rate that was

set 150 basis points above the prevailing federal funds target rate. These options could

be exercised during some specified periods around the century date change. Under the

SFF, demanders of future liquidity were invited to bid for the options at periodic

intervals (in fact seven during Oct through Dec 1999) before the Millennium Date

Change. The Fed’s purpose in issuing these options was to ensure that the bond

markets operate smoothly around the Millennium Date Change so that the Fed could

conduct its monetary policy smoothly without running into difficulties.

In all these policy measures, the central bank put itself as the counterparty to

the repo transactions as well as the options transactions. This eliminated the risk of

counterparty default risk from the perspective of the dealers and banks. In a period of

liquidity crisis, this is clearly an important consideration for banks and dealers. As

Sundaresan and Wang show, participation in these auctions by depository institutions

led to a significant reduction in the liquidity premium in the markets, measured by the

on-the-run versus off-the-run spread for treasury securities (Figures IV.7 and IV.8).

The evidence from the auctions suggests that these facilities were used to a large

extent by financial institutions. Specifically, the demand was on average 50 billion

dollars for each of the three strips of Y2K options – maturing on December 23,

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December 30, and January 6 – and in each of the seven auctions, the demand being

greater for December 30 and January 6 strips.

Alternately, if central bank support is anticipated (implicitly or explicitly)

through its regular lender-of-last-resort activity, then banks and financial institutions

can park their capital in the form of standby letters of credit from other banks and

financial institutions. Either the institution itself benefits from flight to quality effects,

in which case these standby guarantees are not required, or the institution can draw

down the standby letters of credit issued by those institutions that benefit from flight

to quality effects. Since institutions domiciled in a deposit-insurance regime are a

priori more likely to benefit from flight to quality effects, the natural suggestion here

is to employ capital to purchase letters of credit with such insured institutions. The

advantage over cash and treasuries is again that a unit of capital invested in

purchasing letters of credit can create far more liquidity in stress time than a unit of

cash and treasuries. The disadvantage relative to government-issued liquidity options

is that there is always some counterparty risk when a letter of credit is issued by a

financial institution rather than by the central bank.

With these suggestions for better employment of capital to manage liquidity

risk, we examine some of the operational issues of liquidity-risk management. It is

interesting that many banks and financial institutions do consider liquidity risk as a

separate source of risk in their risk management. Furthermore, typical liquidity risk is

managed by projections of cash flows and funding sources based on stress tests and

scenarios (for example, going concern scenario, liquidity squeeze, bank-specific

crisis, general market crisis, with additional qualifications based on currency-specific,

market-specific, sector-specific, and country-specific risks). Horizons for making

these projections seem to vary across institutions: some adopt an yearly approach

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recognizing the limitation that positions evolve dynamically, whereas others adopt a 1

month or 1 week horizon to match the period by which assets may get sold without

engaging in disorderly or fire-sale liquidations, and partly to match central bank

requirements such as the five-day worth liquidity reserve requirement by Bank of

England. Finally, there are contingency plans put in place that detail the specific

aspects of coordination across desks, locations, and possibly currencies.

While the specifics of liquidity risk-management process do warrant careful

attention, especially for institutions and their risk-management desks, we focus here

on a final set of broad observations.

What are the merits of treating liquidity risk as a separate source of risk?

Liquidity issues are generally followed by asset shocks of some sort. The covariance

between liquidity risk and asset return risk must thus be taken into account. A catch

here is that liquidity risk is typically highly non-linear in asset return risk. The

feedback between funding and market liquidity risks makes this problem particularly

severe from the standpoint of capturing liquidity risk adequately by merely appealing

to asset return risk, and recognizing that liquidity risk may be correlated with it. On

the one hand, this discussion implies that liquidity risk can be partly hedged by better

management of asset return risk. Nevertheless, complete hedging of liquidity risk may

be economically infeasible and most likely too expensive. On the other hand, the

discussion also implies that liquidity risk does have a “sudden” or a “jump”

component to it, which may be best hedged against by some kind of stress or scenario

analysis, similar to the current practice at banks and financial institutions.

We believe however that tying the modelling of stress scenarios for liquidity

risk to institution’s asset return risk would be fruitful for risk-management desks. A

good example is based on correlation risk. As discussed earlier, correlation risk can

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arise from liquidity affecting prices of a spectrum of securities during stress times.

Correlation risk is typically considered a trading desk-level risk. However, when

correlations are induced by market liquidity, correlation risk is most likely to be

associated with funding risk at the overall firm level. If funding risk and correlation

risk are positively correlated (depending on being long or short correlation), then the

stress scenarios may be more adverse than anticipated based on funding risk alone. By

the same token, if funding risk and correlation risk are negatively correlated, lack of

modelling of this association would lead to over-hedging in the form of excessively

large cash or buffers of quality collateral.

A final observation regarding liquidity risk management is in order. The recent

literature, specifically, Caballero and Krishnamurthy (Working Paper, 2005) has

attributed “Knightian uncertainty”, put simply economic behaviour that takes

decisions to minimize the worst-case scenario for an objective function, as being at

the root of flights of capital and liquidity observed in the markets. Their premise is

that institutions and fund-managers exhibit the usual risk-averse behaviour in markets

they understand well, but have “ambiguity aversion” towards investments in markets

they do not regularly participate in. During crisis times, this leads to restricted flows

of capital across markets. This also leads to flight to quality in crisis times as

uncertainty about underlying fundamentals of some markets increases. Scenario-based

stress tests and resulting liquidity risk management resemble to some degree

behaviour that would be observed under Knightian uncertainty preferences. One

wonders whether there is a feedback at a general equilibrium level of how institutions

manage liquidity risk to how liquidity flows in times of stress, but that is a much

deeper question than can be handled in the last paragraph of this report.

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Figure IV.1

Source: Gatev and Strahan (2005)

75

Figure IV.2

Source: Gatev and Strahan (2005)

76

Figure IV.3

Source: Furfine (2001)

77

Figure IV.4

Source: Furfine (2001)

78

Figure IV.5

Source: Acharya and Pedersen (2005)

79

Figure IV.6

(Prepared with the help of Ronald Johannes of Bank of England)

Chart 1: GM/Ford bond spreads Chart 5: Equity and mezzanine tranche spreads of US CDS index(a)

0

100

200

300

400

500

600

700

800

900

1,000

Jan. Apr. Jul. Oct. Jan. Apr. Jul. Oct. Jan. Apr. Jul.

GMFordMerrill Lynch high-yield indexMerrill Lynch investment grade index

2003 04 05

Basis points

(a)

(b)

(c)

100125150175200225250275300325350375

Jun. Aug. Oct. Dec. Feb. Apr. Jun.202530354045505560657075

2004 05

Mezzanine (3 to 7%) tranche (left-hand scale)

Equity (0 to 3%) tranche(right-hand scale)

Per cent of notional(b)Basis points

Source: Merrill Lynch. Spreads option adjusted. (a) GM profit warning, 16th March. (b) Ford profit wanting, 8th April. (c) Ford and GM downgrade to junk by S&P, 5th May.

Source: JP Morgan Chase and Co. (a) Five-year on-the-run Dow Jones CDX North America investment grade index (DJ.CDX.NA.IG). (b) Equity tranches are quoted as an upfront price (a per cent of the notional transaction size). A higher price for credit protection indicates an increase in tranche risk, so the upfront price acts like a spread.

Chart 7: Selected bank CDS premia(a)

0

10

20

30

40

50

60

Mar.01 Mar.22 Apr.12 May.03 May.24 Jun.14 Jul.05

Goldman SachsLehman brothersJP Morgan ChaseMerrill LynchMorgan StanleyDeutsche Bank

2005

Basis points

Source: MarkIt. (a) 5-year senior debt CDS contracts.

80

Figure IV.7

Source: Sundaresan and Wang (2004)

81

Figure IV.8

Source: Sundaresan and Wang (2004)

82

Table IV.1

Source: Berger and Bouwman (2005)

83

Table IV.2

Source: Berger and Bouwman (2005)

84

References

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Pastor, Lubos and Robert Stambaugh, (2003) “Liquidity Risk and Expected Stock Returns”, Journal of Political Economy, 111(3), 642-685 Repullo, Rafael, (2003) “Liquidity, Risk Taking and the Lender of Last Resort”, Working Paper, CEMFI, Madrid, Spain Sundaresan, Suresh and Zhenyu Wang, (2004) “Public Provision of Private Liquidity: Evidence From the Millennium Date Change”, Working Paper, Columbia University. Tucker, P M W, (2005) “Where Are the Risks?” Speech at the Euromoney Global Borrowers and Investors Forum, London, 23 June 2005

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