Ways Derivatives are Used To hedge risks 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 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Foreign Exchange Quotes for GBP, July 20, 2007 (See page 4) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull BidOffer Spot month forward month forward month forward

Forward Price The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) The forward price may be different for contracts of different maturities Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Terminology The party that has agreed to buy has what is termed a long position The party that has agreed to sell has what is termed a short position Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Example (page 4) On July 20, 2007 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of This obligates the corporation to pay $2,048,900 for £1 million on January 20, 2008 What are the possible outcomes? Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Profit from a Long Forward Position Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Profit Price of Underlying at Maturity, S T K

Profit from a Short Forward Position Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Profit Price of Underlying at Maturity, S T K

Futures Contracts (page 6) Agreement to buy or sell an asset for a certain price at a certain time Similar to forward contract Whereas a forward contract is traded OTC, a futures contract is traded on an exchange Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Exchanges Trading Futures Chicago Board of Trade Chicago Mercantile Exchange LIFFE (London) Eurex (Europe) BM&F (Sao Paulo, Brazil) TIFFE (Tokyo) and many more (see list at end of book) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Examples of Futures Contracts Agreement to: Buy 100 oz. of US$900/oz. in December (NYMEX) Sell US$/£ in March (CME) Sell 1,000 bbl. of US$120/bbl. in April (NYMEX) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

1. Gold: An Arbitrage Opportunity? Suppose that: The spot price of gold is US$900 The 1-year forward price of gold is US$1,020 The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity? Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

2. Gold: Another Arbitrage Opportunity? Suppose that: - The spot price of gold is US$900 - The 1-year forward price of gold is US$900 - The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity? Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

The Forward Price of Gold If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then F = S (1+r ) T where r is the 1-year (domestic currency) risk-free rate of interest. In our examples, S = 900, T = 1, and r =0.05 so that F = 900(1+0.05) = 945 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Example of a Futures Trade (page 26-28) An investor takes a long position in 2 December gold futures contracts on June 5 contract size is 100 oz. futures price is US$600 margin requirement is US$2,000/contract (US$4,000 in total) maintenance margin is US$1,500/contract (US$3,000 in total) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

A Possible Outcome Table 2.1, Page 28 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull DailyCumulativeMargin FuturesGain AccountMargin Price(Loss) BalanceCall Day(US$) ,000 5-Jun597.00(600) 3, Jun593.30(420) (1,340) 2,6601, Jun587.00(1,140) (2,600) 2,7401, Jun (1,540) 5, = 4,000 3,000 + = 4,000 <

A Possible Outcome Table 2.1, Page 28 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull DailyCumulativeMargin FuturesGain AccountMargin Price(Loss) BalanceCall Day(US$) ,000 5-Jun597.00(600) 3, Jun593.30(420) (1,340) 2,6601, Jun587.00(1,140) (2,600) 2,7401, Jun (1,540) 5, = 4,000 3,000 + = 4,000 <

Convergence of Futures to Spot (Figure 2.1, page 26) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Time (a)(b) Futures Price Futures Price Spot Price

Forward Contracts vs Futures Contracts Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Contract usually closed out TABLE 2.3 (p. 39) Private contract between 2 partiesExchange traded Non-standard contractStandard contract Usually 1 specified delivery dateRange of delivery dates Settled at end of contractSettled daily Delivery or final cash settlement usually occursprior to maturity FORWARDSFUTURES Some credit risk Virtually no credit risk

Hedging Strategies Using Futures Chapter 3 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Long & Short Hedges A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future and want to lock in the price Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Arguments in Favor of Hedging Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Arguments against Hedging Shareholders are usually well diversified and can make their own hedging decisions It may increase risk to hedge when competitors do not Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Convergence of Futures to Spot (Hedge initiated at time t 1 and closed out at time t 2 ) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Time Spot Price Futures Price t1t1 t2t2

Basis Risk Basis is the difference between the spot and futures price Basis risk arises because of the uncertainty about the basis when the hedge is closed out Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Long Hedge We define F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price If you hedge the future purchase of an asset by entering into a long futures contract then Cost of Asset= S 2 – (F 2 – F 1 ) = F 1 + Basis Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Short Hedge Again we define F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price If you hedge the future sale of an asset by entering into a short futures contract then Price Realized= S 2 + (F 1 – F 2 ) = F 1 + Basis Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Choice of Contract Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging. Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Swaps Chapter 7 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

An Example of a “Plain Vanilla” Interest Rate Swap An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million Next slide illustrates cash flows that could occur Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Cash Flows to Microsoft (See Table 7.1, page 149) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Millions of Dollars LIBORFLOATINGFIXEDNet DateRateCash Flow Mar.5, % Sept. 5, %+2.10–2.50–0.40 Mar.5, %+2.40–2.50–0.10 Sept. 5, %+2.65– Mar.5, %+2.75– Sept. 5, %+2.80– Mar.5, %+2.95–

Typical Uses of an Interest 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 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Intel and Microsoft (MS) Transform a Liability (Figure 7.2, page 150) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull IntelMS LIBOR 5% LIBOR+0.1% 5.2%

Financial Institution is Involved (Figure 7.4, page 151) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull F.I. LIBOR LIBOR+0.1 % 4.985% 5.015% 5.2% IntelMS Financial Institution has two offsetting swaps

Intel and Microsoft (MS) Transform an Asset ( Figure 7.3, page 151) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Intel MS LIBOR 5% LIBOR-0.2% 4.7%

Financial Institution is Involved (See Figure 7.5, page 152) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Intel F.I.MS LIBOR 4.7% 5.015%4.985% LIBOR-0.2%

Valuation of an Interest Rate Swap That Is Not New Interest rate swaps can be valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bond Alternatively, they can be valued as a portfolio of forward rate agreements (FRAs) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Valuation in Terms of Bonds The fixed rate bond is valued in the usual way The floating rate bond is valued by noting that it is worth par immediately after the next payment date Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Valuation in Terms of FRAs Each exchange of payments in an interest rate swap is an FRA The FRAs can be valued on the assumption that today’s forward rates are realized Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

An Example of a Currency Swap An agreement to pay 5% on a sterling principal of £10,000,000 & receive 6% on a US$ principal of $18,000,000 every year for 5 years Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Exchange of Principal In an interest rate swap the principal is not exchanged In a currency swap the principal is usually exchanged at the beginning and the end of the swap’s life Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

The Cash Flows (Table 7.7, page 164) Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull Year DollarsPounds $ millions – – – – – −10.50 £

Typical Uses of a Currency Swap Conversion from a liability in one currency to a liability in another currency Conversion from an investment in one currency to an investment in another currency Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Valuation of Currency Swaps Like interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contracts Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Swaps & Forwards A swap can be regarded as a convenient way of packaging forward contracts Although the swap contract is usually worth zero at the outset, each of the underlying forward contracts are not worth zero Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull