Introduction

In this chapter, we will delve into the practical application of effective duration and convexity in the context of hedging within the fixed income market. Hedging is a risk management strategy used to offset potential losses due to adverse price movements. By understanding effective duration and convexity, we can develop strategies to protect our fixed income portfolios from interest rate fluctuations. This chapter will illustrate how these concepts are employed in a real-world hedging scenario.

Hedging with Effective Duration and Convexity

Effective duration and convexity play a crucial role in constructing hedges for fixed income portfolios. Let’s consider an example to understand how these concepts can be applied effectively.

Example: Imagine you manage a portfolio of bonds with a total market value of USD 10 million, and you anticipate that interest rates may rise in the near future. As interest rates rise, bond prices typically fall, potentially leading to losses in your portfolio. To mitigate this risk, you decide to hedge your portfolio using Treasury bond futures contracts.

Step 1: Calculate the Portfolio’s Effective Duration
Effective duration measures the sensitivity of a bond or portfolio’s price to changes in interest rates. To calculate the effective duration of your portfolio, follow this formula:

$$\text{Effective Duration} = \frac{(\Delta P/P)}{\Delta Y}$$

Where:

• $\Delta P$ is the change in the portfolio’s market value due to an interest rate change.
• $P$ is the initial market value of the portfolio.
• $\Delta Y$ is the change in interest rates. Let’s assume that the effective duration of your USD 10 million portfolio is 7.2 years.

Step 2: Calculate the Treasury Bond Futures Needed
Next, you need to determine how many Treasury bond futures contracts are required to hedge your portfolio effectively. Treasury bond futures are often used for interest rate hedging because they have a duration of approximately 10 years.

To hedge your USD 10 million portfolio with an effective duration of 7.2 years, you would need to short-sell Treasury bond futures contracts equivalent to a duration of 7.2 years. Since each Treasury bond futures contract has a duration of 10 years, you would need to short-sell 0.72 (7.2/ 10) futures contracts.

Step 3: Monitoring and Adjusting the Hedge
As interest rates change, the effective duration of your portfolio may also change. To maintain an effective hedge, you must continuously monitor the portfolio’s effective duration and adjust the number of futures contracts accordingly.