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**

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