Empirical Duration vs. Analytical Duration | CFA Level I Fixed Income

In this lesson, we’ll explore the difference between empirical and analytical duration.

Understanding Duration

Duration measures the sensitivity of a bond’s price to changes in interest rates. So far, we’ve discussed analytical duration, which is based on mathematical analysis, such as expected future cash flows and maturity. Another approach is empirical duration, which uses historical relationships between benchmark yields and bond prices.

Empirical Duration for Corporate Bonds

This distinction is particularly relevant for corporate bonds, which have a credit spread above the benchmark yield. Using analytical duration to estimate the change in the price of a corporate bond assumes that the credit spread remains constant, which might not be accurate.

In a “flight to quality” scenario, investors sell risky assets to purchase government bonds. This can cause the benchmark yield to decrease while the credit spread increases. Using analytical duration to estimate the increase in the price of a corporate bond may be inappropriate, as the price may increase less or even decrease, depending on its credit quality.

On the other hand, empirical duration is based on historical relationships and factors in the relationship between credit spreads and benchmark bond yields. It may produce more accurate estimates of changes in corporate bond prices. The empirical duration of a corporate bond portfolio is likely to be lower than its analytical duration.

Government Bonds and Duration

For government bonds, the yield is fully the benchmark yield, so the change in interest rate is the change in benchmark yield. As a result, the analytical duration of a government bond portfolio is likely to be very close to its empirical duration. Both can provide a good estimate of the change in price due to a change in benchmark yield.