# How to Calculate Total Portfolio Volatility Using Duration

by Bryan Keythman

A bond’s duration measures its volatility based on changes in interest rates. A higher duration represents greater volatility and greater risk. Duration represents the approximate percentage a bond’s price moves in the opposite direction of a 1 percent change in interest rates, assuming the bond has fixed cash flows. A bond portfolio’s duration is equal to the weighted average of each bond’s duration in the portfolio. If you know the duration of each bond in a portfolio, you can calculate the portfolio’s duration to measure its volatility.

1. Determine each bond’s value in your portfolio, the total value of your portfolio and the known duration of each bond. You can contact broker or institution that sold you a bond to determine its duration. For example, assume your portfolio’s total value is \$10,000, which includes \$6,000 in a bond with a duration of 1.95 and \$4,000 of a bond with a duration of 1.47.

2. Divide each bond’s value by the total portfolio value, and then multiply each result by the bond’s duration to calculate the weighted duration of each bond. In the example from the previous step, divide \$6,000 by \$10,000 to get 0.6. Multiply 0.6 by 1.95 to get a weighted duration of 1.17 for the first bond. Divide \$4,000 by \$10,000 to get 0.4. Multiply 0.4 by 1.47 to get a weighted duration of 0.59 for the second bond.

3. Add together each weighted duration to calculate the portfolio’s duration. Continuing with the example, add 1.17 and 0.59 to get a portfolio duration of 1.76. This means that the portfolio’s value would move by approximately 1.76 percent in the opposite direction of a 1 percent change in interest rates.

4. Determine a hypothetical percentage change in interest rates to determine how much the bond portfolio may change. In this example, assume interest rates may decrease by 2 percent.

5. Multiply the hypothetical change in interest rates as a decimal by the negative of the portfolio’s duration. Make the interest rate change negative for a decrease and positive for an increase. Continuing with the example from the previous step, multiply -0.02, by -1.76 to get 0.0352.

6. Multiply the result by 100 to calculate the approximate percentage by which the portfolio’s value would change based on the hypothetical interest rate move. In this example, multiply 0.0352 by 100 to get 3.52, which means the portfolio’s value would increase by approximately 3.52 percent if interest rates decrease by 2 percent.

#### Tip

• Use the portfolioâ€™s duration to calculate different price movements based on different changes in interest rates.