Final answer:
To reduce the portfolio beta from 1.5 to 1.0 for a $75 million portfolio, the company needs to sell 200 futures contracts on an index with a futures price of 3,750 and a contract multiplier of $50.
Step-by-step explanation:
To calculate the number of futures contracts needed to adjust the portfolio's beta to 1.0, we need to determine the change in beta required and the beta per contract, and then use these to find the number of contracts to trade.
The current portfolio value is $75 million with a beta of 1.5. The objective is to lower the beta to 1.0. Each futures contract is based on an index times $50, and the futures price is 3,750.
First, calculate the hedge ratio: (Current Beta - Desired Beta) / Index Beta. Since the index beta is typically 1 (as it represents the market), the hedge ratio is (1.5 - 1.0) / 1 = 0.5. Then, determine the position size that needs to be hedged: $75 million * 0.5 = $37.5 million. Finally, divide the position size by the value of one contract: $37.5 million / ($50 * 3750) = 200 contracts. Therefore, to adjust the portfolio's beta to 1.0, the company needs to sell 200 futures contracts.