Introduction

In fixed income analysis, understanding the measures of price sensitivity is paramount for making informed investment decisions. Two widely used measures in this context are DV01 (Dollar Value of 01) and effective duration. Both DV01 and effective duration provide insights into how the price of a fixed income security or portfolio may change in response to changes in interest rates. However, they serve different purposes and have distinct characteristics. In this chapter, we will delve into a detailed comparison and contrast of DV01 and effective duration, shedding light on their unique roles and applications.

DV01: Dollar Value of 01

DV01, often referred to as the “dollar duration”, quantifies the change in the price of a fixed income security or portfolio for a 1-basis point (0.01%)$ change in yield. It is a linear measure of price sensitivity and is particularly useful for assessing the immediate impact of small changes in interest rates. The formula for calculating DV01 is as follows:

$$DV01=-\frac{d P}{d y}$$

Where:

• $DV01$ is the Dollar Value of 01
• $dP$ is the change in the price of the security or portfolio
• $dy$ is the change in yield in decimal form (e.g., 0.01 for a 1-basis point change)

Effective Duration

Effective duration, on the other hand, provides a measure of the weighted average time to receive the cash flows from a fixed income security or portfolio, taking into account both its coupon payments and principal repayment. It accounts for the non-linear relationship between bond prices and yields, making it a more accurate measure of price sensitivity when interest rate changes are substantial. The formula for calculating effective duration is as follows:

$$\text {Effective Duration}=-\frac{1}{P} \times \frac{dP}{dy}$$

Where:

• Effective Duration is the effective duration of the security or portfolio
• $P$ is the current price of the security or portfolio
• $dP$ is the change in the price of the security or portfolio
• $dy$ is the change in yield in decimal form

Comparison and Contrast

Linearity vs. Non-Linearity

• DV01 is a linear measure, assuming a constant price-yield relationship, which is suitable for small yield changes.
• Effective duration accounts for non-linearity in the price-yield relationship, providing a more accurate measure for larger yield changes.

Immediate vs Weighted Impact

• DV01 measures the immediate price impact of a 1-basis point yield change.
• Effective duration considers the weighted average time it takes to receive cash flows, reflecting the timing of interest and principal payments.