An asset manager holds an equity portfolio valued at $25m with a beta of 0.

The portfolio's beta is 0.8, and therefore in order to completely hedge the portfolio (ie reduce beta to 0), the portfolio manager would need to short 0.8 * $25m/(1450*$250) = 55.17 contracts, or 55 contracts. However, the ask here is to reduce the beta to 0.6, and not 0.

The number of contracts required to reduce the beta of a portfolio from ߠto ߱ is give by (ߠ- ߱) * Value of portfolio / Value of a single contract. In this case, this calculation works out to (0.8 - 0.6) * $25m/(1450*250) = 13.8, or roughly 14 contracts.

The portfolio manager should short 14 index futures contracts to reduce the total portfolio beta to 0.6.