# Dollar Duration

### How long is the dollar

The dollar duration measures the change in dollar value of a bond relative to a change in the market interest rate. The dollar duration is used by professional bond fund managers to estimate the portfolio’s interest rate risk. The duration of the dollar is one of the different measures of the duration of bonds.

As duration measures the sensitivity of a bond price to changes in interest rates, the duration in dollars seeks to give these variations a real amount in dollars.

### Key points to remember

• The dollar duration is used by bond fund managers to measure the interest rate risk of a portfolio and compares the change in the value of a bond to market interest rates.
• Dollar duration calculations can also be used to calculate risk for other fixed income products such as futures, par rates, zero coupon bonds, etc.
• There are two limits to dollar durations: they can be approximated, and they assume bonds have fixed rates with payments at fixed intervals.

### Basic Principles of Dollar Duration

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

Mathematically, dollar duration measures the change in the value of a bond portfolio for every 100 basis points change in interest rates. The duration of the dollar is often called DV01 (dollar value for 01). Remember, 0.01 is 1%, 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.

Duration of the dollar = DUR ​​x (∆ i / 1 + i) x P

While the dollar duration refers to the price of an individual bond, the sum of the dollar durations of the weighted bonds in a portfolio corresponds to the dollar duration of the portfolio. The dollar term can be applied to other fixed income products such as futures, au pair rates, zero coupon bonds and many more.

### Limits

The duration of the dollar has its limits. First, because it is a linear line with a negative slope and it assumes that the yield curve moves in parallel, 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 calculating the term in dollars assumes that the bond has fixed rates with payments at fixed intervals. However, bond interest rates differ depending on market conditions and the introduction of synthetic instruments.

### comparisons

The duration of the dollar differs from the Macaulay duration and the modified duration in that the modified duration is a measure of the price sensitivity of the change in yield, which means that 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.