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

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.

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