© 2008 Pearson Education Canada13.1 Chapter 13 Hedging with Financial Derivatives

© 2008 Pearson Education Canada13.2Hedging Hedge - engage in a financial transaction that reduces or eliminates risk Long position - taking a position associated with the purchase of an asset Short position – taking a position associated with the sale of an asset

© 2008 Pearson Education Canada13.3 Hedging (Cont’d) Basic hedging principle: Hedging risk involves engaging in a financial transaction that offsets a long position by taking a additional short position, or offsets a short position by taking a additional long position

© 2008 Pearson Education Canada13.4 Forward Markets A forward contract is an agreement (at time 0) between a buyer and a seller that an asset will be exchanged for cash at some later date at a price agreed upon now

© 2008 Pearson Education Canada13.5 Interest Rate Forward Contracts An interest rate forward contract involves the future sale (purchase) of a debt instrument and has several dimensions: 1.Specification of the debt instrument 2.Amount of the instrument to be delivered 3.The price (interest rate) on the instrument when it is delivered 4.The date when delivery takes place

© 2008 Pearson Education Canada13.6 Interest-Rate Forward Markets Long position = agree to buy securities at future date Hedges by locking in future interest rate if funds coming in future Short position = agree to sell securities at future date Hedges by reducing price risk from change in interest rates if holding bonds

© 2008 Pearson Education Canada13.7 Interest-Rate Forward Markets (Cont’d) Pros 1.Flexible (can be used to hedge completely the interest rate risk) Cons 1.Lack of liquidity: hard to find a counterparty to make a contract with 2.Subject to default risk: requires information to screen good from bad risk

© 2008 Pearson Education Canada13.8 Financial Futures Markets Financial futures are classified as Interest-rate futures Stock index futures, and Currency futures

© 2008 Pearson Education Canada13.9 Interest Rate Futures Markets (Cont’d) Interest Rate Futures Contract 1.Specifies delivery of type of security at future date 2.Arbitrage  at expiration date, price of contract = price of the underlying asset delivered 3.i , long contract has loss, short contract has profit 4.Hedging similar to forwards

© 2008 Pearson Education Canada13.10 Interest Rate Futures Markets (Cont’d) At the expiration date of a futures contract, the price of the contract is the same as the price of the underlying asset to be delivered The elimination of riskless profit opportunities in the futures market is referred to as arbitrage A micro hedge occurs when the institution is hedging the interest rate for a specific asset it is holding A macro hedge is when the hedge is for the entire portfolio

© 2008 Pearson Education Canada13.11 Interest Rate Futures Markets Success of Futures Over Forwards 1.Futures more liquid: standardized, can be traded again, delivery of range of securities 2.Delivery of range of securities prevents corner 3.Mark to market: avoids default risk 4.Don’t have to deliver: netting

© 2008 Pearson Education Canada13.12 Stock Index Futures Contracts Stock index futures were designed to manage stock market risk and are now among the most widely traded of all futures contracts The S&P Index measures the value of 500 of the most widely traded stocks in the United States

© 2008 Pearson Education Canada13.13 Stock Index Futures Contracts (Cont’d) Stock index future contracts differ form most other types of financial futures contracts in that they are settled in cash delivery rather than delivery of a security Cash settlement gives a high degree of liquidity For a S&P 500 Index, contract, at the final settlement date, the cash delivery due is $250 times the Index

© 2008 Pearson Education Canada13.14 Stock Index Futures Contracts (Cont’d) If the Index is 1000 on the settlement date, $ is the amount due. The price quotes for the contract are also quoted in terms of index points, so a change of one point represents a change of $250 in the contract’s value

© 2008 Pearson Education Canada13.15 Stock Index Futures Contracts (Cont’d) Suppose on February 1 you sell one June contract at a price of 1000 ($ ) If the S&P falls to 900 on the expiration date, the buyer of the contract will have lost $ (loss of 100 $250 a point) Buyer agreed to pay $ (1000 x $250) for something currently valued at $ (900 x $250)

© 2008 Pearson Education Canada13.16 Stock Index Futures Contracts (Cont’d) The seller of the contract will profit $ (100 x $250) as you agreed to receive $ as the purchase price for the contract which is now valued at $ Because the amounts are payable/due are netted out, only $ changes hands as you the seller receive this amount from the buyer

© 2008 Pearson Education Canada13.17 Options A call option is an option that gives the owner the right (but not the obligation) to buy an asset at a pre specified exercise (or strike) price within a specified period of time. Since a call represents an option to buy, the purchase of a call is undertaken if the price of the underlying asset is expected to go up. The buyer of a call is said to be long in a call and the writer is said to be short in a call. The buyer of a call will have to pay a premium in order to get the writer to sign the contract and assume the risk.

© 2008 Pearson Education Canada13.18 Options (Cont’d) There are two types of option contracts: 1. American options that can be exercised any time up to the expiration date 2.European options that can be exercised only on the expiration date

© 2008 Pearson Education Canada13.19 The Payoff from Buying a Call To understand calls, let's assume that you hold a European call on an asset with an exercise price of X and a call premium of α. If at the expiration date, the price of the underlying asset, S, is less than X, the call will not be exercised, resulting in a loss of the premium. At a price above X, the call will be exercised. In particular, at a price between X and X + α, the gain would be insufficient to cover the cost of the premium, while at a price above X + α the call will yield a net profit. In fact, at a price above X + α, each $1 rise in the price of the asset will cause the profit of the call option to increase by $1.

© 2008 Pearson Education Canada13.20 The Payoff from Writing a Call The payoff function from writing the call option is the mirror image of the payoff function from buying the call. Note that the writer of the call receives the call premium, α, up front and must stand ready to sell the underlying asset to the buyer of the call at the exercise price, X, if the buyer exercises the option to buy.

© 2008 Pearson Education Canada13.21 Profits from Buying and Writing a Call Option

© 2008 Pearson Education Canada13.22 Summary and Generalization In general, the value of a call option, C, at expiration with asset price S (at that time) and exercise price X is C = max (0, S - X) In other words, the value of a call option (intrinsic value) at maturity is S - X, or zero, whichever is greater. If S > X, the call is said to be in the money, and the owner will exercise it for a net profit of C - α. If S < X, the call is said to be out of the money and will expire worthless. A call with S = X is said to be at the money (or trading at par).

© 2008 Pearson Education Canada13.23 Buying and Writing Puts A second type of option contract is the put option. It gives the owner the right (but not the obligation) to sell an asset to the option writer at a pre specified exercise price. As a put represents an option to sell rather than buy, it is worth buying a put when the price of the underlying asset is expected to fall. As with calls, the owner of a put is said to be long in a put and the writer of a put is said to be short in a put. Also, as with calls, the buyer of a put option will have to pay a premium (called the put premium) in order to get the writer to sign the contract and assume the risk.

© 2008 Pearson Education Canada13.24 The Payoff from Buying a Put Consider a put with an exercise price of X and a premium of β β. At a price of X or higher, the put will not be exercised, resulting in a loss of the premium. At a price below X - β, the put will yield a net profit. In fact, between X - β and X, the put will be exercised, but the gain is insufficient to cover the cost of the premium.

© 2008 Pearson Education Canada13.25 The Payoff from Writing a Put The payoff function from writing a put is the mirror image of that from buying a put. As with writing a call, the writer of a put receives the put premium, β, up front and must sell the asset underlying the option if the buyer of the put exercises the option to sell.

© 2008 Pearson Education Canada13.26 Profits From Buying and Writing a Put Option

© 2008 Pearson Education Canada13.27 Summary and Generalization In general, the value of a put option, P, at the expiration date with exercise price X and asset price S (at that time) is P = max (X - S, 0) That is, the value of a put at maturity is the difference between the exercise price of the option and the price of the asset underlying the option, X - S, or zero, whichever is greater. If S > X, the put is said to be out of the money and will expire worthless. If S < X, the put is said to be in the money and the owner will exercise it for a net profit of P - β. If S = X, the put is said to be at the money.

© 2008 Pearson Education Canada13.28 Futures Options

© 2008 Pearson Education Canada13.29 Factors Affecting Option Premium 1. Higher strike price  lower premium on call options and higher premium on put options 2.Greater term to expiration  higher premiums for both call and put options 3.Greater price volatility of underlying instrument  higher premiums for both call and put options

© 2008 Pearson Education Canada13.30 Interest Rate Swaps Interest-rate swaps involve the exchange of one set of interest payments for another set of interest payments, all denominated in the same currency

© 2008 Pearson Education Canada13.31 Interest Rate Swaps (Cont’d)

© 2008 Pearson Education Canada13.32 Advantages of Interest Rate Swaps Advantages of interest rate swaps 1.Reduce risk, no change in balance-sheet 2.Longer term than futures or options Disadvantages of interest rate swaps 1.Lack of liquidity 2.Subject to default risk Financial intermediaries help reduce disadvantages of swaps