Lesson 5 of 5 · 11 min
Empirical versus analytical duration
Analytical duration comes from pricing formulas that treat benchmark yields and spreads as independent; empirical duration is estimated from historical price data and captures the fact that spreads often widen just as government yields fall.
In short
- Analytical duration (and convexity): estimated with mathematical formulas. Every measure so far, including effective and key rate duration, is analytical.
- Analytical estimates implicitly assume benchmark yields and credit spreads are uncorrelated.
- Empirical duration (and convexity): estimated from historical data in statistical models that include several factors affecting bond prices.
- In a flight to quality, government yields fall while credit spreads widen: they are negatively correlated, so a risky bond's price rises less than analytical duration predicts.
- For bonds with credit risk, empirical duration is lower and usually more accurate; for government bonds the two are similar.
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