1.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-1 Risk Management and Hedging Chapter 27

2.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-2 Hedging Foreign Exchange Risk 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

3.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-3 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

4.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-4 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

5.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-5 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

6.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-6 Hedge Ratio: Text Example H = = Change in the portfolio value Profit on one futures contract $600,000 $6,250 = 96 contracts short

7.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-7 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

8.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-8 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

9.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-9 Hedge Ratio: Text Example H = = PVBP for the portfolio PVBP for the hedge vehicle $9,000 $90 = 100 contracts

10.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-10 Hedging On Mispriced Options Option value is positively related to volatility If an investor believes that the implied 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

11.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-11 Hedging and Delta The appropriate hedge will depend on the delta Recall from Chapter 21 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

12.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-12 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

13.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-13 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

14.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-14 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

15.  The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 27-15 Hedging Demands on Capital Market Equilibrium CAPM assume that investors face only risk about the uncertain value of securities Many additional elements of risk are present - Uncertain prices on consumption, energy or housing - Uncertain future interest rates Hedging activity associated with these elements of risk are consistent with the multifactor arbitrage pricing model