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21 DERIVATIVES OHT 21. 1 LEARNING OBJECTIVES • Explain the nature of options and 21 DERIVATIVES 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 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 2 DERIVATIVES • A derivative instrument is an asset whose 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. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 3 It is the legal right that becomes an asset, 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 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 4 OPTIONS An option is a contract giving one party 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 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 5 CALL OPTION HOLDER (CALL OPTION BUYER) Cadbury Schweppes Intrinsic 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 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 21 DERIVATIVES Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 OHT 21. 6

21 DERIVATIVES Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 21 DERIVATIVES Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 OHT 21. 7

21 DERIVATIVES CALL OPTION WRITERS Glen Arnold: Corporate Financial Management, Second edition © Pearson 21 DERIVATIVES CALL OPTION WRITERS Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 OHT 21. 8

21 DERIVATIVES OHT 21. 9 PUT OPTIONS A put option gives the holder the 21 DERIVATIVES OHT 21. 9 PUT OPTIONS A 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 Schweppes Purchase, for a premium of 19. 5 p per share (£ 195 in total), the right to sell 1, 000 shares on or before late January 2002 at 460 p. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 10 USING SHARE OPTIONS TO REDUCE RISK: HEDGING Options can 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 (482 p 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 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 11 If share price falls to 380 p in late 21 DERIVATIVES OHT 21. 11 If share price falls to 380 p in late April: Loss on underlying shares £ 1, 020 Intrinsic value of put option £ 800 ((460 -380) x 1000) Below 460 p for every 1 p lost in share price 1 p 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. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 21 DERIVATIVES Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 OHT 21. 12

21 DERIVATIVES OHT 21. 13 INDEX OPTIONS • Options on whole share indices can 21 DERIVATIVES 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 MARKET A fund manager controlling a £ 30 m 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 £ 30 m portfolio: £ 30 m £ 54, 310 = 552 contracts Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

OHT 21. 14 21 DERIVATIVES Buy 552 December 5425 puts for 229 points per OHT 21. 14 21 DERIVATIVES 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: £ 30 m 0. 15 = £ 4, 500, 000 Gain on options: (5425 – 4616) 552 £ 10 = Less option premium paid £ 4, 465, 680 £ 1, 264, 080 £ 3, 201, 600 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 15 CORPORATE USES OF OPTIONS 1 Share options schemes 2 21 DERIVATIVES OHT 21. 15 CORPORATE USES OF OPTIONS 1 Share options schemes 2 Warrants 3 Convertible bonds 4 Rights issues 5 Share underwriting 6 Commodities Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 16 OPERATIONAL AND STRATEGIC DECISIONS WITH OPTIONS (REAL OPTIONS) • 21 DERIVATIVES OHT 21. 16 OPERATIONAL AND STRATEGIC DECISIONS WITH OPTIONS (REAL OPTIONS) • The expansion option • The option to abandon • Option on timing True NPV takes into account the value of options. True NPV = Crude NPV + NPV of expansion option + NPV of of the timing other option to option abandon possibilities Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 17 FORWARDS AND FUTURES CONTRACTS Forwards A forward contract is 21 DERIVATIVES OHT 21. 17 FORWARDS AND FUTURES CONTRACTS Forwards A 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 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES FORWARDS AND FUTURES CONTRACTS Glen Arnold: Corporate Financial Management, Second edition © 21 DERIVATIVES FORWARDS AND FUTURES CONTRACTS Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 OHT 21. 18

OHT 21. 19 21 DERIVATIVES MARKING TO MARKET AND MARGINS • • • Daily OHT 21. 19 21 DERIVATIVES MARKING TO MARKET AND MARGINS • • • Daily marking to market Member’s margin account Initial margin Maintenance margin Variation margin Day £ Monday Value of future (based on daily closing price) Buyers’ position Initial margin Variation margin (+ credited) (– debited) Accumulated profit (loss) Sellers’ position Initial margin Variation margin (+ credited) (– debited) Accumulated profit (loss) Tuesday Wednesday Thursday Friday 50, 000 49, 000 44, 000 50, 000 55, 000 0 – 1, 000 – 5, 000 +6, 000 +5, 000 0 – 1, 000 – 6, 000 0 +5, 000 0 +1, 000 +5, 000 – 6, 000 – 5, 000 0 +1, 000 +6, 000 0 – 5, 000 Exhibit 21. 16 Example of initial margin and marking to market Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES • Leverage Glen Arnold: Corporate Financial Management, Second edition © Pearson Education 21 DERIVATIVES • Leverage Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 OHT 21. 20

21 DERIVATIVES • Settlement: Physical delivery Cash Glen Arnold: Corporate Financial Management, Second edition 21 DERIVATIVES • Settlement: Physical delivery Cash Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002 OHT 21. 21

21 DERIVATIVES OHT 21. 22 SHORT-TERM INTEREST RATE FUTURES Notional fixed-term deposits, usually for 21 DERIVATIVES 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. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 23 SHORT-TERM INTEREST RATE FUTURES The unit of trading for 21 DERIVATIVES OHT 21. 23 SHORT-TERM INTEREST RATE FUTURES 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 – i where: P = price index; i = the future interest rate in percentage terms. Tick A 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. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 24 FORWARD RATE AGREEMENTS (FRAs) Agreements about the future level 21 DERIVATIVES 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. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 25 FRA Example: A company needs to borrow £ 6 21 DERIVATIVES OHT 21. 25 FRA Example: A company needs to borrow £ 6 m 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: £ 6 m 0. 085 = £ 510, 000 (£ 90, 000 more than if rate is 7%) Bank Y pays (0. 085 -0. 07) £ 6 m = £ 90, 000 If rates fall below 7% company compensates Bank Y. A “sale” of an FRA: protects against a fall in rates. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

OHT 21. 26 21 DERIVATIVES A comparison of options, futures and forward rate agreements OHT 21. 26 21 DERIVATIVES A comparison of options, futures and forward rate agreements Exhibit 21. 22 Options Futures FRAs Downside risk is limited but the buyer is able to participate in favourable movements. Specific rates are locked in. No right to let the contract lapse, as with options. No margins or premiums payable. Available on or off exchanges. Exchange regulation and clearing house reduce counterparty default risk for those options traded on exchanges. No premium is payable. (However margin payments are required. ) Tailor-made, not standardised as to size, duration and terms. Usually highly liquid markets. Very liquid markets. Able to reverse transactions quickly and cheaply. Can create certainty. Locks in specific effective interest rate. May be useful if no strong view is held on direction of underlying. Exchange regulation and clearing house reduce counterparty default risk. Advantages Disadvantages Premium payable reduces returns. If the underlying transaction does not materialise, potential loss is unlimited. Benefits from favourable movements in rates are forgone. Margin r equired on written options. Many exchange restrictions on size, duration, trading times. Greater risk of counterparty default – not exchange traded. Margin calls require daily work for ‘back office’. More difficult to liquidate. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 27 CAPS An interest cap is a contract that gives 21 DERIVATIVES OHT 21. 27 CAPS An 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 £ 20 m for 5 years from Bank A at variable interest rate Libor + 1. 5% (interest reset every 3 months – currently 7%) • Concern: interest rates rise Buys an interest rate cap set at Libor of 8. 5% • Cost, say 2. 3% payable now for 5 year cover (£ 20 m x 0. 023=£ 460, 000) • 3 rd 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 collars If the interest rate falls below an agreed level, the seller (the floor writer) makes compensatory payments to the floor buyer. Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 28 SWAPS A swap is an exchange of cash payment 21 DERIVATIVES 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 £ 150 m 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 interestrate 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 Floating Cat can borrow at 10% Libor +2% Dog can borrow at 8% Libor +1% Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

OHT 21. 29 21 DERIVATIVES SWAPS CAT AND DOG Fixed 9. 5% Cat Dog OHT 21. 29 21 DERIVATIVES SWAPS CAT AND DOG Fixed 9. 5% Cat Dog Libor +2% Bank A Fixed 8% Bank B Exhibit 21. 23 An interest rate swap Cat: Pays Receives Pays Net payment Libor +2% Fixed 9. 5% Dog: Pays Fixed 8% Receives Fixed 9. 5% Pays Libor +2% Net payment Libor +0. 5% Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 30 DERIVATIVES USERS • Hedgers To hedge is to enter 21 DERIVATIVES 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 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 Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

OHT 21. 31 21 DERIVATIVES OVER-THE-COUNTER (OTC) AND EXCHANGE-TRADED DERIVATIVES Advantages OTC derivative Contracts OHT 21. 31 21 DERIVATIVES OVER-THE-COUNTER (OTC) AND EXCHANGE-TRADED DERIVATIVES Advantages OTC derivative Contracts can be tailor -made, which allows perfect hedging and permits hedges of more unusual underlyings. Disadvantages Ther e is a risk (credit risk) that the counterparty will fail to honour the transaction. Low level of market regulation with resultant loss of transparency and price dissemination. 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 transparency and openness on the price of recent trades. Liquidity is usually much higher than for OTC – large orders can be cleared quickly due to high daily volume of trade. Positions can be reversed by closing quickly – an equal and opposite transaction is completed 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. Exhibit 21. 25 OTC and exchange-traded derivatives Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002

21 DERIVATIVES OHT 21. 32 OPTION PRICING Notation to be used: C = value 21 DERIVATIVES OHT 21. 32 OPTION PRICING Notation 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 C³ 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 Intrinsic value = S – (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

OHT 21. 33 21 DERIVATIVES BLACK AND SCHOLES’ OPTION PRICING MODEL C = SN(d OHT 21. 33 21 DERIVATIVES BLACK AND SCHOLES’ OPTION PRICING MODEL C = SN(d 1) – X N (d ) 2 erf t where: N (. ) = cumulative normal distribution function of d 1 and d 2; d 1 = ln(S/X) + (rf + 2/2)t t ln = natural log d 2 = d 1 – t Glen Arnold: Corporate Financial Management, Second edition © Pearson Education Limited 2002