Financial Risk Manager Part 2

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Explanation:

The optimal hedge ratio ( $\beta$ ) that minimizes the variance of the hedged portfolio is calculated using the formula: $\beta = \rho(Y_h, Y_p) \times \frac{\sigma(Y_p)}{\sigma(Y_h)}$ Given the data: $\rho(Y_h, Y_p) = 0.6$ $\sigma(Y_p) = 0.08$ $\sigma(Y_h) = 0.05$

Substituting the values into the formula: $\beta = 0.6 \times \left( \frac{0.08}{0.05} \right) = 0.6 \times 1.6 = 0.96$

Explanation:

Substituting the values into the formula: $\beta = 0.6 \times \left( \frac{0.08}{0.05} \right) = 0.6 \times 1.6 = 0.96$

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Q.56 An investment analyst is tasked with calculating the hedge ratio (β) for a bond portfolio using bond futures. The following data is provided:

The correlation between the returns of the bond portfolio and the bond futures:
$\rho(Y_h, Y_p) = 0.6$

The standard deviation of the bond portfolio returns: $\sigma(Y_p) = 0.08$

The standard deviation of the bond futures returns: $\sigma(Y_h) = 0.05$

What is the hedge ratio (β) required to minimize the bond portfolio's exposure to interest rate risk?

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Last updated: July 5, 2026 at 08:32

1.92

1.50

1.20

0.96