FNCE4030 Investments and Portfolio Management -...

University of Colorado at Boulder – Leeds School of Business – FNCE4030

FNCE4030 – Investments and

Portfolio Management

Introduction on Derivatives


What is a Derivative?

• A derivative is an instrument whose value

depends on, or is derived from, the value of

another asset.

• Examples:

– Futures

– Forwards

– Swaps

– Options

– Exotics

– …


Why Derivatives Are Important

• Key role in transferring risks in the economy

• Underlying assets include stocks, currencies,

interest rates, commodities, debt instruments,

electricity, insurance payouts, weather, etc.

• Many financial transactions have embedded

derivatives

• The real options approach to assessing

capital investment decisions has become

widely accepted


How Derivatives Are Traded

• On exchanges such as the Chicago Board

Options Exchange

• In the over-the-counter (OTC) market where

traders working for banks, fund managers

and corporate treasurers contact each other

directly


Size of OTC & Exchange-Traded Markets

Source: Bank for International Settlements. Chart shows total principal amounts for

OTC market and value of underlying assets for exchange market


Growth of OTC Market by Product

0

100

200

300

400

500

600

700

Jun.98 Jun.99 Jun.00 Jun.01 Jun.02 Jun.03 Jun.04 Jun.05 Jun.06 Jun.07 Jun.08 Jun.09 Jun.10 Jun.11 Jun.12

Commodity

Equity-linked

Credit default swaps

Interest rate

FX

$ trilli

ons


How Derivatives are Used

• To hedge risks – e.g. you are a producer of oil or a consumer of

soy beans, or are paid in a different currency

• To speculate (take a view on the future

direction of the market)

• To lock in an arbitrage profit

• To change the nature of a liability

• To change the nature of an investment

without incurring the costs of selling one

portfolio and buying another


Forwards


Forward Price

• DEFINITION: the delivery price that

would be applicable to the contract if

negotiated today

(i.e. the delivery price that would make

the contract worth exactly zero today)

• The forward price may (and will likely)

be different for contracts of different

maturities


Some Terminology (more to come)

• The party that has agreed to buy has a long

position

• The party that has agreed to sell has a short

position

• Selling a derivative is sometimes referred to

writing a derivative (forwards, options, etc.)

• The contract delivery date is sometimes

referred to expiration date, or maturity date


Forward Example

• On Jan 10, 2013 the treasurer of a

corporation enters into a long forward

contract to buy £1 million in six months at an

exchange rate of 1.6115

• This contract obligates the corporation to pay

$1,611,500 for £1 million on the maturity date

(July 10, 2013)

• What are the possible outcomes?


Profit from a Long Forward

• K = delivery price = forward price at time

contract is entered into

Profit

Price of Underlying at

Maturity, ST K


Profit from a Short Forward

• K = delivery price = forward price at time

contract is entered into

Profit

Price of Underlying at

Maturity, ST K


Futures Contracts


Futures Contracts

• Agreement to buy or sell an asset for a

certain price at a certain time

• Similar to forward contract, but there are

• Differences:

– A forward contract is traded OTC, a futures

contract is traded on an exchange

– A futures contract requires daily settlement of the

value of the contract, a forward contract has a

cash flow only a maturity

• WARNING– This is what the book says but it is not

strictly true. More on this later.


Exchanges Trading Futures

• CME Group (formerly Chicago Mercantile

Exchange and Chicago Board of Trade)

• NYSE Euronext

• BM&F (Sao Paulo, Brazil)

• TIFFE (Tokyo)

• and many more (see list at end of Hull book)


Examples of Futures Contracts

• You think gold will appreciate during the year:

Buy 100 oz. of gold @ 1662 $/oz in Dec.

• You will receive GBP in March but want USD:

Sell £62,500 @ 1.661 US$/£ in March

• You are an oil producer and want to hedge:

Sell 1,000 bbl. of oil @ 92 $/bbl in April

• You are a soybean buyer looking to lock your

input costs:

Buy 1mm bushels of soybean in 6m


Futures/Forwards vs. Options

• A futures/forward

contract gives the

holder the

obligation to buy

or sell at a certain

price

• An option contract

gives the holder

the right to buy or

sell at a certain

price


Who Trades Derivatives?

• Hedgers use derivatives to mitigate the risk

they are already exposed to, coming from

their business or assets/liabilities

• Speculators use derivatives to express a

view – often with leverage – on a financial

sector/asset

• Arbitrageurs use derivatives to lock in a

specific payout for a risk-free profit


Hedging Examples (pages 10-12)

• A US company will pay £10 million for imports

from Britain in 3 months and decides to

hedge using a long position in a forward

contract

• An investor owns 1,000 Microsoft shares

currently worth $26.88 per share. A two-

month put with a strike price of $27.00 costs

$1. The investor decides to hedge by buying

10 contracts


Speculation Example

• You have $2,000 to invest

• You believe that a stock price will increase

over the next 2 months

• The current stock price is $20

• The price of a 2-month call option with a

strike of 22.50 is $1

• What are the alternative strategies?


Arbitrage Example

• A stock price is quoted both in London and in

New York. The prices are:

– £100 in London

– $155 in New York

• The current exchange rate is 1.6100

• (ask your self what are the units of that figure)

• Is there an arbitrage opportunity?

• If so what is it?


Dangers

• Traders can switch from being hedgers to

speculators or from being arbitrageurs to

speculators

• It is important to set up controls to ensure that

trades are using derivatives in for their

intended purpose

• SocGen is an example of what can go wrong (see Hull, Business Snapshot 1.3 on page 17)


Hedge Funds (see Business Snapshot 1.2, page 11)

• Mutual Funds must

– disclose investment policies,

– makes shares redeemable at any time

– limit use of leverage

– take no short positions.

• Hedge Funds

– Are not subject to the same rules as mutual funds

– Cannot offer their securities publicly

– Use complex trading strategies are big users of

derivatives for hedging, speculation and arbitrage


Swaps

C le an up s lid e sC le an up s lid e s


Nature of Swaps

• A swap is an agreement to exchange

cash flows at specified future times

according to certain specified rules – Typically swaps have two legs as there are two

parties…swapping cash flows

Counterparty

A

Counterparty

B

Cash flow

Cash flow


Vanilla Interest Rate Swap

• An agreement to swap fixed rate cash flows

for floating cash flows over a specified period

of time

– Tenor

• determines how often payments are made

• In the US

– floating payments are generally every 3 months

– Fixed payments are made every 6 months

– Floating cash flows reference a “trusted”

benchmark rate – e.g. LIBOR

• Generally the reference rate is fixed at the beginning of

a period and paid at the end


E.g. “Plain Vanilla” Int. Rate Swap

• An agreement by Microsoft to

– receive 6-month LIBOR

– pay a fixed rate of 5% per annum every 6 months

– Start date: 5 March 2012,

– Maturity: 5 March 2015

– Notional: $100m

• Next slide illustrates* cash flows that could

occur

* illustrative trade, day count conventions are not

considered, payment frequency not typical


A Possible Outcome for Cash Flows

Date LIBOR Floating Cash

Flow

Fixed Cash

Flow

Net Cash

Flow

Mar 5, 2012 4.20%

Sep 5, 2012 4.80% +2.10 −2.50 −0.40

Mar 5, 2013 5.30% +2.40 −2.50 −0.10

Sep 5, 2013 5.50% +2.65 −2.50 + 0.15

Mar 5, 2014 5.60% +2.75 −2.50 +0.25

Sep 5, 2014 5.90% +2.80 −2.50 +0.30

Mar 5, 2015 +2.95 −2.50 +0.45


Typical Uses of an Int. Rate Swap

• Converting a liability from

– fixed rate to floating rate

– floating rate to fixed rate

• Converting an investment from

– fixed rate to floating rate

– floating rate to fixed rate


Swap Fixed for Floating

• You enter an interest rate swap

– Notional: 100m

– Maturity: 5 March 2015

– Semi-annual payments

– Pay Fixed: 5%

– Receive Floating: 6 Month USD LIBOR

5 March

2013

5 Sep

2013

5 March

2014

5 Sep

2014

5 March

2015

2.5% 2.5% 2.5% 2.5% 2.5%

6M LIBOR 6M LIBOR 6M LIBOR 6M LIBOR 6M LIBOR


Other types of swaps

• Credit Default Swaps (CDS)

• Currency Swaps

• Commodity Swaps

• Mortgage Swaps

• Equity Swaps (on price or dividends)

• Variance Swaps

• etc.


Options

C le an up s lid e sC le an up s lid e s


Basic Option Terminology

An option gives the holder the

right but not the obligation to

buy(sell) the underlying asset

at some time or times in the

future.


Underlying Assets

• Stocks

• Currencies

• Stock Indices (not indexes)

• Futures

• Commodities (individual and index)

• Interest Rates (swaptions)

• Credit products (credit default swaptions)

• etc.


Option Types

• A Call option is

an option to buy

a certain asset by

a certain date for

a certain price

(the strike price)

• A Put option is an

option to sell

a certain asset by

a certain date for

a certain price

(the strike price)


Options Style

• An American

option can be

exercised at

any time

during its life

• A European

option can be

exercised only

at maturity

A Bermudan option can be

exercised only at fixed times

before maturity (e.g. monthly)


Option Contracts Specs

• Expiration date

• Strike price (or Exercise price)

• European or American (option style)

• Call or Put (option class or type)

• Delivery details

– Cash or Physical delivery


Mechanics of Options

Markets


Payoff Diagrams

• A common technique for understanding

options is to draw a payoff diagram

• This will usually show the value of the option

at expiry

• Note – you will see payoff diagrams that

deduct the the premium paid from the payoff

– Many diagrams in the Hull book do this

– Generally this is frowned upon in the industry,

because you are adding values at different times

– The following slides will chart just payoffs


Long Call Option

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10

Payo

ff

Terminal Asset Price

Payoff for a European Call option with a strike of $5

𝑃𝑎𝑦𝑜𝑓𝑓 = 𝑀𝑎𝑥[0, 𝑆𝑇 − 𝐾]


Short Call Option

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5 6 7 8 9 10

Payo

ff


Payoff for a European Call option with a strike of $5

𝑃𝑎𝑦𝑜𝑓𝑓 = −𝑀𝑎𝑥[0, 𝑆𝑇 − 𝐾]


Long Put Option

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10

Payo

ff


Payoff for a European Put option with a strike of $5

𝑃𝑎𝑦𝑜𝑓𝑓 = 𝑀𝑎𝑥[0, 𝐾 − 𝑆𝑇]


Short Put Option

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5 6 7 8 9 10

Payo

ff


Payoff for a European Put option with a strike of $5

𝑃𝑎𝑦𝑜𝑓𝑓 = −𝑀𝑎𝑥[0, 𝐾 − 𝑆𝑇]

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