Empirical Duration

Empirical Duration is the calculation of a bond's duration based on historical data rather than a formula.

One can estimate empirical duration statistically using historical market-based bond prices and historical market-based Treasury yields. When the historical yields rise or fall, the historical bond prices will rise or fall accordingly, and this data forms the basis for empirical duration. Regression analysis is the statistical process by which a person can estimate empirical duration.

Empirical duration expresses the inverse relationship of bond interest rates and prices. When interest rates for new bond issues go up, prices for existing bonds go down as they become relatively less attractive to investors. With duration, investors can get a viable estimate of how much their bond’s price will go down in the event that rates go up. That’s because in general, whenever rates for new bonds rise by one percentage point, prices for existing bonds will fall by their duration expressed as a percentage.

For instance, say you’re comparing two bonds that share a coupon rate of 5 percent. In looking more closely at each one, you notice the first bond has a duration of 4.8 years while the second bond has a duration of 9.2 years. This means if interest rates rise to 6 percent, the first bond’s price will fall by only about 4.8 percent while the second bond’s price will fall by nearly double that, or about 9.2 percent. In this sense, duration gives investors a key measure of volatility when comparing multiple bond investments. Controlling for other factors, a bond with shorter duration will suffer less volatility than a bond with longer duration.

Empirical duration has some advantages and disadvantages over modified duration, which has investors use a formula to figure out what would happen to a bond’s price if interest rates shift by one percentage point.

The advantages of empirical duration include that the estimate does not rely on theoretical formulas and analytic assumptions; the investor only needs a reliable series of bond prices and a reliable series of Treasury yields. Disadvantages include that a reliable series of a bond's price may not be available, and the series of prices that is available might not be market based, but rather modeled or matrix priced (the price is based on a similar security).