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FN307 Derivatives 1, Tutorial #2

1. Consider a portfolio consisting of \$50000 of IBM shares and \$40000 of Apple shares.  Apples shares have a market index beta of 1.2 whereas IBM shares have a market index beta of 1.1.  The market index futures price is \$150.00 and the index futures contract is for 10 times the index. What is the risk-minimizing hedge for this portfolio using futures on the market index to hedge? Write the answer in terms of the (fractional) number of contracts.

 amount weight beta ibm 50000 0.555556 1.1 apple 40000 0.444444 1.2 total 90000 1 1.144444 units per contract 10 future price 150 contracts 68.66667 short
1. It is July 1st. A coffee manufacturer plans to purchase 600,000 pounds of coffee in 30 days.  In order to partially hedge its risk, it goes long 15 coffee futures contracts for delivery in three months (futures delivery date is October 1st).  Each coffee futures contract is for delivery of 37,500 pounds.  On July 1st the spot price of coffee is \$1.30 per pound and the futures price is \$1.32 per pound.  On July 31st the spot price of coffee is \$1.24 per pound and the futures price is \$1.25 per pound.  What is the coffee manufacturers effective purchase price for coffee?
 units per contract 37500 number of contracts 15 final futures price 1.25 initial futures price 1.32 spot price on termination date 1.24 number of units of actual 600000 cash purchase 744000 hedging profit -39375 effective purchase price 1.30563

1. Consider a portfolio consisting of two stocks, 70% invested in IBM Inc. shares and 30% invested in Apple Inc. shares.  IBM shares have a per-annum return standard deviation of 35% whereas Apple Inc. shares have a per-annum return standard deviation of 20%; the correlation between the two returns is .35.  What is the per-annum standard deviation of the portfolio’s return?
 amount weight stand dev correlation variance ibm 700000 0.7 0.35 0.35 apple 300000 0.3 0.2 0.271873 0.073915

1. A trader has a short position of 450 contracts in the FTSE futures contract.  Each contract is for £10 times the index.  If the index futures price increases from 1175 to 1185 over the course of a trading day (close to close) what is the daily mark-to-market cash settlement on the trader’s position?

 number of contracts 450 units per contract 10 initial futures price 1175 closing futures price 1185 daily settlement -45000

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