1、INVESTMENTS | BODIE, KANE, MARCUS Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 20 Futures, Swaps, and Risk Management INVESTMENTS | BODIE, KANE, MARCUS 20-2 Futures can be used to hedge specific sources of risk. Hedging instruments include: Foreign
2、 exchange futures Stock index futures Interest rate futures Swaps Commodity futures Futures INVESTMENTS | BODIE, KANE, MARCUS 20-3 Foreign Exchange Futures Foreign exchange risk: You may get more or less home currency than you expected from a foreign currency denominated transaction. Foreign currenc
3、y futures are traded on the CME and the London International Futures Exchange. INVESTMENTS | BODIE, KANE, MARCUS 20-4 Figure 20.2 Foreign Exchange Futures INVESTMENTS | BODIE, KANE, MARCUS 20-5 Interest rate parity theorem Developed using the US Dollar and British Pound T UK US r r EF 1 1 00 where F
4、0 is todays forward rate E0 is the current spot rate Pricing on Foreign Exchange Futures INVESTMENTS | BODIE, KANE, MARCUS 20-6 Text Pricing Example rus = 4% ruk = 5%E0 = $2.00 per pound T = 1 yr 981. 1$ 05. 1 04. 1 00. 2$ 1 0 F If the futures price varies from $1.981 per pound, covered interest arb
5、itrage is possible. INVESTMENTS | BODIE, KANE, MARCUS 20-7 Direct Versus Indirect Quotes Direct exchange rate quote: The exchange rate is expressed as dollars per unit of foreign currency Indirect exchange rate quote: The exchange rate is expressed as foreign currency units per dollar INVESTMENTS |
6、BODIE, KANE, MARCUS 20-8 Hedging Foreign Exchange Risk A US exporter wants to protect against a decline in profit that would result from depreciation of the pound. The current futures price is $2/1. Suppose FT = $1.90? The exporter anticipates a profit loss of $200,000 if the pound declines by $.10
7、Short or sell pounds for future delivery to avoid the exposure. INVESTMENTS | BODIE, KANE, MARCUS 20-9 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 pound
8、s to be delivered Hedge Ratio in contracts Each contract is for 62,500 pounds or $6,250 per a $.10 change $200,000 / $6,250 = 32 contracts INVESTMENTS | BODIE, KANE, MARCUS 20-10 Figure 20.3 Profits as a Function of the Exchange Rate INVESTMENTS | BODIE, KANE, MARCUS 20-11 Available on both domestic
9、 and international stocks Settled in cash Advantages over direct stock purchase lower transaction costs better for timing or allocation strategies takes less time to acquire the portfolio Stock Index Contracts INVESTMENTS | BODIE, KANE, MARCUS 20-12 Table 20.1 Major Stock-Index Futures INVESTMENTS |
10、 BODIE, KANE, MARCUS 20-13 Table 20.2 Correlations among Major U.S. Stock Market Indexes INVESTMENTS | BODIE, KANE, MARCUS 20-14 Creating Synthetic Positions with Futures Index futures let investors participate in broad market movements without actually buying or selling large amounts of stock. Resu
11、lts: Cheaper and more flexible Synthetic position; instead of holding or shorting all of the actual stocks in the index, you are long or short the index futures INVESTMENTS | BODIE, KANE, MARCUS 20-15 Creating Synthetic Positions with Futures Speculators on broad market moves are major players in th
12、e index futures market. Strategy: Buy and hold T-bills and vary the position in market-index futures contracts. If bullish, then long futures If bearish, then short futures INVESTMENTS | BODIE, KANE, MARCUS 20-16 Exploiting mispricing between underlying stocks and the futures index contract Futures
13、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 INVESTMENTS | BODIE, KANE, MARCUS 20-17 This is difficult to implement in practice Transactions costs are often too large Trades cannot be done
14、 simultaneously Development of Program Trading Used by arbitrageurs to perform index arbitrage Permits quick acquisition of securities Index Arbitrage and Program Trading INVESTMENTS | BODIE, KANE, MARCUS 20-18 Hedging Systematic Risk To protect against a decline in stock prices, short the appropria
15、te number of futures index contracts. Less costly and quicker Use the beta for the portfolio to determine the hedge ratio. INVESTMENTS | BODIE, KANE, MARCUS 20-19 Hedging Systematic Risk Example Portfolio Beta = .8S&P 500 = 1,000 Decrease = 2.5%S&P falls to 975 Portfolio Value = $30 million Projecte
16、d 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. (The contract multiplier is $250). INVESTMENTS | BODIE, KANE, MARCUS 20-20 Hedge Ratio Example H = = Change in the portfolio value Profit on
17、 one futures contract $600,000 $6,250 = 96 contracts short INVESTMENTS | BODIE, KANE, MARCUS 20-21 Figure 20.4 Predicted Value of the Portfolio as a Function of the Market Index INVESTMENTS | BODIE, KANE, MARCUS 20-22 Uses of Interest Rate Hedges A bond fund manager may seek to protect gains against
18、 a rise in rates. Corporations planning to issue debt securities want to protect against a rise in rates. A pension fund with large cash inflows may hedge against a decline in rates for a planned future investment. INVESTMENTS | BODIE, KANE, MARCUS 20-23 Hedging Interest Rate Risk Example Portfolio
19、value = $10 million Modified duration = 9 years If rates rise by 10 basis points (.1%), then Change in value = ( 9 ) ( .1%) = .9% or $90,000 Price value of a basis point (PVBP) = $90,000 / 10 = $9,000 per basis point INVESTMENTS | BODIE, KANE, MARCUS 20-24 Hedge Ratio Example H = = PVBP for the port
20、folio PVBP for the hedge vehicle $9,000 $90 = 100 T-Bond contracts INVESTMENTS | BODIE, KANE, MARCUS 20-25 Hedging The T-bond contracts drive the interest rate exposure of a bond position to zero. This is a market neutral strategy. Gains on the T-bond futures offset losses on the bond portfolio. The
21、 hedge is imperfect in practice because of slippage the yield spread does not remain constant. INVESTMENTS | BODIE, KANE, MARCUS 20-26 Figure 20.5 Yield Spread INVESTMENTS | BODIE, KANE, MARCUS 20-27 Swaps Swaps are multi- period extensions of forward contracts. Credit risk on swaps An interest rate
22、 swap calls for exchanging cash flows based on a fixed rate for cash flows based on a floating rate. The foreign exchange swap calls for an exchange of currencies on several future dates. INVESTMENTS | BODIE, KANE, MARCUS 20-28 Interest Rate Swap: Text Example INVESTMENTS | BODIE, KANE, MARCUS 20-29
23、 The Swap Dealer Dealer enters a swap with Company A Pays fixed rate and receives LIBOR Dealer enters another swap with Company B Pays LIBOR and receives a fixed rate When two swaps are combined, dealers position is effectively neutral on interest rates. INVESTMENTS | BODIE, KANE, MARCUS 20-30 Figur
24、e 20.6 Interest Rate Swap INVESTMENTS | BODIE, KANE, MARCUS 20-31 Figure 20.7 Interest Rate Futures INVESTMENTS | BODIE, KANE, MARCUS 20-32 Swaps are essentially a series of forward contracts. We need to find the level annuity, F *, with the same present value as the stream of annual cash flows that
25、 would be incurred in a sequence of forward rate agreements. 2 21 2 2 2 1 1 )1 ()1 ()1 ()1 ( * y F y F y F y F Pricing on Swap Contracts INVESTMENTS | BODIE, KANE, MARCUS 20-33 Figure 20.8 Forward Contracts versus Swaps INVESTMENTS | BODIE, KANE, MARCUS 20-34 Credit Default Swaps Payment on a CDS is
26、 tied to the financial status of one or more reference firms. Allows two counterparties to take positions on the credit risk of those firms. Indexes of CDS have now been introduced. INVESTMENTS | BODIE, KANE, MARCUS 20-35 Commodity Futures Pricing General principles that apply to stocks apply to com
27、modities. However Carrying costs are more for commodities. Spoilage is a concern. INVESTMENTS | BODIE, KANE, MARCUS 20-36 Commodity Futures Pricing :then define Now )1 ( 0 00 P C c CrPF f Let F0 = futures price, P0 = cash price of the asset , and C = Carrying cost )1 ( 00 crPF f INVESTMENTS | BODIE,
28、 KANE, MARCUS 20-37 Futures Pricing F0 = P0(1+rf+c) is a parity relationship for commodities that are stored. The formula works great for an asset like gold, but not for electricity or agricultural goods which are impractical to stockpile. INVESTMENTS | BODIE, KANE, MARCUS 20-38 Figure 20.9 Typical
29、Agricultural Price Pattern over the Season INVESTMENTS | BODIE, KANE, MARCUS 20-39 Example 2.8 Commodity Futures Pricing The T-bill rate is 5%, the market risk premium is 8%, and the beta for orange juice is 0.117. Orange juice discount rate is 5% + .117(8%) = 5.94%. Let the expected spot price in 6 months be $1.45. $1.45/(1.0594)0.5 = $1.409 = PV juice F0/(1.05)0.5 = 0.976F0 = PV futures 0.976F0 = $1.409 F0 =$1.444
