Question

It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the December futures contract on a stock index to change beta of the portfolio to 0.5 during the period July 16 to November 16. The index is currently 2,000, and each contract is on $250 times the index. What position should the company take? long 140 contracts short 140 contracts long 240 contracts short 240 contracts

Answer 1

Answer:short 140 contracts

Explanation: Using the formulae

Number of Contracts (Company's position )=( Desired Beta of the portfolio - beta of the portfolio) x Portfolio of stocks) / ( Future Value )

Future Value = Index futures price x Multiplier

=2000 x 250

=$500,000

Putting the values, we have that

Company position =(0.5 -1.2) x $100 million) / $500,000

Company position=-0.7 x $100 million/500,000

Company position=-$70,000,000/500,000

Number of contracts (Company position)=-140 contract

A negative sign means that the contract is going short.

Therefore,

A total of 140 contracts by the company should be short.