USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Consider a portfolio manager with a $20,500,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1250 and has a multiplier of 250. The portfolio beta is 1.25.
-Refer to Exhibit 15.10. Assume that a month later the equity portfolio has a market value of $20,000,000 and the stock index future is priced at 1150 with a multiplier of 250. Calculate the profit on the stock index futures position.
A) $1,550,000
B) -$2,000,000
C) $2,050,000
D) -$5,000,000
E) $2,400,000

Question

Quizplus · Accepted Answer

To hedge against a decline in share values using stock index futures, the manager needs to sell futures contracts.
Number of contracts = (Portfolio value * beta) / (futures contract price * futures multiplier)
Number of contracts = (20,500,000 * 1.25) / (1250 * 250) = 65
After a month, the portfolio value has declined to $20,000,000, resulting in a loss of $500,000. However, the stock index futures contract has gained $100 per unit (1250 - 1150) resulting in a profit of $25,000 per contract.
Profit on futures position = 65 * 250 * $25,000 = $2,050,000.