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Answer: Short 9.0 contracts
To reduce a portfolio’s beta using stock index futures, the required number of contracts is \[ N = \frac{(\beta_P - \beta_T) \times V_P}{F \times Q_F} \] where: - \(\beta_P = 1.30\) - \(\beta_T = 0.70\) - \(V_P = 9{,}000{,}000\) - Futures price \(F = 2{,}400\) - Contract multiplier \(Q_F = 250\) Contract value: \[ 2{,}400 \times 250 = 600{,}000 \] Difference in beta: \[ 1.30 - 0.70 = 0.60 \] Thus: \[ N = \frac{0.60 \times 9{,}000{,}000}{600{,}000} = 9 \] Because the goal is to reduce beta, Sally should **short 9 futures contracts**.
Author: Manit Arora
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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
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