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CHAPTER 20

CHAPTER 20. Futures, Swaps, and Risk Management. Futures can be used to hedge specific sources of risk. Hedging instruments include: Foreign exchange futures Stock index futures Interest rate futures Swaps Commodity futures. Futures. Foreign Exchange Futures.

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CHAPTER 20

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  1. CHAPTER 20 Futures, Swaps, and Risk Management

  2. Futures can be used to hedge specific sources of risk. Hedging instruments include: Foreign exchange futures Stock index futures Interest rate futures Swaps Commodity futures Futures

  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 currency futures are traded on the CME and the London International Futures Exchange.

  4. Figure 20.2 Foreign Exchange Futures

  5. Pricing on Foreign Exchange Futures • Interest rate parity theorem • Developed using the US Dollar and British Pound where F0is today’s forward rate E0 is the current spot rate

  6. Text Pricing Example rus = 4% ruk = 5% E0 = $2.00 per pound T = 1 yr If the futures price varies from $1.981 per pound, covered interest arbitrage is possible.

  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

  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 Short or sell pounds for future delivery to avoid the exposure.

  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 pounds 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

  10. Figure 20.3 Profits as a Function of the Exchange Rate

  11. Available on both domestic 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

  12. Table 20.1 Major Stock-Index Futures

  13. Table 20.2 Correlations among Major U.S. Stock Market Indexes

  14. Creating Synthetic Positions with Futures Index futures let investors participate in broad market movements without actually buying or selling large amounts of stock. Results: 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

  15. Creating Synthetic Positions with Futures Speculators on broad market moves are major players in the 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

  16. 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

  17. 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 quick acquisition of securities Index Arbitrage and Program Trading

  18. Hedging Systematic Risk To protect against a decline in stock prices, short the appropriate number of futures index contracts. Less costly and quicker Use the beta for the portfolio to determine the hedge ratio.

  19. Hedging Systematic Risk Example Portfolio Beta = .8 S&P 500 = 1,000 Decrease = 2.5% S&P falls to 975 Portfolio Value = $30 million Projected 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).

  20. Hedge Ratio Example Change in the portfolio value Profit on one futures contract $600,000 $6,250 H = = = 96 contracts short

  21. Figure 20.4 Predicted Value of the Portfolio as a Function of the Market Index

  22. Uses of Interest Rate Hedges A bond fund manager may seek to protect gains against 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.

  23. Hedging Interest Rate Risk Example Portfolio 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

  24. Hedge Ratio Example PVBP for the portfolio PVBP for the hedge vehicle $9,000 $90 H = = = 100 T-Bond contracts

  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 hedge is imperfect in practice because of slippage – the yield spread does not remain constant.

  26. Figure 20.5 Yield Spread

  27. Swaps Swaps are multi-period extensions of forward contracts. Credit risk on swaps An interest rate 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.

  28. Interest Rate Swap: Text Example

  29. 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, dealer’s position is effectively neutral on interest rates.

  30. Figure 20.6 Interest Rate Swap

  31. Figure 20.7 Interest Rate Futures

  32. Pricing on Swap Contracts 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 would be incurred in a sequence of forward rate agreements.

  33. Figure 20.8 Forward Contracts versus Swaps

  34. Credit Default Swaps Payment on a CDS is 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.

  35. Commodity Futures Pricing • General principles that apply to stocks apply to commodities. However… • Carrying costs are more for commodities. • Spoilage is a concern.

  36. Commodity Futures Pricing Let F0 = futures price, P0 = cash price of the asset , and C = Carrying cost

  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.

  38. Figure 20.9 Typical Agricultural Price Pattern over the Season

  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

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