A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.9

Answer: Short 48 contracts.

Explanation: Portfolio beta is a systematic measure, that checks all the risk in a portfolio of investments. It is used in calculating the Treynors measure in a portfolio.

The trade necessary to reduce beta;

Take the change in beta

1.2 - 0.9 = 0.3

Using the beta formula; beta coefficient multiplied by the weight of the portfolio.

0.3 * $36,000,000 = $10,800,000

The future contract times the index can be traded on

900 * $250 = $225,000

Therefore the trade necessary to reduce beta will be

$10,800,000 : $225,000 = 48

This means that we have to short 48 contract if we want beta to reduce from 1.2 to 0.9