Class HW 4 Solution PDF

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Class HW #4 Solutions...

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Finance 4720

Class Homework #4 Solution

Professor Joel Rentzler

Test whether the gold and copper futures markets are at full carry (i.e. whether the convenience value is approximately zero) by examining the relationship on October 12, 1988 between the December 1988 and February 1989 gold futures settlement prices and the December 1988 and March 1989 copper futures settlement prices. Assume the following: (1)The holding period between the gold contracts is two months and the holding period between the copper contracts is 3 months. (2) The 3-month T-Bill rate implied by the October 12, 1988 T-bill futures contract was 7.36%. (3) The storage costs for gold is $6/month plus a $14 one-time transfer fee for the gold covered by each gold futures contract. (4) The storage costs for copper is $39.50/month plus a $3.95 one-time transfer fee for the copper covered by each copper futures contract. (5) The costs in (3) and (4) are paid when the metal is taken out of storage. tFT2= tFT1 ( 1 + T1rT2 ) + T1CT2- T1CVT2 GOLD t = 10/12/88, T1 = 12/88, T2 = 2/89, tFT1 = $412.20 T1CT2 = 6 ( 2 ) + 14 = $ 26 / 100 oz. = $ .26 / oz. E tF T2 = equilibrium futures price if market at full carry = 412.20 [ 1 + ( 2 / 12 ) ( .0736 ) ] + .26 = $ 417.53 E tF T2 - tFT2 = 417.53 - 417.40 = $ .13 = T1CVT2 Since .13 / 412.20 = .03% of the 12/88 Futures Price this ⇒ T1CVT2 is approximately zero. COPPER t = 10/12/88, T1 = 12/88, T2 = 3/89, tFT1 = $1.2030 T1CT2 = 39.50 (3)+3.95= $122.45/25000 lbs. = $0.0049 / lb. E T1F T2 = 1.2030 [ 1 + ( 3 / 12 ) ( .0736 ) ] + .0049 = $1.2300 E tF T2 - tFT2 = 1.2300 - 1.0700 = $ .16 = T1CVT2 Since .16 / 1.2030 = 13% of 12/88 Futures Price this ⇒ T1CVT2 is significantly different from zero. American Airlines believes that it will need to buy 840,000 gallons of jet fuel in 3 months. The st. dev. of the change in price per gallon of jet over a 3 month period is calculated as 0.032 The company chooses to hedge by taking a position in futures contracts on heating oil. The st. dev. of the change in the futures price over a 3-month period is 0.040. The coefficient of correlation between the 3-month change in the price of jet fuel and the 3-month change in the futures price is 0.8, One heating oil futures contract is on 42,000 gallons. 1. What type of hedger should American be long or short? 2. What is the minimum variance hedge ratio? 3. How many futures contracts should they use to obtain the minimum variance hedge ratio? 4. What could happen to jeopardize this hedge? What is this risk called? 1. American should be a long hedger. 2. h* = R( Δ S , Δ F )( σ Δ S / σ Δ F ) = 0.8 * (0.032/0.040) =0.64 3. NF*=h* (S/F) =0.64(840,000/42,000) =13 Contacts 4. a. American Air will need to have contracts in place b. Risk is called Quantity Risk Example 4.8 On May 20, a corporate treasurer learns that $3.3 million will be received on August 5. The funds will be needed for a major capital investment the following February. The treasurer therefore plans to invest the funds in 6-month Treasury bills as soon as they are received. The current yield on 6-month Treasury bills, expressed with semiannual compounding, is 11.20%. The treasurer is concerned that this may decline between May 20 and August 5 and decides to hedge using Treasury bill futures. The quoted price for the September T-bill futures contract is 89.44. In this case the

company will lose money if interest rates go down. The hedge must therefore provide a positive profit when rates go down or equivalen when Treasury bill prices go up. This means that a long hedge is required. DF=100-FIMM = (100-89.44) = 10.56 FC= 1M(1-(Nf/360)*DF) =1M(1-(90/360)*0.1056) =973,600 NF*= (3.3M*0.5)/(973,600*0.25) = 6.78 ~ 7 T-bill FC Worried about prices going UP, as a result u r a LH Example 4.9 It is August 2 and a fund manager with $10 M invested in government bonds is fund that interest expected to be highly volatile over the next 3 months. The manager decides to use the December T-bond futures contract to hedge the value of the portfolio. The current futures price is 93-02 or 93.0625 Since each contract is for the delivery of $100,000 face value of bonds, the futures contract price is $93,062.50. The average duration of the bond portfolio over the next 3 months will be 6.80 years. The cheapest-to-deliver bond in the T-bond contract is expected to be a 20-year 12% per annum coupon bond. The yield on this bond is currently 8.80% per annum, and the duration will be 9.20 years at maturity of the futures contract. FCbf= 93-02=$93,062.50 basis of 100k Bill ⇒ FC=$93,062.50 NF*=(10M*6.8)/(93,062.50*9.2) = 79.42 =79 Bond futures Contracts T-bill=1M par Value T-Bond= 100k par value Worried about prices going down, as a result u r a SH...