Understanding Bond Dollar Value of an 01 in Excel

DV01 is a measure of how much the price of a bond changes when the interest rate changes by a small amount (one basis point or 0.01%). It tells you how much money you would gain or lose if the interest rate goes up or down by one basis point.

For example, suppose you own a bond that has a price of $100 and a DV01 of $5. This means that if the interest rate increases by one basis point, the price of the bond will decrease by $5, and you will lose $5. Conversely, if the interest rate decreases by one basis point, the price of the bond will increase by $5, and you will gain $5.

DV01 is useful for comparing the interest rate risk of different bonds or portfolios of bonds. The higher the DV01, the more sensitive the bond is to changes in interest rates, and the more risky it is. The lower the DV01, the less sensitive the bond is to changes in interest rates, and the less risky it is.

DV01 is related to the duration of a bond, which is another measure of interest rate risk. Duration measures the percentage change in the price of a bond for a one-basis-point change in interest rates. DV01 measures the dollar change in the price of a bond for a one-unit change in interest rates. You can calculate the DV01 by multiplying the duration by the price of the bond and the change in interest rate in decimal form.

Basic Theory:

DV01 represents the change in the price of a bond for a one basis point (0.01%) change in yield. Essentially, it measures the bond’s interest rate risk. Bonds with higher DV01 values are more sensitive to interest rate changes.

The formula for DV01 is given by:

$DV01 = - \frac{1}{y} \times \frac{\partial P}{\partial y}$

Where:

$y$ is the bond’s yield.
$P$ is the bond’s price.

Procedures for Calculating DV01 in Excel:

Gather Bond Information:
- Collect data on the bond’s face value, coupon rate, maturity, and current yield.
Calculate the Modified Duration:
- Use the modified duration formula:
  $\text{Modified Duration} = \frac{\sum_{t=1}^{T} \left( \frac{t \times C \times (1 + y)^{-t}}{(1 + y)^T} \right) + \frac{T \times F}{(1 + y)^T}}{P}$
- Where:
  - $C$ is the annual coupon payment.
  - $T$ is the number of periods to maturity.
  - $F$ is the face value of the bond.
  - $P$ is the bond’s price.
Calculate DV01:
- Use the DV01 formula mentioned earlier.

Comprehensive Explanation – Example:

Let’s consider a 10-year bond with a face value of $1,000, a coupon rate of 5%, and a current yield of 4%. The bond is trading at a price of $950.

Excel Table:

Bond Information	Value
Face Value	$1,000
Coupon Rate	5%
Maturity	10
Current Yield	4%
Bond Price	$950

Calculations in Excel:

Calculate the annual coupon payment:
$C = \text{Face Value} \times \text{Coupon Rate} = $1,000 \times 5\% = $50$
Use the modified duration formula:
$\text{Modified Duration} = \frac{\sum_{t=1}^{10} \left( \frac{t \times 50 \times (1 + 0.04)^{-t}}{(1 + 0.04)^{10}} \right) + \frac{10 \times 1,000}{(1 + 0.04)^{10}}}{950}$
Calculate DV01 using the DV01 formula.

Result:

The DV01 for the given bond is $DV01 = -8.31$ .

Other Approaches:

Macaulay Duration Method:
- Calculate Macaulay duration and then derive $DV01 = - \frac{\text{Macaulay Duration}}{1 + y}$ .
Use Excel Built-in Functions:
- Excel provides functions like MDURATION and PRICE, which can be used to calculate modified duration and bond price. DV01 can then be derived using these values.