Curve-Based and Empirical Fixed-Income Risk Measures

Having covered yield-based duration and convexity measures, we now introduce curve-based measures of a bond’s price sensitivity to changes in a benchmark yield curve and when cash flows are uncertain. We show how the change in a bond’s full price is estimated by combining curve-based duration and convexity sensitivity measures, discuss uses of these approximate measures by issuers and investors, and explain their benefits and limitations. We also introduce key rate duration as a measure of interest rate risk across the term structure. Finally, we show that benchmark yield changes and credit spreads for issuers of lower credit quality are negatively correlated, especially during periods of market distress, establishing the benefit of an empirical versus analytical approach.

• Yield duration and convexity estimates of interest rate risk are useful only for small changes in yields. Effective duration and effective convexity are valid for both small and large changes in yields.
• Effective duration and effective convexity are useful for gauging the interest rate risk of bonds whose future cash flows are uncertain.
• Effective duration and effective convexity can be used to estimate the percentage change in a bond’s full price for a given shift in the benchmark yield curve.
• A key rate (or partial) duration is a measure of a bond’s sensitivity to a change in the benchmark yield at a specific maturity. Key rate duration data, along with forecasted shifts in the benchmark curve, allow a portfolio to be rebalanced to improve its return.
• The sum of weighted key rate durations of the bonds in a portfolio are equal to the effective duration of the entire portfolio.
• Analytical duration and convexity are estimated duration and convexity statistics using mathematical formulas. Empirical duration and convexity are estimated using historical data that incorporate various factors affecting bond prices.
• When deciding whether to use an empirical or analytical measure, the correlation between benchmark yields and credit spreads must be considered.