1. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-1 Chapter 18 Interest Rate Risk Management: Index Futures, Options, Swaps and Other Derivatives

2. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-2 Stock Index Futures They are instruments for hedging exposure to changes in the market value of equity portfolios. Their value is pegged to movements in one of several aggregate measures of stock market performance.

3. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-3 Characteristics of Stock Index Futures They differ from other types of futures contracts in that it is not possible to make or take physical delivery of an index. If closure does not occur before the delivery month, the contract’s settlement level is the same as the level of the index on a given date in either March, June, September, or December. The value of the contract is calculated as the level of the index multiplied by an established amount, usually $500.

4. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-4 They are subject to daily trading limits. The price volatility of each index futures contract is greater than the price volatility of the underlying index.

5. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-5 Number of Contracts Beta is a relative measure of volatility. A portfolio of stocks underlying a market index is assumed to have a beta of 1. If a portfolio to be hedged has a beta greater or less than 1, changes in the value of the hedged portfolio will be more or less than changes in the index underlying the futures contract.

6. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-6 where: B p = the beta of the portfolio to be hedged The number of futures contracts (NF) is given by:

7. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-7 The Use of Stock Index Futures Illustrated Suppose that a pension fund manager holds a stock portfolio of $450 million in January, and the NYSE index is at 600.24. The equity markets have been in an upswing, but the surge is expected to end soon. The manager chooses to sell NYSE stock index futures. The previous day’s index settlement level on March futures contract was 602.75

8. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-8 THE SHORT HEDGE: PORTFOLIO BETA OF 1.0 (FORECAST: BEAR MARKET) A short hedge with index futures is used when falling securities prices are forecasted. The profit on the futures position can be used to offset losses in a portfolio of stocks. Cash Market Futures Market January NYSE Index: 600.24NYSE Index settlement level 602.75 Stock portfolio value:Sell 1,493 contracts a $450,000,000602.75 × $500 × 1,493 = $449,952,875 March Market decline = 2.5%NYSE Index settlement level: NYSE Index: 585.23602.75(1 - 0.025) = 587.68 Stock portfolio value:Close out position buying 1,493 contracts: $450,000,000(1 - 0.025 )= $438,750,000587.68 × $500 × 1,493 = $438,703,120 Cash Market LossFutures Market Gain January value$450,000,000January sale$449,952,875 March value 438,750,000March purchase 438,703,120 Loss($ 11,250,000)Gain$ 11,249,755 Net Loss ($245)

9. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-9 Cash Market LossFutures Market Gain January value$450,000,000January sale$449,952,875 March value 438,750,000March purchase 438,703,120 Loss($ 11,250,000)Gain$ 11,249,755 Net Loss ($245)

10. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-10 THE SHORT HEDGE: PORTFOLIO BETA OF 1.3 (FORECAST: BEAR MARKET) Short hedges with index futures must take into account the market risk (as measured by beta) of the hedged portfolio. Portfolios with high betas must be hedged with a larger number of index futures contracts than portfolios with lower betas. Cash MarketFutures Market January NYSE Index: 600.24NYSE Index settlement level 602.75 Stock portfolio value:Sell 1,941 contracts a $450,000,000602.75 × $500 × 1,941 = $584,968,875 March Market decline = 2.5%NYSE Index settlement level: Stock portfolio value change:602.75(1 - 0.025) = 587.68 -2.5% × 1.3 = 3.25% Stock portfolio value:Close out position buying 1,941 contracts: $450,000,000(1 - 0.0325) = $435,375,000587.68 × $500 × 1,941 = $570,343,440

11. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-11 Cash Market LossFutures Market Gain January value$450,000,000January sale$584,968,875 March value 435,375,000March purchase 570,843,440 Loss($ 14,625,000)Gain$ 14,625,435 Net Gain $435

12. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-12 Index Arbitrage Index Arbitrage is the simultaneous trading of stock and stock index futures to profit from changes in the spread between the two. Arbitragers are not attempting to use futures to offset adverse changes in a portfolio held in the normal course of operations. Arbitragers attempt to profit from fluctuations in the basis.

13. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-13 INDEX ARBITRAGE Index arbitrage is the simultaneous trading of index futures and stocks composing the underlying index. Computer programs are used to determine when stocks and futures are bought and sold to profit from temporary price discrepancies in the two markets. Cash MarketFutures Market February 26 MMI: 311.74MMI settlement level 313.55 Buy 2,000 shares of each MMI stockSell 18 contracts Value = $2,749,000313.55 × $500 × 18 = $2,821,950 If Prices Increase by March 21 MMI increase = 5.23%MMI settlement level: MMI: 328.07328.07, an increase of 4.631% Stock portfolio value:Close out position buying 18 contracts: $2,893,000328.07 × $500 × 18 = $2,952,630 Cash Market GainFutures Market Loss 3/21 value$2,893,0002/26 sale$2,821,950 2/26 value 2,749,0003/21 purchase 2,952,630 Gain$ 144,000Loss($ 130,680) Net Gain $13,320

14. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-14 Cash MarketFutures Market If Prices Decrease by March 21 MMI decrease= 5.23%MMI settlement level: MMI: 295.41295.41, a decrease of 5.785% Stock portfolio value:Close out position buying 18 contracts: $2,605,000295.41 × $500 × 18 = $2,658,690 Cash Market LossFutures Market Gain 3/21 value$2,605,0002/26 sale$2,821,950 2/26 value 2,749,0003/21 purchase 2,658,690 Loss($ 144,000)Gain $ 163,260 Net Gain $19,260

15. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-15 Options Defined An option is an agreement giving its holder the right to buy or sell a specified asset, over a limited time period, at a specified price (exercise price or strike price). An option writer creates the option and stands ready to buy or sell the asset when the holder wishes to make a transaction. Options are traded on organized exchanges. Options are available on financial assets and on futures contracts.

16. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-16 Differences Between Options and Futures An option does not obligate the holder to undertake the purchase or sale. The holder may choose not to exercise the option to buy or sell. American options can be exercised at any point during their lives. With futures, an exchange of securities takes place only on the specified delivery date. Futures are similar to European options which can be exercised only at expiration.

17. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-17 Call Options A call option is an agreement in which the option writer sells the holder the right to buy a specified asset on or before a future date. The buyer of the call expects the price of the asset to increase over the life of the option, eventually exceeding the exercise price. The value of the option rises as the price of the asset rises.

18. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-18 Put Options A put option is an agreement in which the option writer sells the holder the right to sell a specified asset on or before a future date at the strike price. The buyer of the put expects the price of the asset to fall below the strike price. The value of the option rises as the price of the asset declines.

19. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-19 Option Premiums It is the price paid to purchase the option. It reflects the cost of the option. If the option is not exercised, the cost of the option is the option premium. Since a large asset price change is necessary to cover the cost of the premium, it is better to hedge instruments with large expected price changes with options.

20. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-20 Market Forecasts and Option Hedges Falling stock prices or rising interest rates suggest the use of puts. Rising stock prices or falling interest rates suggest the use of calls.

21. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-21 Hedging With Options: An Illustration Suppose that in June, 2002, the bond portfolio manager for a large insurance firm forecasts a sharp decline in interest rates over the next 3 months. The insurance company is expecting a large inflow from sales of insurance policies in August. The manager wants to hedge the opportunity loss on the investment of those premiums. However, the manager of a money market fund holds the opposite expectations for interest rate movements. She is willing to write a call option on T-bond futures contracts. Suppose T-bond futures for September delivery are currently trading at 75.5% of par. The call option has a strike price of 76, a premium of $1,187.50 and an expiration of August 2002.

22. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-22 HEDGING WITH OPTIONS ON T-BOND FUTURES CONTRACTS An option provides the opportunity to limit losses to the amount of the option premium if forecasts are incorrect. If forecasts are correct, gains on a hedge can be used to offset losses in cash markets. Treasury Bond Call Option Premium:$1,187.50 Strike price:76 Expiration date:August 2002 Security:Treasury bond futures contract for September delivery $100,000 face value Current market value: 75.5 Scenario 1: Interest Rate Increase T-bond futures contract value: < 76 Call option not exercised. Results of the hedge: -$1,187.50 (premium)

23. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-23 Scenario 2: Interest Rates Fall Slightly T-bond futures contract market value: 77 Call option exercised. Contract purchased at 76 and sold at 77. Result of hedge $1,000.00Profit from futures trade [(77-76) = 1 or 1% of face value] - 1,187.50Premium ($187.50)Loss Scenario 3: Interest Rates Fall Significantly T-bond futures contract market value: 81 Call option exercised. Contract purchased at 76 and sold at 81. Result of hedge $5,000.00Profit from futures trade [(81-76) = 5 or 5% of face value] - 1,187.50Premium $3,812.50Gain

24. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-24 HEDGING WITH T-BOND FUTURES CONTRACTS Futures hedges also provide opportunities to gain if forecasts are correct. If forecasts are incorrect, however, losses on a futures position can be larger than losses on comparable hedging strategies. The Long Hedge Treasury bond futures contract for September delivery $100,000 face value Current market value: 75.5 Scenario 1: Interest Rates IncreaseScenario 2: Interest Rates Fall Slightly T-bond futures contracts market value: 70T-bond futures contract market value: 77 Position closed at loss of 5.5 of contract.Pos. closed at profit of 1.5 of contract. Results of hedge: -$5,500 lossResults of the hedge: $1500 profit Scenario 3: Interest Rates Fall Significantly T-bond futures contract market value: 81 Position closed at profit of 5.5 of contract. Results of the hedge: $5,500 profit

25. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-25 Interest Rate Swaps A swap agreement is an exchange of cash flows between two parties. Parties in a swap agreement are referred to as counterparties. In the simplest interest rate swap one counterparty exchanges a fixed-rate payment obligation for a floating-rate one, while the other counterparty exchanges floating for fixed.

26. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-26 Savings Association Commercial Bank Counterparty S&L Pays Interest on $50 Million at 8.5% Bank Pays Interest on $50 Million at LIBOR + 0.25% 8.5% Fixed-Rate Obligation in Eurodollar Markets Variable Rate Obligation on Deposits Exchange of Obligations in an Interest Rate Swap

27. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-27 Details on Interest Rate Swaps Initially, the floating rate will probably be lower than the fixed rate. The relationship could change over the life of the swap as interest rate levels fluctuate. The differential between the floating-rate and fixed-rate can be viewed as the insurance premium paid to transfer interest rate risk exposure to the counterparty accepting the floating-rate obligation.

28. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-28 Important Factors in a Swap: Maturity and Interest Rate Index Long-term interest rate swaps are available but short-term swaps are more popular. Termination clauses are usually included in agreement. The party who unwinds the swap pays a penalty.

29. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-29 Many participants make agreements to reverse a swap in the event of unfavorable rate movement. The LIBOR rate is the predominant index used in swap transactions.

30. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-30 Important Interest Rate Factors: Brokers and Dealers and Credit Risk Many large institutions in the U.S., U.K. and Japan serve as broker/dealers. As brokers, institutions bring two parties together. As dealers they may take the counterparty position in an agreement.

31. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-31 COMPARING INTEREST RATE FUTURES AND INTEREST RATE SWAPS These comparisons show that swaps are more flexible hedging tools than futures, but futures markets are large, more well-developed, and more standardized. FeatureFuturesSwaps Maturities available1½ to 2 years1 month to 20 years CostsMargins and commissionsBrokers’/dealers’ fees Size of hedge availableStandardized contract valuesAny amount over $1m Contract expiration dateFixed quarterly cycleAny dates Difficulty of managementComplexSimple Termination positionsClosed out with opposite Unwound or reversed contract Transactions completed throughOrganized exchangesCommercial or investment banks

32. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-32 Swap Options and Futures A call swaption gives the buyer an opportunity to enter into a swap agreement in the future to receive a fixed rate and pay a floating rate. A put swaption gives the buyer the right to make a future swap agreement to receive a floating rate and pay a fixed rate.

33. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-33 A swap future is a futures contract in which the “cash instrument” is a generic, plain vanilla swap with a 3 to 5 year life.

34. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-34 Interest Rate Caps, Floors, and Collars The purchaser of an interest rate cap pays a premium for the right to limit the cost of its liabilities to a specific rate. For a premium, the purchaser of an interest rate floor owns the right to receive interest payments at the strike level. Interest rate collars require the purchase and/or sale of caps and floors, hedging against increases and decreases in rates.

35. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-35 Other Derivatives Option Contracts for Insured Losses from Catastrophic Events Total Return Swaps Credit Swaps

36. Copyright © by 2000 Harcourt, Inc. All rights reserved. 18-36 A dealer in the intermediary role guarantees the continuation of the cash flows for the swap, even if one counterparty defaults. The financial strength of the counterparties is important to the dealer. The financial strength of the dealer is important to the counterparties.