## What is the Dollar Duration

The dollar duration measures the dollar change in a bond's value to a change in the market interest rate. The dollar duration is used by professional bond fund managers as a way of approximating the portfolio's interest rate risk. Dollar duration is one of the several different measurements of bond duration.

As duration measures the sensitivity of a bonds price in interest rate changes, dollar duration seeks to give these changes an actual dollar amount.

### Key Takeaways

• Dollar duration is used by bond fund managers to measure a portfolio's interest rate risk, and compares the change in a bond's value to market interest rates.
• Dollar duration calculations can also be used to calculate risk for other fixed income products such as forwards, par rates, zero coupon bonds, etc.
• There are two limitations to dollar durations: it may result in an approximation and it assumes that bonds have fixed rates with fixed interval payments.

## Basics of Dollar Duration

Dollar duration is based on a linear approximation of how a bond's value will change in response to changes in interest rates. The actual relationship between a bond's value and interest rates is not linear. Therefore, dollar duration is an imperfect measure of interest rate sensitivity, and it will only provide an accurate calculation for small changes in interest rates.

Mathematically, the dollar duration measures the change in the value of a bond portfolio for every 100 basis point change in interest rates. Dollar duration is often referred to as DV01 (dollar value per 01). Remember 0.01 being 1 percent which is 100 basis points. To calculate the dollar duration of a bond you need to know its duration, the current interest rate and the change in interest rates.

Dollar Duration = DUR x (∆ i/1+ i) x P

While dollar duration refers to an individual bond price, the sum of the weighted bond dollar durations in a portfolio is the portfolio dollar duration. Dollar duration can be applied to other fixed income products such as forwards, par rates, zero coupon bonds and many more.

## Limitations

Dollar duration has its limitations. Firstly, because it is a negative sloping linear line and it assumes the yield curve moves in parallels the result is only an approximation. However, if you have a large bond portfolio, the approximation becomes less of a limitation. Another limitation is that the dollar duration calculation assumes the bond has fixed rates with fixed interval payments. However, interest rates for bonds differ based on market conditions as well as introduction of synthetic instruments.

## Comparisons

Dollar duration differs from Macaulay duration and modified duration in that modified duration is a price sensitivity measure of the yield change, meaning it is a good measure of volatility, and Macaulay duration uses the coupon rate and size plus the yield to maturity to assess the sensitivity of a bond.