1. FINA7351EXAM I ANS Q1. 1.1 The clearinghouse gives every trader of futures an absolute guarantee that the contract will be honored at delivery if he/she goes to delivery. That is, the long (short) is guaranteed to be able to take delivery and pay the contract price (deliver and receive the contract price) if he/she gets to delivery. 1.2Liquidity is defined to be the ease (speed) witch with traders can enter and exit the market. The easier it is, the more liquid the market is said to be. The guarantee implies no default at delivery. Thus, no credit risk nor completion risk exists. Hence, the market is anonymous - It makes no difference whatsoever who is the counterparty to any trade. So, a trader with any position, long or short, may exit the market instantly by opening a position that exactly offsets his/hers current position. With two offsetting position, a trader commits to buy and at the same time sell the same commodity on the same delivery date and thus, the trader is simply out of the market. Clearly, the offsetting position is opened at the current market price and profit or loss may occur. It follows that entry and exit from the futures market can be achieved instantly. Thus, the clearinghouse guaranty provides high liquidity in the futures market.

2. Q2. Observe the following wheat futures prices for three consecutive days: AUG 13, 2010, AUG 14, 2010 and AUG 15, 2010: Prices are given in cents per bushel. Wheat contract = 5,000 bushels. Delivery_____ Settlement Prices MonthAUG 13AUG 14 AUG 15 SEP10327.00327.50327.75 DEC10331.25331.75330.65 MAR11342.75343.00342.10 MAY11347.25346.75348.00 JUL11351.50351.00351.50 Your positions at the opening of trading on AUG 14 were: { 10 long SEP10; 30 long MAR11; 10 long JUL11; 20 short DEC10; 20 short MAY11 } You did not trade on AUG14 and not on AUG 15. Explain the cash flows into and out of your margin account by the end of trading on AUG 14 and AUG15 and calculate the net effect of these cash flows on the amount of capital in your margin account. Position Margin account AUG 14AUG 15 10 long SEP 10($.005)50,000 = $250($.0025)50,000 = $125 20 short DEC 10-($.005)100,000 = -$500($.011)100,000 = $1,100 30 long MAR 11($.0025)150,000 = $375-($.009)150,000 = -$1,350 20 short MAY 11($.005)100,000 = $500-($0.0125)100,000 = -$1,250 10 long JUL 11-($.005)50,000 = -$250($.005)50,000 = $250 Total change$375-$1,125

3. Q3. 3.1 The Basis on date j for a futures contract with delivery date T, B j,T for j ≤ T, is defined to be the difference between the commodity’s spot price on date j, S j, minus the date j futures price for delivery on date T, F j,T : B j,T = S j – F j,T 3.2 Suppose that when a hedger opens a short hedge at time t, and the basis is: - $1/unit. Later, on date k, the hedge is closed and the basis is: -$1/unit. DateSpot MarketFutures MarketBasis tS t Short a futures for-$1.00 delivery at T. F t,T kSell commodity for S k Long a futures for-$1.00 delivery at T. F k,T The actual selling price is: S k + F t,T – F k,T = F t,T + B k,T = F t,T – 1 = F t,T + B t,T = F t,T + S t - F t,T = S t. Alternatively, we showed in class that the selling price is: S k + F t,T – F k,T + S t – S t Rearranging the terms in the last equation yields: = S t + B k – B t. In our case the result is that the actual selling price is the initial spot price because B k = B t = -$1.

4. Q4. I agree with the statement. PROOF: In case of a long hedge we have: A LONG HEDGE TIMESPOTFUTURESB tContract to buyLONG F t,T B t Do nothing k BUY S k SHORT F k,T B k T Delivery Actual purchase price: = S k + F t,T - F k,T = F t,T + [S k - F k,T ] = F t,T + BASIS k In the case of a short hedge we have: A SHORT HEDGE TIMESPOTFUTURESB tContract to sellSHORT F t,T B t Do nothing k SELL S k LONG F k,T B k T Delivery Actual selling price: = S k + F t,T - F k,T = F t,T + [S k - F k,T ] = F t,T + BASIS k So in either hedge the actual price consists of the known futures price on date t plus the unknown and hence, risky, basis value on date k. In conclusion, opening a hedge implies that the original spot price risk is exchanged with the basis risk. This completes the proof that the statement is correct.

5. Q5. A speculator observe the following futures prices on FEB 3: F FEB3, JUL = $3.25/bushel; F FEB3, OCT = $3.95/bushel The speculator expects the spread to narrow. 5.1 Sell the spread: Short the OCT futures and Long the JUL futures. 5.2 On JUN 1 the market futures prices are: F JUN1, JUL = $2.85/bushel; F JUN1, OCT = $3.15/bushel, Close the spread: Long the OCT futures and Short the JUL futures. The speculator Profit per unit: $3.95 - $3.25 - $3.15 + $2.85 = $.40.

6. Q6. 6.1 DATESPOT MARKETFUTURES MARKET MAR 15Contracts to:Long 50 OCT WTI F = $53.90/barrel Buy 50,000 barrels WTI Sell 840,000 gallons GASShort 20 OCT GAS F = $1.57/ gallon on SEP 20 Do Nothing 6.2 DATESPOT MARKETFUTURES MARKET SEP 20Buy 50,000 barrels Short 50 OCT WTI F = $62.34/barrel WTI: S(WTI) = 59.00 Long 20 OCT GAS F = $1.47/gallon Sell 840,000 gallons of G: S(GAS) = 1.48 WTI purchase price = 53.90 + [59.00 – 62.34] = $50.56/barrel. GAS selling price = 1.57 + [1.48 – 1.47] = $1.58/gallon.

7. Q7. 7.1 Calculate the cash flow associated with this agreement on SEP 20. The payments are according to the contract between the refinery and ZZZ: 7.2 In the previous question we found that The refinery sells the GAS for $1.57/gallon. Now, together with the agreement with ZZZ, the refinery receives: 1.58 -.08 = $1.50/gallon. Notice that this selling price is the original spot price of $1.50/gallon on MAR 15. Refinery ZZZ 1.48 – 1.47 =.01 1.50 – 1.57 = -.07 Thus, the CF to the Refinery is: -.01 + (-.07) = -.08, which implies that the refinery pays ZZZ eight cents per gallon.

8. Q8. 8.1 The interest is paid out on a quarterly basis thus, we first, must make sure that the annual rate with quarterly compounding is equivalent to the annual rate of 10% with daily compounding. This ensures that at the end of five years the total amount in the account will be the same, regardless of the way the interest was paid out. Thus, by the definition of equivalent annual rates we have: $25,000[1+.1/365] 365(5) = $25,000[1+R 4 /4] 4(5) R 4 = 4([1+.1/365] 365/4 – 1) R 4 =.101246 or 10.1246% The quarterly interest paid out by the account is: $25,000[.101246]/4 = $632.7875. 8.2 r C, the annual rate with continuous compounding that is equivalent to the given 10% annual rate with daily compounding is defined by the following equality: $25,000e 5rC = $25,000[1+.1/365] 365(5) r C = 365ln[1 +.1/365] r C =.099986 or 9.9986 %