Answer-first summary for fast verification
Answer: d) Short 250 S&P futures contracts
The portfolio beta relative to the index is: \[ \beta_{p,i} = \rho_{p,i}\frac{\sigma_p}{\sigma_i} = 0.75 \times \frac{40\%}{20\%} = 1.50 \] One S&P 500 futures contract has a value of: \[ 250 \times 1320 = 330{,}000 \] The number of contracts needed is: \[ N = \beta \times \frac{V_p}{V_f} = 1.5 \times \frac{55{,}000{,}000}{330{,}000} = 250 \] Because the manager wants to hedge a long equity exposure, the correct trade is to **short 250 S&P futures contracts**.
Author: Manit Arora
Ultimate access to all questions.
Question 155.1. An investment manager holds a large-cap equity portfolio with a current market value of $55 million. The portfolio has a return volatility of 40% compared to the S&P 500 index volatility of 20%. The correlation between the portfolio returns and index returns is 0.75. Finally, the near-term maturity of the S&P 500 futures price is 1,320. The manager wants to hedge against overall market exposure (i.e., the S&P 500 is the imperfect proxy of the overall market). What is the hedge trade?
A
a) Long 125 S&P futures contracts
B
b) Short 125 S&P futures contracts
C
c) Long 250 S&P futures contracts
D
d) Short 250 S&P futures contracts
No comments yet.