Introduction

In this chapter, we delve into the practical aspect of managing key rate risks within a portfolio. Key rate risk refers to the sensitivity of the portfolio’s value to changes in specific key interest rates. To effectively hedge these risks, we need to calculate the positions in hedging instruments such as interest rate derivatives. This process is crucial for minimizing potential losses due to interest rate movements that could adversely affect the portfolio’s value. We will explore the methods and strategies used to compute these positions and ensure effective risk management.

Calculating Positions to Hedge Key Rate Risks

To calculate positions in hedging instruments necessary to hedge key rate risks, we must first identify the specific key rates to which the portfolio is exposed. Key rates are interest rates for various maturities along the yield curve. Once identified, we can determine the portfolio’s sensitivity, often measured in terms of key rate 01 (KRD), to changes in these rates.

The formula to calculate the portfolio’s key rate 01 for a specific key rate is as follows:

$$KR{D}_{\text{Portfolio, Key Rate}}=-\frac{\partial \text{(Portfolio Value)}}{\partial \text{(Key Rate)}}$$

Where:

• $KR{D}_{\text{Portfolio, Key Rate}}$ represents the portfolio’s key rate 01 for a specific key rate
• $\frac{\partial \text{(Portfolio Value)}}{\partial \text{(Key Rate)}}$ represents the change in the portfolio’s value with respect to a change in the specific key rate

Once we have determined the KRD for each key rate to which the portfolio is exposed, we can proceed to hedge these risks. The hedge positions can be calculated as:

$$\text{Hedge Position}=KR{D}_{\text{(Portfolio, Key Rate)}}\times \text{(Change in Key Rate)}\times \text{(Hedge Ratio)}$$

Where:

• Hedge Position is the position in the hedging instrument needed to hedge the key rate risk
• $KR{D}_{\text{(Portfolio, Key Rate)}}$ is the portfolio’s key rate 01 for the specific key rate
• Change in Key Rate is the expected change in the specific key rate
• Hedge Ratio represents the ratio of the hedging instrument to the portfolio

Example: Let’s consider an example where a portfolio has a KRD of -500 for a 2-year key rate. If we expect the 2-year key rate to increase by 1 basis point (0.01%), and our hedge instrument has a hedge ratio of 0.95, we can calculate the hedge position as follows:

$$\text{Hedge Position}=(-500)\times (0.0001)\times (0.95)=-0.0475$$

This means we need to take a short position in the hedging instrument equivalent to -0.0475 units for every 1 basis point increase in the 2-year key rate to hedge our portfolio’s key rate risk.