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Answer: c) Long 20 S&P 500 futures contracts
To increase beta from 0.30 to 1.00, the manager must add positive market exposure through futures. The number of contracts is: \[ N = (\beta_T - \beta_P)\frac{V_p}{V_f} \] where: - \(\beta_T - \beta_P = 1.0 - 0.30 = 0.70\) - \(V_p = 10{,}000{,}000\) - \(V_f = 250 \times 1380 = 345{,}000\) So: \[ N = 0.70 \times \frac{10{,}000{,}000}{345{,}000} \approx 20.29 \] Rounding to the nearest whole number gives **long 20 S&P 500 futures contracts**.
Author: Manit Arora
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Question 155.2. An investment manager owns a large-cap equity portfolio with a market value of $10 million. The portfolio has a beta, with respect to the S&P 500 (as a proxy for the market), of 0.30. The S&P 500 index futures price is 1,380. The manager wants to increase the portfolio’s beta to 1.0. What is the trade?
A
a) Long 9 S&P 500 futures contracts
B
b) Short 9 S&P 500 futures contracts
C
c) Long 20 S&P 500 futures contracts
D
d) Short 20 S&P 500 futures contracts
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