
Explanation:
To reduce a portfolio’s beta using stock index futures, the required number of contracts is
where:
Contract value:
Difference in beta:
Thus:
Because the goal is to reduce beta, Sally should short 9 futures contracts.
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Question 711.3. Sally, the portfolio manager, oversees a $9.0 million large-cap equities portfolio with a beta of 1.30. She has decided the portfolio’s beta is too high and calibrates a new target beta of 0.70. If she employs S&P 500 index futures contracts to reduce the beta when the index futures price is 2,400 (the contract size is $250 * S&P 500 index per the specification), then which is nearest to the trade?
A
Short 9.0 contracts
B
Short 27.0 contracts
C
Short 54.0 contracts
D
Long 13.0 contracts