Explanation:
The number of stock contracts required to hedge the portfolio is calculated as:
Number of contracts = Beta of the portfolio × (Value of the portfolio / (Futures price × Contract multiplier))
Since the portfolio doesn't perfectly mirror the S&P 500 index, the beta of the portfolio of 0.78 will be considered in the calculation.
The initial number of contracts that the manager shorted at the time of purchasing the S&P 500 futures contract was:
Number of contracts required = 0.78 × [672,000,000 / (2,906 × 250)] = 722 contracts.
A month later, when the futures price fell from 2,906 to 2,715, the new number of contracts required to hedge the portfolio is now:
= 0.78 × [672,000,000 / (250 × 2,715)] = 772 contracts
Therefore, the manager must short an additional 50 futures contracts (772 − 722 = 50) on the S&P 500 index.
Q.640 Julia Lange, an investment manager, has constructed a portfolio with a beta of 0.78 that somewhat mirrors the S&P 500 index. The investment manager hedged the portfolio 1 month ago by taking a short position in the S&P 500 futures. The portfolio had a value of $672,000,000, and the S&P 500 index futures price at the time of the purchase was 2,906, with each contract on 250 times the index. If the S&P 500 futures contract price fell to 2,715 this month, then estimate the number of additional contracts Lange should buy/short to hedge her portfolio, assuming that the portfolio value does not change.
A
The manager must short an additional 50 S&P 500 futures contract to hedge the portfolio.
B
The manager must buy 50 S&P 500 futures contracts to hedge the portfolio.
C
The manager must short an additional 2,715 S&P 500 futures contracts to hedge the portfolio.
D
The manager must short an additional 772 S&P 500 futures contracts to hedge the portfolio.
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