USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Consider a portfolio manager with a $10,000,000 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 1350 and has a multiplier of 250. The portfolio beta is 1.50.
-Refer to Exhibit 15.13. Calculate the number of contract required to hedge the risk exposure and indicate whether the manager should be short or long.
A) 100 contracts long
B) 44 contracts long
C) 44 contracts short
D) 100 contracts short
E) 75 contracts short

Question

Quizplus · Accepted Answer

The number of contracts needed to hedge the portfolio is calculated using the formula: $ \text{Number of Contracts} = \frac{(\text{Portfolio Value} \times \text{Portfolio Beta})}{(\text{Index Future Price} \times \text{Multiplier})} $. Substituting the given values: $ \text{Number of Contracts} = \frac{($10,000,000 \times 1.5)}{(1350 \times 250)} = 44.44 $. Since you can't trade a fraction of a contract, you round to the nearest whole number, which is 44. The manager should be short the futures to hedge against a decline in share values, hence 44 contracts short.