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 equity position.
A) $100,000
B) -$200,000
C) $600,000
D) -$500,000
E) $400,000

Question

Quizplus · Accepted Answer

To calculate the profit on the equity position, we need to first calculate the change in the value of the portfolio. The change in the value of the portfolio is:
Change in value of portfolio = $20,500,000 - $20,000,000 = $500,000
Since the portfolio beta is 1.25, the change in the value of the portfolio is expected to be 1.25 times the change in the value of the stock index future. Therefore, the change in the value of the stock index future is:
Change in value of stock index future = Change in value of portfolio / Beta
= $500,000 / 1.25
= $400,000
The profit on the equity position is the change in value of the portfolio minus the change in value of the stock index future. Therefore, the profit is:
Profit = Change in value of portfolio - Change in value of stock index future
= $500,000 - $400,000
= $100,000
Thus, the best choice is D.