FIN 436 – Problem Set #1
PROBLEM SET 1 – FUTURES AND OPTIONS FIN 436 1. You have opened a futures account with a cash deposit of $10,000.00. You decide to sell 8 October contracts of bean meal at 305.4. Contract specs are as follows: CONTRACT UNIT 100 TONS QUOTE UNITS US$ AND CENTS/TON TIC SIZE CONTRACT MOS. 0.10/TON = $10.00 Jan, Mar, May, Jul, Sep, Oct, Dec INITIAL MARGIN $1,122/ CONTRACT MAINT MARGIN $1,020/ CONTRACT If soybean meal drops $.10, what is the equity of the account when marked-to-market? 2. You are day-trading the S&P E-Mini contract with $5,750.00 of equity in your account. Contract specs are as follows: CONTRACT UNIT $50 x S&P 500 INDEX QUOTE UNITS US$ AND CENTS/TIC TIC SIZE CONTRACT MOS. 0.25 INDEX PTS = $12.50 Mar, Jun, Sep, Dec INITIAL MARGIN $907.50/ CONTRACT (DAY-TRADE) MAINT MARGIN $825/ CONTRACT (DAYTRADE) Based on your new sophisticated algorithm, there is an 85% chance that the S & P will fall over the next half hour, so you go all in by selling 6 June contracts. The market rises 5 tics, and then plunges 50 tics when you flatten your position (buy to close them all). What was your gross profit or loss for the day? 3. After the trade in Problem 2, you decide to buy October Copper futures (HGV-). Contract specs are as follows: CONTRACT UNIT 25,000 lbs QUOTE UNITS US$ & CENTS/ib TIC SIZE CONTRACT MOS. $.0005/lb = $12.50 3 NEAREST MOS. + Feb, Apr, Aug, Oct INITIAL MARGIN $5,800/ CONTRACT MAINT MARGIN $5,500/ CONTRACT a. How many contracts can you (safely) buy? b. If HGV then declines $0.0455 per pound, what is the market-to-market equity in the account? 4. You are a trading associate at a major bank. Your supervisor assigns you with an assignment to hedge against increases in future interest rates the bank’s inventory of two-year notes. You have these alternatives: I. Sell the necessary (optimal) amount of 2-year treasury futures, longest delivery date. II. Sell the necessary (optimal) amount of 2-year treasury futures, shortest delivery date. III. Buy necessary (optimal) amount of 2-year treasury futures puts, longest delivery date. IV. Buy necessary (optimal) amount of 2-year treasury futures puts, shortest delivery date. V. Buy necessary (optimal) amount of 2-year treasury futures calls, shortest delivery date. What do you do? a. b. c. d. Either I. or III. Either I., III., or V. Either I., II., III., or IV. Only V. 5. Silver futures and spot silver have a correlation factor of 0.97. If the standard deviation for the futures contract is 2.98 and the standard deviation for the spot is 1.87, what is the optimum hedge ratio? 6. Based on the results in Problem 5, what is the optimum number of SIL contracts to hedge 5,220 troy ounces of silver held in inventory? (Each mini-futures contract represents 1000 troy ounces – SIL is the symbol for Silver Micro-contracts). 7. You are the CFO of an airline and you are concerned that jet fuel prices will increase. You know that there are no futures for jet fuel, but there are futures for gasoline. So, you call decide to check the spot price of jet fuel and gasoline. Changes in their relative prices are as follows: Mo 1 Mo 2 Mo 3 Mo 4 Mo 5 Mo 6 Mo 7 Mo Gas Futures 2.0% 3.0% -4.0% 0.0% 3.5% -3.0% -2.5% 2.0% 3.5% -5.0% 1.0% 2.6% -2.0% -1.0% Mo Jet Fuel If you are trying to hedge 1,000,000 gallons of jet fuel, how many gasoline contracts do you need to buy to adequately hedge your position? (Each futures contract represents 42,000 gallons of gasoline). 8. What is a cross-hedge? a. It is a trade between similar commodities, different delivery dates, intended to hedge against a detrimental change in price. b. It is a trade between two uncorrelated commodities. c. It is a trade between a commodity and a closely price-correlated non-traded commodity, intended to hedge against a detrimental change in price. d. I don’t know, and don’t care. 9. Your futures account had equity of $20,000.00 at the start. Given the following positions, what is the account’s equity balance? (Refer to the contract specifications in the chart following). Cost Basis per POSITIONS QTY Equity Contract Unit, Price Now (Contract Time of Purchase Sep Wheat Dec Gold Dec Cocoa Cash TOTAL 5 1 2 – CONTRACT UNIT QUOTE UNITS TIC SIZE Wheat 5,000 bu ¢/bushel $0.01 Value) 572’0 $1,554.70 $2,526.00 $3,445.00 $20,000.00 Gold 1,000 troy oz $1.00/troy oz $0.10 Cocoa 10 m tons $1.00 $ / ton 559’2 $1,666.50 $2,756.00 $3,445.00 $3,445.00 $ MOS. Mar, May, Jul, Sep, Dec Feb-Apr, Jun, Aug, Dec Mar, May, Jul, Sep, Dec INITIAL MGN MAINT MGN $1,375 $1,250 $5,500 $5,000 $2,090 $1,900 10. Note the following contract specifications: CONTRACT UNIT QUOTE UNITS TIC SIZE INITIAL MGN MOS. MAINT MGN .25c = H,K,N,U,Z $2,805 $2,550 $12.50 1000 $ and cents $.01/bl = WTI Crude Oil (CL) All Mos. $7,260 $6,660 bls /barrel $10.00 50000 cents and $.0001/lb= Cotton (CT) H,K,N,U,Z $3,713 $3,375 lbs 1/100 cents $5.00 Assuming you were long 2 contracts of each of these commodities, how much would the total account value decline if EACH position DECLINED 2.5% (round price to the nearest tic)? Corn (C) 5000 bu 1/4c/bushel 11. You are working for a home builder, and want to hedge against increases in lumber prices. You estimate that you will need 2,687,500 board feet of 2″x4″x84″ stud lumber to complete their tract. Doing some research, you find that contract specs for the closest commodity is for Random Length Lumber: CONTRACT UNIT QUOTE UNITS TIC SIZE MOS. INITIAL MGN MAINT MGN R L Lumber 110,000 bd ft $/1K bd ft $0.10 /bd ft= $11 Jan, Mar, May, Jul, Sep, Nov $2,475 $2,225 Further research has shown that the correlation between spot 2 X 4 lumber and Random Length Lumber is .9275. Meanwhile, the variance of price for 2 X 4 lumber is only .246, while the variance of random length lumber is .378. Given this information, what is the hedge ratio? (Round to the nearest thousandth). 12. You still work for a home builder. Now that you have calculated the hedge ratio (see Problem 11), based on the information in Problem 11, what is the optimal number of contracts you need to hedge your future orders of stud lumber? (Round to the nearest contract – no fractional contracts!).
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