Q.6506 A portfolio manager is hedging the price movements of a corporate bond portfolio ($Y_p$) using a government bond futures contract ($Y_h$). The following data is available:

• The correlation between the returns of the corporate bond portfolio and the government bond futures: $\rho(Y_h, Y_p) = 0.8$
• The standard deviation of the returns of the corporate bond portfolio: $\sigma(Y_p) = 0.05$
• The standard deviation of the returns of the government bond futures: $\sigma(Y_h) = 0.04$

What is the hedge ratio ($\beta$) that the portfolio manager should use to minimize the portfolio's exposure to interest rate risk?