1. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-1 Options Markets: Introduction Chapter 20

2. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-2 Buy - Long Sell - Short Call Put Key Elements -Exercise or Strike Price -Premium or Price -Maturity or Expiration Option Terminology

3. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-3 In the Money - exercise of the option would be profitable. Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable. Call: market price>exercise price Put: exercise price>market price At the Money - exercise price and asset price are equal. Market and Exercise Price Relationships

4. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-4 American - the option can be exercised at any time before expiration or maturity. European - the option can only be exercised on the expiration or maturity date. American vs European Options

5. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-5 Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options Different Types of Options

6. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-6 Notation Stock Price = S T Exercise Price = X Payoff to Call Holder ( S T - X) if S T >X 0if S T < X Profit to Call Holder Payoff - Purchase Price Payoffs and Profits on Options at Expiration - Calls

7. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-7 Payoff to Call Writer - ( S T - X) if S T >X 0if S T < X Profit to Call Writer Payoff + Premium Payoffs and Profits on Options at Expiration - Calls

8. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-8 Profit Profiles for Calls Profit Stock Price 0 Call Writer Call Holder

9. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-9 Payoffs to Put Holder 0if S T > X (X - S T ) if S T < X Profit to Put Holder Payoff - Premium Payoffs and Profits at Expiration - Puts

10. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-10 Payoffs to Put Writer 0if S T > X -(X - S T )if S T < X Profits to Put Writer Payoff + Premium Payoffs and Profits at Expiration - Puts

11. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-11 Profit Profiles for Puts 0 Profits Stock Price Put Writer Put Holder

12. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-12 InvestmentStrategyInvestment Equity onlyBuy stock @ 100300 shares$10,000 Options onlyBuy calls @ 101000 options$10,000 LeveragedBuy calls @ 10100 options $1,000 equityBuy T-bills @ 2% $9,000 Yield Equity, Options & Leveraged Equity - Text Example

13. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-13 IBM Stock Price $95$105$115 All Stock$9,500$10,500$11,500 All Options$0 $5,000$15,000 Lev Equity $9,270 $9,770$10,770 Equity, Options & Leveraged Equity - Payoffs

14. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-14 IBM Stock Price $95$105$115 All Stock-5.0%5.0% 15% All Options-100% -50% 50% Lev Equity -7.3%-2.3% 7.7% Equity, Options & Leveraged Equity - Rates of Return

15. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-15 Protective Put Use - limit loss Position - long the stock and long the put PayoffS T X Stock S T S T Put X - S T 0

16. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-16 Protective Put Profit STST Profit -P Stock Protective Put Portfolio

17. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-17 Covered Call Use - Some downside protection at the expense of giving up gain potential. Position - Own the stock and write a call. PayoffS T X Stock S T S T Call 0 - ( S T - X)

18. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-18 Covered Call Profit STST Profit -P Stock Covered Call Portfolio

19. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-19 Straddle (Same Exercise Price) Long Call and Long Put Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration. Vertical or money spread: Same maturity Different exercise price Horizontal or time spread: Different maturity dates Option Strategies

20. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-20 S T X Payoff for Call Owned 0S T - X Payoff for Put Written-( X -ST) 0 Total Payoff S T - X S T - X Put-Call Parity Relationship

21. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-21 Long Call Short Put Payoff Stock Price Combined = Leveraged Equity Payoff of Long Call & Short Put

22. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-22 Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S 0 - X / (1 + r f ) T If the prices are not equal arbitrage will be possible. Arbitrage & Put Call Parity

23. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-23 Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 10.25% Maturity =.5 yr X = 105 C - P > S 0 - X / (1 + r f ) T 17- 5 > 110 - (105/1.05) 12 > 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative. Put Call Parity - Disequilibrium Example

24. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-24 Put-Call Parity Arbitrage ImmediateCashflow in Six Months PositionCashflowS T 105 Buy Stock-110 S T S T Borrow X/(1+r) T = 100+100-105-105 Sell Call+17 0-(S T -105) Buy Put -5105-S T 0 Total 2 0 0

25. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-25 Optionlike Securities Callable Bonds Convertible Securities Warrants Collateralized Loans

26. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-26 Exotic Options Asian Options Barrier Options Lookback Options Currency Translated Options Binary Options

27. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-27 Option Valuation Chapter 21

28. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-28 Intrinsic value - profit that could be made if the option was immediately exercised. -Call: stock price - exercise price -Put: exercise price - stock price Time value - the difference between the option price and the intrinsic value. Option Values

29. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-29 Time Value of Options: Call Option value X Stock Price Value of Call Intrinsic Value Time value

30. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-30 FactorEffect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expirationincreases Interest rate increases Dividend Ratedecreases Factors Influencing Option Values: Calls

31. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-31 Restrictions on Option Value: Call Value cannot be negative Value cannot exceed the stock value Value of the call must be greater than the value of levered equity C > S 0 - ( X + D ) / ( 1 + R f ) T C > S 0 - PV ( X ) - PV ( D )

32. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-32 Allowable Range for Call Call Value S0S0 PV (X) + PV (D) Upper bound = S 0 Lower Bound = S 0 - PV (X) - PV (D)

33. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-33 100 200 50 Stock Price C 75 0 Call Option Value X = 125 Binomial Option Pricing: Text Example

34. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-34 Alternative Portfolio Buy 1 share of stock at $100 Borrow $46.30 (8% Rate) Net outlay $53.70 Payoff Value of Stock 50 200 Repay loan - 50 -50 Net Payoff 0 150 53.70 150 0 Payoff Structure is exactly 2 times the Call Binomial Option Pricing: Text Example

35. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-35 53.70 150 0 C 75 0 2C = $53.70 C = $26.85 Binomial Option Pricing: Text Example

36. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-36 Alternative Portfolio - one share of stock and 2 calls written (X = 125) Portfolio is perfectly hedged Stock Value50200 Call Obligation 0 -150 Net payoff50 50 Hence 100 - 2C = 46.30 or C = 26.85 Another View of Replication of Payoffs and Option Values

37. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-37 Generalizing the Two-State Approach Assume that we can break the year into two six- month segments. In each six-month segment the stock could increase by 10% or decrease by 5%. Assume the stock is initially selling at 100. Possible outcomes: Increase by 10% twice Decrease by 5% twice Increase once and decrease once (2 paths).

38. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-38 Generalizing the Two-State Approach 100 110 121 95 90.25 104.50

39. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-39 Assume that we can break the year into three intervals. For each interval the stock could increase by 5% or decrease by 3%. Assume the stock is initially selling at 100. Expanding to Consider Three Intervals

40. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-40 S S + S + + S - S - - S + - S + + + S + + - S + - - S - - - Expanding to Consider Three Intervals

41. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-41 Possible Outcomes with Three Intervals EventProbabilityStock Price 3 up 1/8100 (1.05) 3 =115.76 2 up 1 down 3/8100 (1.05) 2 (.97)=106.94 1 up 2 down 3/8100 (1.05) (.97) 2 = 98.79 3 down 1/8100 (.97) 3 = 91.27

42. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-42 C o = S o N(d 1 ) - Xe -rT N(d 2 ) d 1 = [ln(S o /X) + (r +  2 /2)T] / (  T 1/2 ) d 2 = d 1 + (  T 1/2 ) where C o = Current call option value. S o = Current stock price N(d) = probability that a random draw from a normal dist. will be less than d. Black-Scholes Option Valuation

43. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-43 X = Exercise price e = 2.71828, the base of the natural log r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option) T = time to maturity of the option in years ln = Natural log function  Standard deviation of annualized cont. compounded rate of return on the stock Black-Scholes Option Valuation

44. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-44 S o = 100X = 95 r =.10T =.25 (quarter)  =.50 d 1 = [ln(100/95) + (.10+(  5 2 /2))] / (  5 .25 1/2 ) =.43 d 2 =.43 + ((  5 .25 1/2 ) =.18 Call Option Example

45. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-45 N (.43) =.6664 Table 17.2 d N(d).42.6628.43.6664 Interpolation.44.6700 Probabilities from Normal Dist

46. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-46 N (.18) =.5714 Table 17.2 d N(d).16.5636.18.5714.20.5793 Probabilities from Normal Dist.

47. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-47 C o = S o N(d 1 ) - Xe -rT N(d 2 ) C o = 100 X.6664 - 95 e -.10 X.25 X.5714 C o = 13.70 Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock? Call Option Value

48. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-48 Put Value Using Black-Scholes P = Xe -rT [1-N(d 2 )] - S 0 [1-N(d 1 )] Using the sample call data S = 100 r =.10 X = 95 g =.5 T =.25 95e -10x.25 (1-.5714)-100(1-.6664) = 6.35

49. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-49 P = C + PV (X) - S o = C + Xe -rT - S o Using the example data C = 13.70X = 95S = 100 r =.10T =.25 P = 13.70 + 95 e -.10 X.25 - 100 P = 6.35 Put Option Valuation: Using Put-Call Parity

50. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-50 Adjusting the Black-Scholes Model for Dividends The call option formula applies to stocks that pay dividends. One approach is to replace the stock price with a dividend adjusted stock price. Replace S 0 with S 0 - PV (Dividends)

51. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-51 Hedging: Hedge ratio or delta The number of stocks required to hedge against the price risk of holding one option. Call = N (d 1 ) Put = N (d 1 ) - 1 Option Elasticity Percentage change in the option’s value given a 1% change in the value of the underlying stock. Using the Black-Scholes Formula

52. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-52 Buying Puts - results in downside protection with unlimited upside potential. Limitations -Tracking errors if indexes are used for the puts. -Maturity of puts may be too short. -Hedge ratios or deltas change as stock values change. Portfolio Insurance - Protecting Against Declines in Stock Value

53. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-53 Hedging On Mispriced Options Option value is positively related to volatility: If an investor believes that the volatility that is implied in an option’s price is too low, a profitable trade is possible. Profit must be hedged against a decline in the value of the stock. Performance depends on option price relative to the implied volatility.

54. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-54 Hedging and Delta The appropriate hedge will depend on the delta. Recall the delta is the change in the value of the option relative to the change in the value of the stock. Delta = Change in the value of the option Change of the value of the stock

55. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-55 Mispriced Option: Text Example Implied volatility = 33% Investor believes volatility should = 35% Option maturity = 60 days Put price P = $4.495 Exercise price and stock price = $90 Risk-free rate r = 4% Delta = -.453

56. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-56 Hedged Put Portfolio Cost to establish the hedged position 1000 put options at $4.495 / option$ 4,495 453 shares at $90 / share 40,770 Total outlay 45,265

57. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-57 Profit Position on Hedged Put Portfolio Value of put option as function of stock price: implied vol. = 35% Stock Price899091 Put Price $5.254 $4.785 $4.347 Profit (loss) for each put.759.290 (.148) Value of and profit on hedged portfolio Stock Price899091 Value of 1,000 puts $ 5,254 $ 4,785 $ 4,347 Value of 453 shares 40,317 40,770 41,223 Total45,571 45,555 45,570 Profit 306 290 305

58. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-58 Futures Markets Chapter 22

59. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-59 Forward - an agreement calling for a future delivery of an asset at an agreed-upon price Futures - similar to forward but feature formalized and standardized characteristics Key difference in futures -Secondary trading - liquidity -Marked to market -Standardized contract units -Clearinghouse warrants performance Futures and Forwards

60. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-60 Futures price - agreed-upon price at maturity Long position - agree to purchase Short position - agree to sell Profits on positions at maturity Long = spot minus original futures price Short = original futures price minus spot Key Terms for Futures Contracts

61. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-61 Agricultural commodities Metals and minerals (including energy contracts) Foreign currencies Financial futures Interest rate futures Stock index futures Types of Contracts

62. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-62 Clearinghouse - acts as a party to all buyers and sellers. -Obligated to deliver or supply delivery Closing out positions -Reversing the trade -Take or make delivery -Most trades are reversed and do not involve actual delivery Trading Mechanics

63. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-63 Initial Margin - funds deposited to provide capital to absorb losses Marking to Market - each day the profits or losses from the new futures price are reflected in the account. Maintenance or variation margin - an established value below which a trader’s margin may not fall. Margin and Trading Arrangements

64. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-64 Margin call - when the maintenance margin is reached, broker will ask for additional margin funds Convergence of Price - as maturity approaches the spot and futures price converge Delivery - Actual commodity of a certain grade with a delivery location or for some contracts cash settlement Margin and Trading Arrangements

65. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-65 Speculation - -short - believe price will fall -long - believe price will rise Hedging - -long hedge - protecting against a rise in price -short hedge - protecting against a fall in price Trading Strategies

66. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-66 Basis - the difference between the futures price and the spot price -over time the basis will likely change and will eventually converge Basis Risk - the variability in the basis that will affect profits and/or hedging performance Basis and Basis Risk

67. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-67 Spot-futures parity theorem - two ways to acquire an asset for some date in the future Purchase it now and store it Take a long position in futures These two strategies must have the same market determined costs Futures Pricing

68. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-68 Spot-Futures Parity Theorem With a perfect hedge the futures payoff is certain -- there is no risk A perfect hedge should return the riskless rate of return This relationship can be used to develop futures pricing relationship

69. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-69 Hedge Example: pp.753-754 Investor owns and S&P 500 fund that has a current value equal to the index of $1,300 Assume dividends of $20 will be paid on the index at the end of the year Assume futures contract that calls for delivery in one year is available for $1,345 Assume the investor hedges by selling or shorting one contract

70. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-70 Hedge Example Outcomes Value of S T 1,2951,3351,395 Payoff on Short (1,345 - S T ) 50 10 -50 Dividend Income20 20 20 Total1,365 1,365 1,365

71. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-71 Rate of Return for the Hedge

72. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-72 General Spot-Futures Parity Rearranging terms

73. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-73 Arbitrage Possibilities If spot-futures parity is not observed, then arbitrage is possible If the futures price is too high, short the futures and acquire the stock by borrowing the money at the riskfree rate If the futures price is too low, go long futures, short the stock and invest the proceeds at the riskfree rate

74. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-74 Futures Price versus Expected Spot Price: Theories Expectations Normal Backwardation Contango

75. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-75 Contango Normal Backwardation Time Delivery date Futures prices Expectations Hypothesis Futures Price versus Expected Spot Price: Theories

76. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-76 Futures and Swaps: A Closer Look Chapter 23

77. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-77 Futures markets -Chicago Mercantile (International Monetary Market) -London International Financial Futures Exchange -MidAmerica Commodity Exchange Active forward market Differences between futures and forward markets Foreign Exchange Futures

78. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-78 Interest rate parity theorem Developed using the US Dollar and British Pound where F 0 is the forward price E 0 is the current exchange rate Pricing on Foreign Exchange Futures

79. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-79 Text Pricing Example r us = 5% r uk = 6%E 0 = $1.60 per pound T = 1 yr If the futures price varies from $1.58 per pound arbitrage opportunities will be present.

80. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-80 Hedging Foreign Exchange Risk A US firm wants to protect against a decline in profit that would result from a decline in the pound: Estimated profit loss of $200,000 if the pound declines by $.10. Short or sell pounds for future delivery to avoid the exposure.

81. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-81 Hedge Ratio for Foreign Exchange Example Hedge Ratio in pounds $200,000 per $.10 change in the pound/dollar exchange rate $.10 profit per pound delivered per $.10 in exchange rate = 2,000,000 pounds to be delivered Hedge Ratio in contacts Each contract is for 62,500 pounds or $6,250 per a $.10 change $200,000 / $6,250 = 32 contracts

82. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-82 Available on both domestic and international stocks. Advantages over direct stock purchase: -lower transaction costs -better for timing or allocation strategies -takes less time to acquire the portfolio Stock Index Contracts

83. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-83 Using Stock Index Contracts to Create Synthetic Positions Synthetic stock purchase: -Purchase of the stock index instead of actual shares of stock. Creation of a synthetic T-bill plus index futures that duplicates the payoff of the stock index contract.

84. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-84 Pricing on Stock Index Contracts The spot-futures price parity that was developed in Chapter 22 is given as; Empirical investigations have shown that the actual pricing relationship on index contracts follows the spot-futures relationship.

85. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-85 Exploiting mispricing between underlying stocks and the futures index contract. Futures Price too high - short the future and buy the underlying stocks. Futures price too low - long the future and short sell the underlying stocks. Index Arbitrage

86. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-86 This is difficult to implement in practice. Transactions costs are often too large. Trades cannot be done simultaneously. Development of Program Trading Used by arbitrageurs to perform index arbitrage. Permits acquisition of securities quickly. Triple-witching hour Evidence that index arbitrage impacts volatility. Index Arbitrage and Program Trading

87. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-87 Hedging Systematic Risk To protect against a decline in level stock prices, short the appropriate number of futures index contracts. Less costly and quicker to use the index contracts. Use the beta for the portfolio to determine the hedge ratio.

88. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-88 Hedging Systematic Risk: Text Example Portfolio Beta =.8S&P 500 = 1,000 Decrease = 2.5%S&P falls to 975 Portfolio Value = $30 million Project loss if market declines by 2.5% = (.8) (2.5) = 2% 2% of $30 million = $600,000 Each S&P500 index contract will change $6,250 for a 2.5% change in the index

89. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-89 Hedge Ratio: Text Example H = = Change in the portfolio value Profit on one futures contract $600,000 $6,250 = 96 contracts short

90. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-90 Interest Rate Futures Domestic interest rate contracts -T-bills, notes and bonds -municipal bonds International contracts -Eurodollar Hedging -Underwriters -Firms issuing debt

91. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-91 Uses of Interest Rate Hedges Owners of fixed-income portfolios protecting against a rise in rates. Corporations planning to issue debt securities protecting against a rise in rates. Investor hedging against a decline in rates for a planned future investment. Exposure for a fixed-income portfolio is proportional to modified duration.

92. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-92 Hedging Interest Rate Risk: Text Example Portfolio value = $10 million Modified duration = 9 years If rates rise by 10 basis points (.1%) Change in value = ( 9 ) (.1%) =.9% or $90,000 Present value of a basis point (PVBP) = $90,000 / 10 = $9,000

93. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-93 Hedge Ratio: Text Example H = = PVBP for the portfolio PVBP for the hedge vehicle $9,000 $90 = 100 contracts

94. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-94 Commodity Futures Pricing General principles that apply to stock apply to commodities. Carrying costs are more for commodities. Spoilage is a concern. Where; F 0 = futures price P 0 = cash price of the asset C = Carrying cost c = C/P 0

95. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-95 Interest rate swap Foreign exchange swap Credit risk on swaps Swap Variations -Interest rate cap -Interest rate floor -Collars -Swaptions Swaps

96. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 20-96 Swaps are essentially a series of forward contracts. One difference is that the swap is usually structured with the same payment each period while the forward rate would be different each period. Using a foreign exchange swap as an example, the swap pricing would be described by the following formula. Pricing on Swap Contracts