Explanation:

The hedge ratio (β) is calculated using the formula:

\beta = \frac{\text{Cov}(Y_h, Y_p)}{\text{Var}(Y_h)}

First, calculate Cov(Yₕ, Yₚ) using the formula:

\text{Cov}(Y_h, Y_p) = \rho(Y_h, Y_p) \cdot \sigma(Y_h) \cdot \sigma(Y_p)

Substituting the given values:

\text{Cov}(Y_h, Y_p) = 0.6 \cdot 0.05 \cdot 0.08 = 0.0024

Now substitute into the hedge ratio formula:

\beta = \frac{0.0024}{0.0025} = 0.96

Q.6507 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:
ρ(Yₕ, Yₚ) = 0.6

The standard deviation of the bond portfolio returns: σ(Yₚ) = 0.08

The standard deviation of the bond futures returns: σ(Yₕ) = 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 07:08

1.92

1.50

1.20

0.96

Financial Risk Manager Part 2