LEARNING OBJECTIVES Explain the nature of options and the

21 DERIVATIVES

Glen Arnold: Corporate Financial Management, Second edition© Pearson Education Limited 2002

OHT 21.1

LEARNING OBJECTIVES

• Explain the nature of options and the distinction between different kinds of options, and demonstrate their application in a wide variety of areas

• Show the value of the forwards, futures, FRAs, swaps, caps and floors markets by demonstrating transactions which manage and transfer risk

21 DERIVATIVES


OHT 21.2

DERIVATIVES• A derivative instrument is an asset whose

performance is based on (derived from) the behaviour of the value of an underlying asset

• “Underlyings”– Commodities– Shares– Bonds– Share indices– Currencies– Interest rates

Derivatives are contracts that give the holder the right, and sometimes the obligation, to buy or sell a quantity of the underlying, …

…. or benefit in another way from a rise or fall in the value of the underlying.

21 DERIVATIVES


OHT 21.3

It is the legal right that becomes an asset, with its own value.

It is the right that is purchased or sold.

Derivative instruments include the following:

– Futures– Options– Swaps– Forward rate agreements– Forwards

Derivatives can be used to:– Speculate– Hedge– Arbitrage

21 DERIVATIVES


OHT 21.4

OPTIONS

An option is a contract giving one party the right, but not the obligation, to buy or sell a financial instrument, commodity or some other underlying asset at a given price, at or before a specified date.

For example, property development options

Share options• A call option gives the purchaser a right, but not the obligation, to buy a fixed number of shares at a specified price at some time in the future• On LIFFE, one option contract relates to a quantity of 1,000 shares• The seller of the option, who receives the premium, is referred to as the writer• American-style options can be exercised by the buyer at any time up to the expiry date• European-style options can only be exercised on a predetermined future date

21 DERIVATIVES


OHT 21.5

CALL OPTION HOLDER (CALL OPTION BUYER)

Cadbury Schweppes

Intrinsic value – the payoff that would be received if the underlying is at its current level when the option

expires

Time value – the amount by which option premium exceeds the intrinsic value

In-the-money-option – an option with intrinsic value

Out-of-the-money-option – an option with no intrinsic value

At-the-money-option – market price equal to option exercise price

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OHT 21.6

21 DERIVATIVES


OHT 21.7

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OHT 21.8

CALL OPTION WRITERS

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OHT 21.9

PUT OPTIONSA put option gives the holder the right, but not the obligation, to sell a specific quantity of shares on or before a specified date at a fixed exercise price.

Cadbury SchweppesPurchase, for a premium of 19.5p per share (£195 in total), the right to sell 1,000 shares on or before late January 2002 at 460p.

21 DERIVATIVES


OHT 21.10

USING SHARE OPTIONS TO REDUCE RISK: HEDGING

Options can give protection against unfavourable movements in the underlying while permitting the possibility of benefiting from favourable movements

Example:You hold 1,000 shares in Cadbury Schweppes on 13 Aug. 2001, worth £4,820 (482p per share)

Possible takeover bid

Or dramatic price fall

Sell shares? - loss of possible upside

Alternative: Buy put option - a 460 April put purchased, premium £280

21 DERIVATIVES


OHT 21.11

If share price falls to 380p in late April:Loss on underlying shares £1,020Intrinsic value of put option £800

((460-380) x 1000)

Below 460p for every 1p lost in share price 1p is gained on the put option.

Maximum loss is £500 (£220 intrinsic value + £280 option premium)

Hedging reduces the dispersion of possible outcomes. There is a floor below which losses cannot increase, while on the upside the benefit is reduced due to premium.

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OHT 21.12

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OHT 21.13

INDEX OPTIONS

• Options on whole share indices can be purchased• Index options are cash settled• The index is regarded as a price and each one-point movement on the index represents £10

HEDGING AGAINST A DECLINE IN THE MARKETA fund manager controlling a £30m portfolio of shares.Concerned the market might fall.

Number of options needed to hedge:With the index at 5431 on 13 August 2001 and each point of that index settled at £10, one contract has a value of 5431 £10 = £54,310

To cover a £30m portfolio: £30m£54,310 = 552 contracts

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OHT 21.14

Buy 552 December 5425 puts for 229 points per contract.

Premium:

229 points £10 552 = £1,264,080

(4.2% premium)

The index falls 15% to 4616, and the loss on the portfolio is:

£30m 0.15 = £4,500,000

Gain on options:

(5425 – 4616) 552 £10 = £4,465,680

Less option premium paid £1,264,080 £3,201,600

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OHT 21.15

CORPORATE USES OF OPTIONS

1 Share options schemes

2 Warrants

3 Convertible bonds

4 Rights issues

5 Share underwriting

6 Commodities

21 DERIVATIVES


OHT 21.16

OPERATIONAL AND STRATEGIC DECISIONS WITH OPTIONS (REAL OPTIONS)

• The expansion option• The option to abandon• Option on timing

True NPVTrue NPV takes into account the value of options.True NPV = Crude NPV +

+ + +

NPV ofexpansionoption

NPVof the

option toabandon

NPV oftimingoption

NPV ofotheroption

possibilities

21 DERIVATIVES


OHT 21.17

FORWARDS AND FUTURES CONTRACTS

ForwardsA forward contract is an agreement between two parties to undertake an exchange at an agreed future date at a price agreed now.

Example: potato crisp manufacturer

Futures• Agreements between two parties to undertake a transaction at an agreed price on a specified future date• Exchange-based instruments traded on a regulated exchange• The clearing house becomes the formal counterparty to every transaction• Standardised legal agreements traded in highly liquid markets

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OHT 21.18

FORWARDS AND FUTURES CONTRACTS

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OHT 21.19

MARKING TO MARKET AND MARGINS• Daily marking to market• Member’s margin account• Initial margin• Maintenance margin• Variation margin

Day

£ Monday Tuesday Wednesday Thursday Friday

Value of future(based on daily closing price) 50,000 49,000 44,000 50,000 55,000

Buyers’ positionInitial margin 5,000Variation margin (+ credited) 0 –1,000 –5,000 +6,000 +5,000

(– debited)Accumulated profit (loss) 0 –1,000 –6,000 0 +5,000

Sellers’ positionInitial margin 5,000Variation margin (+ credited) 0 +1,000 +5,000 –6,000 –5,000

(– debited)Accumulated profit (loss) 0 +1,000 +6,000 0 –5,000

Exhibit 21.16 Example of initial margin and marking to market

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OHT 21.20

• Leverage

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OHT 21.21

• Settlement:

Physical delivery

Cash

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OHT 21.22

SHORT-TERM INTEREST RATE FUTURES

Notional fixed-term deposits, usually for three-month periods starting at a specific time in the future.• The buyer of one contract is buying the right to deposit money at a particular rate of interest for three months at least notionally.

21 DERIVATIVES


OHT 21.23

The unit of trading for a three-month sterling time deposit is £500,000.Cash delivery is the means of settlement. Delivery defines the date and time of the expiry of the contact – September, December, March and June.Price is defined as:

P = 100 – iwhere:

P = price index;i = the future interest rate in percentage terms.

TickA tick is the minimum price movement on a future.On a three-month sterling interest rate contract a tick is a movement of 0.01 per cent on a trading unit of £500,000.£12.50 is the value of a tick movement in a three-month sterling interest rate futures contract.

SHORT-TERM INTEREST RATE FUTURES

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OHT 21.24

FORWARD RATE AGREEMENTS (FRAs)

Agreements about the future level of interest rates.

The rate of interest at some point in the future is compared with the level agreed when the FRA was established and compensation is paid by one party to the other based on the difference.

Certainty over the effective interest cost of borrowing is generated in the future if an FRA is bought.

The sale of an FRA by a company protects against a fall in interest rates.

21 DERIVATIVES


OHT 21.25

FRA Example:

A company needs to borrow £6m in six months’ time for a period of one year

• It arranges this with bank X• The current rate of interest is 7%• Concern: interest rates will be higher when

the loan is drawn down

• Purchase FRA at 7% from bank Y to take effect 6 months from now and relate to 12 month loan

• Six months later:Spot interest rates for 1 year borrowing = 8.5%Payment to bank X: £6m 0.085 = £510,000(£90,000 more than if rate is 7%)Bank Y pays (0.085-0.07) £6m = £90,000

If rates fall below 7% company compensates Bank Y.A “sale” of an FRA: protects against a fall in rates.

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OHT 21.26

Exhibit 21.22 A comparison of options, futures and

forward rate agreementsOptions Futures FRAs

Advantages

Downside risk is limited but Specific rates are locked in. No margins or premiums the buyer is able to participate No right to let the contractin favourable movements. lapse, as with options.

Available on or off exchanges. No premium is payable. (However Tailor-made, not standardised asExchange regulation and clearing margin payments are required.) to size, duration and terms.house reduce counterparty default risk for those options traded on exchanges.

Usually highly liquid markets. Very liquid markets. Able to Can create certainty. Locks inreverse transactions quickly specific effective interest rate.and cheaply.

May be useful if no strong view Exchange regulation and clearingis held on direction of underlying. house reduce counterparty

default risk.

Disadvantages

Premium payable reduces returns. If the underlying transaction does Benefits from favourable not materialise, potential loss is movements in rates are forgone.unlimited.

Margin required on written Many exchange restrictions Greater risk of counterparty options. on size, duration, trading times. default – not exchange traded.

Margin calls require daily work More difficult to liquidate.for ‘back office’.

payable.

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OHT 21.27

CAPSAn interest cap is a contract that gives the purchaser the right to effectively set maximum level for interest rates payable.Compensation is paid to the purchaser of a cap if interest rates rise above an agreed level.

Example:• Oakham borrows £20m for 5 years from Bank A at

variable interest rate Libor + 1.5% (interest reset every 3 months – currently 7%)

• Concern: interest rates riseBuys an interest rate cap set at Libor of 8.5%

• Cost, say 2.3% payable now for 5 year cover (£20m x 0.023=£460,000)

• 3rd Year: Libor = 9.5%• Oakham pays to Bank A 9.5+1.5%

Receives 1% from cap seller

If rates fall Oakham benefits

Floors and collarsIf the interest rate falls below an agreed level, the seller (the floor writer) makes compensatory payments to the floor buyer.

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OHT 21.28

SWAPS

A swap is an exchange of cash payment obligations.

Cat plc and Dog plc• Cat plc and Dog plc both want to borrow £150m for eight years• Cat would like to borrow on a fixed-rate basis because this would better match its asset position• Dog prefers to borrow at floating rates because of optimism about future interest- rate falls• Cat could obtain fixed-rate borrowing at 10 per cent and floating rate at Libor +2 per cent• Dog is able to borrow at 8 per cent fixed and Libor +1 per cent floating:

Fixed FloatingCat can borrow at 10% Libor +2%Dog can borrow at 8% Libor +1%

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OHT 21.29

SWAPS CAT AND DOG

Exhibit 21.23 An interest rate swap

Cat:Pays Libor +2%Receives Libor +2%Pays Fixed 9.5%Net payment Fixed 9.5%

Dog:Pays Fixed 8%Receives Fixed 9.5%Pays Libor +2%Net payment Libor +0.5%

Fixed 8%

Cat Dog

Bank BBank A

Libor +2%

Libor +2%

Fixed 9.5%

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OHT 21.30

DERIVATIVES USERS

• Hedgers

To hedge is to enter into transactions which protect a business or assets against changes in some underlying

• Speculators

Speculators take a position in financial instruments and other assets with a view to obtaining a profit on changes in value.

• Arbitrageurs

The act of arbitrage is to exploit price differences on the same instrument or similar assets

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OHT 21.31

OVER-THE-COUNTER (OTC) AND EXCHANGE-TRADED DERIVATIVES

Exhibit 21.25 OTC and exchange-traded derivatives

Advantages OTC derivative

Contracts can be tailor -made, which allows perfect hedging and permits hedges ofmore unusual underlyings.

Disadvantages

Ther e is a risk (credit risk) that the counterparty will fail to honour the transaction.

Often difficult to reverse a hedge once the agreement has been made.

Higher transaction costs.

Advantages Exchange-traded derivative

Credit risk is reduced because the clearing house is counterparty.

High regulation encourages transpar ency and openness on the price of recent trades.

Liquidity is usually much higher than for OTC – large orders can be cleared quicklydue to high daily volume of trade.

Positions can be reversed by closing quickly – an equal and opposite transaction iscompleted in minutes.

Disadvantages

Standardisation may be restrictive, e.g. standardised terms for quality of underlying,quantity, delivery dates.

The limited trading hours and margin requirements may be inconvenient.

Low level of market regulation with resultant loss of transparency and price dissemination.

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OHT 21.32

OPTION PRICINGNotation to be used: C = value of call option S = current market price of share X = future exercise price Rf = risk-free interest rate (per annum) T = time to expiry (in years)= standard deviation of the share price E = mathematical fixed constants: 2.718....

• Options have a minimum value of zero C 0• The market value of an option will be greater than the intrinsic value at any time prior to expiry Market value = intrinsic value + time value• Intrinsic value (S – X) rises as share price increases or exercise price falls

X (1 + rf)t

• The higher the risk-free rate of return the higher will be intrinsic value• The maximum value of an option is the price of the share C < S• A major influence boosting the time value is the volatility of the underlying share price

Intrinsic value = S –

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OHT 21.33

BLACK AND SCHOLES’ OPTION PRICING MODEL

C = SN(d1) – X er

t

where:N (.) = cumulative normal distribution function of d1 and d2;

ln(S/X) + (rf + 2/2)t

t ln = natural log

d2 = d1 – t

N (d2)

d1 =

f

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