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 increase the portfolio beta to 1.30 (rounded to the nearest integer)?
A) sell 70 contracts
B) buy 70 contracts
C) buy 87 contracts
D) buy 98 contracts
E) sell 67 contracts

Question

Quizplus · Accepted Answer

To increase the portfolio beta from 1.25 to 1.30, we need to add more risk to the portfolio. Since the beta of the futures contract is lower than the current portfolio beta, we need to buy futures contracts to increase our exposure to the market. The formula for calculating the required number of contracts is:

Number of contracts = (Desired new beta - Current beta) x Portfolio value / Futures contract value x Futures contract beta

Number of contracts = (1.30 - 1.25) x $150 million / ($250 x 1.0) = 0.05 x $600,000 = $30,000

To round this to the nearest integer, we divide by the dollar value of one contract:

$30,000 / ($250 x 1.0) = 120 contracts

Therefore, we should buy 120 contracts, which is closest to option C (buy 87 contracts).