Introduction

In the realm of interest rate risk management, the concept of duration plays a crucial role. Duration provides insights into the sensitivity of a bond’s price to changes in interest rates. To effectively manage this risk, investors often employ a duration-based hedging strategy using interest rate futures. This chapter explores how to calculate the duration-based hedge ratio and design a strategy that aims to mitigate interest rate fluctuations.

Calculating the Duration-Based Hedge Ratio

The duration-based hedge ratio represents the ratio of the change in the value of a portfolio’s assets to the change in the value of the interest rate futures contract. Mathematically, the duration-based hedge ratio can be expressed as:

$$H=\frac{M D_A}{M D_F}$$

Where:

• $H$ is the duration-based hedge ratio.
• $M D_A$ is the modified duration of the portfolio of assets.
• $M D_F$ is the modified duration of the interest rate futures contract.

Creating a Duration-Based Hedging Strategy:

To implement a duration-based hedging strategy, follow these steps:

Step 1: Determine the Portfolio’s Modified Duration $(MD_A)$
Calculate the modified duration of the portfolio of assets. Modified duration represents the sensitivity of the portfolio’s value to changes in interest rates. It can be computed using the formula:

$$MD_A=-\frac{1}{P_A} \times \frac{d P_A}{d y}$$

Where:

• $P_A$ is the initial value of the portfolio.
• $\frac{d P_A}{d y}$ is the change in the value of the portfolio due to a small change in yield $(d y)$.

Step 2: Calculate the Modified Duration of the Futures Contract $(MD_F)$
Determine the modified duration of the specific interest rate futures contract that you intend to use for hedging.

Step 3: Compute the Duration-Based Hedge Ratio (H)
Apply the duration-based hedge ratio formula to find the appropriate ratio for your hedging strategy.

Step 4: Select the Quantity of Futures Contracts to Hedge
Multiply the calculated hedge ratio by the value of the portfolio to determine the number of futures contracts needed for effective hedging.

Step 5: Monitor and Adjust the Hedge
Continuously monitor the market and the portfolio’s performance. If necessary, adjust the hedge ratio based on changes in market conditions or the portfolio’s composition.

Example: Assume a portfolio of bonds with a modified duration $(MD_A​)$ of 5 years and an interest rate futures contract with a modified duration $(MD_F​)$ of 4 years. Calculate the duration-based hedge ratio (H) and determine the appropriate number of futures contracts to hedge a USD 1 million portfolio.

Solution: $$H=\frac{M D_A}{M D_F}=\frac{5}{4}=1.25$$

If each futures contract covers USD 100,000 notional, then the number of contracts needed would be: $$\text { Number of contracts }=H \times \frac{\text { Portfolio value }}{\text { Contract notional }}=1.25 \times \frac{1,000,000}{100,000}=12.5$$

In practice, you would round up to 13 contracts to ensure adequate hedging.