Question

Suppose that a portfolio is worth $600 million. The beta of the portfolio is 1.5. The portfolio manager would like to use the CME December futures contract on the S&P 500 to change the beta of the portfolio to 0.5. The index is currently 2,400, and each contract is $250 times the index.

1. What is the future position required to reach this goal?

2.Long or short?

3.How many contracts?

Answer 1

Portfolio worth = $600 million.

Beta of the portfolio = 1.5.

Targeted Beta of the portfolio = 0.5. The portfolio manager would like to use the CME December futures contract on the to change the beta of the portfolio to 0.5.

S&P 500 index current value = 2,400,

CME December futures contract size = $250 times the index.

The manager wants to reduce the Beta from 1.5 to 0.5. To reduce the beta of the portfolio, the future position required will be to short (sell) the contracts so as to reduce the volatility.

Number of contracts to be sold = ((Current Beta-Target Beta)*Value of portfolio)/(Contract size*index value)

= ((1.5-0.5)*600,000,000)/(250*2400) =  600,000,000/600,000 = 1,000 contracts