USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
As a portfolio manager, you are responsible for a $150 million portfolio, 90 percent of which is invested in equities, with a portfolio beta of 1.25. You are utilizing the S&P 500 as your passive benchmark. Currently the S&P 500 is valued at 1202. The value of the S&P 500 futures contract is equal to $250 times the value of the index. The beta of the futures contract is 1.0.
-Refer to Exhibit 15.11. How many contracts should you buy or sell in order to reduce the portfolio beta to 0.80 (rounded to the nearest integer)?
A) sell 162 contracts
B) buy 162 contracts
C) sell 324 contracts
D) buy 324 contracts
E) buy 234 contracts

Question

Quizplus · Accepted Answer

To adjust the portfolio beta to 0.80 from 1.25, you need to calculate the number of futures contracts to sell. The formula to determine the number of contracts is: $ \Delta Beta \times \frac{Portfolio Value}{Futures Price} $. Here, $ \Delta Beta = 0.80 - 1.25 = -0.45 $, Portfolio Value = $150 million \times 90% = $135 million, and Futures Price = $250 \times 1202 = $300,500. Thus, the number of contracts = $ -0.45 \times \frac{135,000,000}{300,500} $ = -162 (rounded to the nearest integer). Selling 162 contracts will adjust the portfolio beta to 0.80.