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Chapter 3 Derivatives and Hedging Risk McGraw-Hill/Irwin Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Understand the basics of forward and futures contracts Understand how derivatives can be used to hedge risks faced by the corporation 25-1 Derivatives, Hedging, and Risk Derivatives defined as securities whose values are determined by the market price of some other assets. When the firm reduces its risk exposure with the use of derivatives – hedging 25-2 Forward Contracts A forward contract specifies that a certain commodity will be exchanged at a specified time in the future at a price specified today. Its not an option: both parties are expected to hold up their end of the deal. If you have ever ordered a textbook that was not in stock, you have entered into a forward contract. 25-3 Futures Contracts A futures contract is like a forward contract: It specifies that a certain commodity will be exchanged at a specified time in the future at a price specified today. A futures contract is different from a forward: Futures are standardized contracts trading on organized exchanges with daily resettlement (“marking to market”) through a clearinghouse. 25-4 Futures Contracts Standardizing Features Contract Size Delivery Month Daily resettlement Minimizes the chance of default Initial Margin About 4-10% of contract value Cash or T-bills held in a street name at your brokerage 25-5 Daily Resettlement: An Example Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically, you think that the dollar will appreciate). Japan (yen) 1-month forward 3-months forward 6-months forward U.S. $ equivalent Wed Tue 0.007142857 0.007194245 0.006993007 0.007042254 0.006666667 0.006711409 0.00625 0.006289308 Currency per U.S. $ Wed Tue 140 139 143 142 150 149 160 159 Currently $1 = ¥140. The 3-month forward price is $1=¥150. 25-6 Daily Resettlement: An Example Currently $1 = ¥140, and it appears that the dollar is strengthening. If you enter into a 3-month futures contract to sell ¥ at the rate of $1 = ¥150 you will profit if the yen depreciates. The contract size is ¥12,500,000 Your initial margin is 4% of the contract value: $3,333.33 = 0.04 × ¥12,500,000 × $1 ¥150 25-7 Daily Resettlement: An Example If tomorrow the futures rate closes at $1 = ¥149, then your position’s value drops (¥ appreciated). Your original agreement was to sell ¥12,500,000 and receive $83,333.33: $83,333.33 = ¥12,500,000 × $1 ¥150 But, ¥12,500,000 is now worth $83,892.62: $83,892.62 = ¥12,500,000 × $1 ¥149 You have lost $559.29 overnight. 25-8 Daily Resettlement: An Example The $559.29 comes out of your $3,333.33 margin account, leaving $2,774.04. This is short of the $3,355.70 required for a new position. $3,355.70 = 0.04 × ¥12,500,000 × $1 ¥149 Your broker will let you slide until you run through your maintenance margin. Then you must post additional funds, or your position will be closed out. This is usually done with a reversing trade. 25-9 Futures Markets The Chicago Mercantile Exchange (CME) is by far the largest. Others include: The Philadelphia Board of Trade (PBOT) The MidAmerica Commodities Exchange The Tokyo International Financial Futures Exchange The London International Financial Futures Exchange 25-10 Basic Futures Relationships Open Interest refers to the number of contracts outstanding for a particular delivery month. Open interest is a good proxy for the demand for a contract. Some refer to open interest as the depth of the market. The breadth of the market would be how many different contracts (expiry month) are outstanding. 25-11 Hedging Two counterparties with offsetting risks can eliminate risk. For example, if a wheat farmer and a flour mill enter into a forward contract, they can eliminate the risk each other faces regarding the future price of wheat. Hedgers can also transfer price risk to speculators, who absorb price risk from hedgers. Speculating: Long vs. Short 25-12 Hedging and Speculating: Example You speculate that copper will go up in price, so you go long 10 copper contracts for delivery in 3 months. A contract is 25,000 pounds in cents per pound and is at $0.70 per pound, or $17,500 per contract. If futures prices rise by 5 cents, you will gain: Gain = 25,000 × .05 × 10 = $12,500 If prices decrease by 5 cents, your loss is: Loss = 25,000 ×( –.05) × 10 = –$12,500 25-13 Hedging: How many contracts? You are a farmer, and you will harvest 50,000 bushels of corn in 3 months. You want to hedge against a price decrease. Corn is quoted in cents per bushel at 5,000 bushels per contract. It is currently at $2.30 cents for a contract 3 months out, and the spot price is $2.05. To hedge, you will sell 10 corn futures contracts: 50,000 bushels 10 contracts = 5,000 bushels per contract Now you can quit worrying about the price of corn and get back to worrying about the weather. 25-14 TEST Golden Grain Farms (GGF) expects to harvest 50,000 bushels of wheat in September. GGF is concern about the possibility of price fluctuations from now until September. The futures price for September wheat is $2 per bushel and the relevant contract calls for 5,000 bushels. Three month later, the price of on September futures turns out to be $3. Evaluate GGF’s number of contract and profit or loss in the future position. 25-15 3.5 Interest Rate Futures Contracts i. ii. iii. iv. Pricing of Treasury Bonds Pricing of Forward Contracts Futures Contracts Hedging in Interest Rate Futures 25-16 i. Pricing of Treasury Bonds Consider a Treasury bond that pays a semiannual coupon of $C for the next T years: The yield to maturity is R 0 C C C 1 2 3 … CF 2T Value of the T-bond under a flat term structure = PV of face value + PV of coupon payments F C 1 PV 1 T T (1 R ) R (1 R ) 25-17 Pricing of Treasury Bonds If the term structure of interest rates is not flat, then we need to discount the payments at different rates depending upon maturity. 0 C C C 1 2 3 … CF 2T = PV of face value + PV of coupon payments C C C CF PV 2 3 T (1 R1 ) (1 R2 ) (1 R3 ) (1 R2T ) 25-18 TEST A Treasury note with a maturity of 4 years pays interest semiannually on 9 percent annual coupon rate. The RM1,000 face value is returned at maturity. If the effective annual yield for all maturities is 12 percent annually, compute the current price of the Treasury note. 25-19 ii. Pricing of Forward Contracts An N-period forward contract on that T-Bond: Pforward C C C CF … 0 N N+1 N+2 N+3 N+2T Can be valued as the present value of the forward price. PV Pforward (1 R N ) N C C C CF 2 3 (1 R N 1 ) (1 R N 2 ) (1 R N 3 ) (1 R N 2T )T PV (1 R N ) N 25-20 Pricing of Forward Contracts: Example Find the value of a 5-year forward contract on a 20-year T-bond. The coupon rate is 6 percent per annum, and payments are made semiannually on a par value of $1,000. 40 = 20 × 2 The Yield to Maturity is 5 percent. I/Y 5 PV –1,125.51 First, set your calculator to 2 payments per year. N PMT FV 30 = 1,000 1,000 × .06 2 Then enter what you know and solve for the value of a 20-year Treasury bond at the maturity of the forward contract. 25-21 iii. Pricing of Futures Contracts The pricing equation given above will be a good approximation. The only real difference is the daily resettlement. 25-22 iv. Hedging in Interest Rate Futures A mortgage lender who has agreed to loan money in the future at prices set today can hedge by selling those mortgages forward. It may be difficult to find a counterparty in the forward who wants the precise mix of risk, maturity, and size. It is likely to be easier and cheaper to use interest rate futures contracts. 25-23 3.6 Duration Hedging As an alternative to hedging with futures or forwards, one can hedge by matching the interest rate risk of assets with the interest rate risk of liabilities. Duration is the key to measuring interest rate risk. 25-24 Duration Hedging Duration measures the combined effect of maturity, coupon rate, and YTM on a bond’s price sensitivity to interest rates. Measure of the bond’s effective maturity Measure of the average life of the security Weighted average maturity of the bond’s cash flows 25-25 Duration Formula PV (C1 ) 1 PV (C2 ) 2 PV (CT ) T D PV N Ct t t t 1 (1 R ) D N Ct t t 1 (1 R ) 25-26 Calculating Duration: Example Calculate the duration of a three-year bond that pays a semiannual coupon of $40 and has a $1,000 par value when the YTM is 8%. 25-27 Duration Properties: Longer maturity, longer duration Duration increases at a decreasing rate Higher coupon, shorter duration Higher yield, shorter duration Zero coupon bond: duration = maturity 25-28 TEST SAM Berhad is issuing new bonds in order to get additional capital for financing its business operation. The par value is RM2,300. The bonds offer 9 percent coupon rate that will be compounded every six months with maturity period of 5 years. The required rate of return is 12 percent. Based on the information given, calculate duration of bond. 25-29 TUTORIAL Q: 1, 2, 6, 9, 11, 12 Page: 792 - 793