What should he do to make the beta of his portfolio zero?

An equity portfolio manager desires to be ‘market neutral’. His portfolio is valued at $10m and has a beta of 0.7 to the broad market index. The index is currently at 1000 and an index contract multiplier is specified as 250.

What should he do to make the beta of his portfolio zero?
A . Sell 40 contracts of the index futures contract
B . Buy 28 contracts of the index futures contract
C . Buy 40 contracts of the index futures contract
D . Sell 28 contracts of the index futures contract

View Answer

Answer: D

Explanation:

In terms of beta, his exposure is $10m*0.7 = $7m. This exposure is long. In order order to neutralize his long exposure, he needs to have an equal an identical short position with the same beta as this long position (of course, in the short direction). We need to figure out how many contracts will have a beta equal to his held position. (The beta of a futures contract is slightly different from 1 when compared to spot, but in the absence of other information in the question it is always okay to assume that the beta of the futures contract is 1. Such precision does not matter because of other errors such as rounding etc that cannot be anyway done away with.)

He needs to short futures contracts on the index with $7m in notional value. The value of each contract is currently 1000*250 =$250,000. He therefore needs to short $7m/$250,000 = 28 contracts to become market or beta neutral.