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Fn 307 Question Answers

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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

1.305625

  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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