CFA Level I Exam · Curve-Based and Empirical Fixed-Income Risk Measures

Empirical Duration and Yield Volatility for CFA Level I

Updated 7 October 2026 · Fact-checked

Empirical duration is a bond's price sensitivity estimated from history. You regress observed bond price changes on yield changes of a benchmark, and the slope, with the sign flipped, is the duration. It suits credit-risky bonds, whose spreads move with the economy, but it depends on the data and period chosen.

Understand Empirical Duration and Yield Volatility

Analytical duration (Macaulay, modified, effective) comes from a formula or a pricing model. It assumes you know the cash flows and the yield curve shift. It answers: if this bond's own yield changes by 1%, how much does the price change?

Empirical duration answers a different question: how did this bond's price actually react when market yields moved? You collect historical price changes and historical yield changes, then fit a regression line. The slope of that line is the sensitivity. Duration is the negative of the slope, because prices fall when yields rise.

Why bother? For credit-risky bonds, especially high-yield bonds, the bond's yield is a benchmark yield plus a credit spread. The spread does not move independently of the benchmark. In a stock market sell-off, government yields often fall (flight to quality) while high-yield spreads widen. The bond's own yield can rise while the government yield falls. A formula using the bond's own yield change misses this. A regression of the bond's price changes on government yield changes captures it. The result can be a much lower duration than the analytical figure, and sometimes even the wrong sign.

The idea of a yield beta links to this. Yield beta is the slope of a regression of a bond's yield changes on benchmark yield changes. Suppose a corporate bond's yield moves 0.8% for every 1% move in the government yield. Its yield beta is 0.8. Empirical (effective) duration is then roughly the analytical duration multiplied by the yield beta. Treat that as an approximation, not an exact identity.

Yield volatility matters because price risk equals duration times how much yields move. Historical yield volatility is typically measured as the standard deviation of yield changes. Volatility differs across maturities and over time. In some periods, short-term yields have been more volatile than long-term yields. So duration alone does not determine price risk, and a long-duration bond is not automatically riskier than a shorter one. Empirical duration folds this behaviour in, but only for the period you sampled.

Key formulas to remember

Empirical regression: %ΔPrice = a + b × ΔYield(benchmark) + error; Fit on historical data. b is the slope and is normally negative for a bond.
Empirical duration: Empirical duration = −b; The slope equals duration (with the sign flipped) only when %ΔPrice and ΔYield are in the same unit: both in decimals, or both in percent and percentage points. Mixing units, such as price in percent and yield in decimal, scales the slope by 100.
Yield beta: Yield beta = slope from regressing Δ(bond yield) on Δ(benchmark yield); A beta below 1 means the bond's yield moves less than the benchmark's.
Adjusted duration estimate: Empirical duration ≈ Analytical duration × Yield beta; Approximation for a bond whose yield moves with the benchmark by a stable beta.
Price change estimate: %ΔPrice ≈ −Duration × ΔYield; Use the benchmark yield change with empirical duration.

How to solve Empirical Duration and Yield Volatility questions

Use this method for any question on empirical duration, yield beta or yield volatility.

1Identify what the question gives: a regression slope, a yield beta, an analytical duration, or yield change data.
2Decide which yield the duration refers to. Empirical duration is tied to the benchmark yield used in the regression.
3If given a regression of price change on yield change, take the negative of the slope as duration.
4If given a yield beta and analytical duration, multiply them for the approximate empirical duration.
5Apply %ΔPrice ≈ −duration × ΔYield, keeping units consistent (1 basis point = 0.01%).
6Check the sign and size: does the answer make sense given the bond's credit risk?
7If the question is conceptual, ask whether the bond is credit-risky, whether spreads move with the benchmark, and whether the data period is representative.

Quickest way: Beta times duration shortcut

When to use it: When the question gives an analytical duration and a yield beta, or asks which duration is more reliable for a bond.

Multiply analytical duration by yield beta to get the approximate empirical duration.
Multiply by the benchmark yield change in decimals to get the price change.
For concept questions: credit-risky or high-yield bond with spread linked to the economy points to empirical duration; option-free government bond points to analytical duration.
Eliminate options that say empirical duration needs no historical data, or that it is always larger than analytical duration.

Common mistakes in Empirical Duration and Yield Volatility

Reporting the regression slope as duration without flipping the sign.
Students remember that duration is a positive number but read the slope directly.
Fix: Empirical duration is the negative of the slope when regressing price changes on yield changes.
Assuming empirical duration is always lower than analytical duration.
Textbook high-yield examples show a lower figure.
Fix: It depends on the yield beta. A beta above 1 gives a larger empirical duration. Calculate rather than assume.
Using the bond's own yield change instead of the benchmark yield change.
Analytical duration uses the bond's own yield, so habit takes over.
Fix: Check which yield sits on the x-axis of the regression and use the same one in the price estimate.
Treating empirical duration as a forward-looking, model-based measure.
The word duration suggests a formula.
Fix: It is estimated from past data. A different sample period or frequency can give a different answer.
Thinking longer duration always means higher risk regardless of yield volatility.
Duration is taught as the single risk number.
Fix: Price risk depends on duration and the size of yield changes. Yield volatility can differ by maturity.
Mixing units, such as percent price change with basis point yield change.
Data are quoted in different units.
Fix: Convert everything to decimals or percentage points before computing.

Worked examples

Example 1

A high-yield bond has an analytical modified duration of 6.0. A regression of its yield changes on Treasury yield changes gives a yield beta of 0.4. Treasury yields rise by 50 basis points. Estimate the bond's percentage price change using empirical duration.

Show the solution

Empirical duration ≈ 6.0 × 0.4 = 2.4.
Yield change = 0.50% = 0.0050.
%ΔPrice ≈ −2.4 × 0.0050 = −0.0120.
That is a decline of 1.20%.

Answer: About −1.20%. Ignoring the beta and applying 6.0 to the 0.50% yield rise would give −3.00%, which overstates the price fall.

Example 2

An analyst regresses weekly percentage price changes of a corporate bond on weekly changes in a government benchmark yield, with yield changes in percentage points. The estimated slope is −3.5. What is the empirical duration, and what price change is expected if the benchmark yield falls by 20 basis points?

Show the solution

Empirical duration = −(−3.5) = 3.5.
A slope of −3.5 means a 1 percentage point yield rise cuts price by 3.5%.
Yield change = −0.20 percentage points.
%ΔPrice = −3.5 × (−0.20) = +0.70%.

Answer: Empirical duration is 3.5, and the expected price change is +0.70%.

Exam tips

Questions are three-option MCQs. Eliminate any option that states empirical duration needs no historical data or is a purely formula-based measure.
For credit-risky bonds with spreads that move against or with benchmark yields, expect empirical duration to be the answer to 'which measure is more appropriate'.
Watch the units. Basis points to decimals is the most common loss of marks in these calculations.
Remember the limitation: results depend on the sample period, data frequency and the benchmark chosen, and the relationship may not persist.

Practice questions from Curve-Based and Empirical Fixed-Income Risk Measures

Empirical Duration and Yield Volatility: frequently asked questions

What is empirical duration in CFA Level I?

It is a bond's price sensitivity to yield changes estimated from historical data using regression. The negative of the slope of price change on yield change is the duration. It reflects how the bond actually behaved, not how a formula says it should.

Why is empirical duration used for high-yield bonds?

High-yield bond spreads tend to move with the economy and equity markets, and not with government yields. An analytical formula based on the bond's own yield misses this link. A regression on the benchmark yield captures it.

What is yield beta?

It is the slope from regressing changes in a bond's yield on changes in a benchmark yield. A beta of 0.5 means the bond's yield moved about half as much as the benchmark's. Empirical duration is roughly analytical duration times yield beta.

What are the limitations of empirical duration?

It depends on the sample period, data frequency and chosen benchmark, and past relationships may not hold in the future. It also needs enough reliable price data, which is often scarce for illiquid bonds.