Key Rate Exposures
We will cover following topics
Introduction
Understanding key rate exposures and their characteristics is crucial in modeling non-parallel term structure shifts and effective hedging. In this chapter, we will delve into the concept of key rate exposures, examining what they represent and their significance in risk management. Additionally, we will explore the intricacies of key rate exposure factors, including partial 01s and forward-bucket 01s, with practical examples to illustrate their applications.
Key Rate Exposures
Key rate exposures are measures of the sensitivity of a bond or portfolio’s value to changes in specific key interest rates along the yield curve. These key interest rates are often referred to as “key rates” or “benchmark rates”. The purpose of measuring key rate exposures is to assess how a bond or portfolio would perform when specific interest rates change, allowing for effective risk management.
Characteristics of Key Rate Exposure Factors
Now, let’s break down the characteristics of key rate exposure factors:
1) Partial 01(P01)
Partial 01 measures the sensitivity of a bond’s or portfolio’s value to a 1 basis point (0.01%) change in the yield of a specific key rate while keeping other rates constant. Partial 01 can be calculated using below formula:
$$P01=- \frac{\Delta P}{\Delta y}$$
Where:
- $\Delta P$ is the change in the bond’s or portfolio’s value
- $\Delta y$ is the change in the key rate
Example: Consider a portfolio of bonds with a total value of USD 1,000,000. If the 2 -year key rate increases by 1 basis point, causing the portfolio value to decrease by USD 500, the partial 01 for the 2-year key rate is $\frac{-500}{0.01}$ = -50,000.
2) Forward-Bucket 01 (FB01)
Forward-bucket 01 measures the sensitivity of a bond’s or portfolio’s value to a 1 basis point change in the yield of a key rate within a specific future time bucket while keeping other rates constant. Forward-Bucket 01 can be calculated using below formula:
$$FB01=- \frac{\Delta P}{\Delta y}$$
Where:
- $\Delta P$ is the change in the bond’s or portfolio’s value
- $\Delta y$ is the change in the key rate within the time bucket
Example: Suppose a bond’s value decreases by USD 700 when the 5-year key rate within the 3to 5 -year time bucket increases by 1 basis point. In this case, the forward-bucket 01 for the 3- to 5-vear kev rate is $\frac{-700}{0.01}$ = -70.000.
Conclusion
Understanding key rate exposures and their associated factors, such as partial 01s and forward-bucket 01s, is fundamental in managing interest rate risk. These measures enable risk managers and investors to assess how their portfolios respond to changes in specific interest rates, aiding in effective hedging and decision-making. In the next chapters, we will further explore techniques for applying these exposure factors in practical risk management scenarios.