How Effective and Key Rate Duration Work, How They Differ, and What the Exam Tests

Effective duration measures how much a bond’s price is expected to change when the whole yield curve moves up or down by the same amount, while allowing for the fact that embedded options, such as a call feature, can change the bond’s cash flows. Key rate duration measures how much the price changes when the yield at just one maturity point on the curve moves, while every other point stays the same.

In short, effective duration answers the question “what happens if all rates move together?” Key rate duration answers “what happens if only the 10-year rate moves?” Together they give a much fuller picture of interest rate risk than a single duration number.

This guide covers what each measure means, how to calculate them, how they relate to Macaulay and modified duration, worked examples, a client scenario, the exam traps and five practice questions with explanations. Preparing for your exam? Watch FRC’s Series 65 playlist on YouTube, with exam traps called out in every topic.

Why Duration Needs More Than One Number

Duration is the standard way to measure how sensitive a bond’s price is to changes in interest rates. The higher the duration, the more the price moves when rates change.

The basic measures, Macaulay and modified duration, rest on two assumptions. They assume the bond’s cash flows will not change when rates change, and they assume every point on the yield curve moves by the same amount.

Neither assumption always holds. Callable bonds and mortgage-backed securities can see their cash flows change when rates fall, and yield curves often steepen, flatten or twist rather than shifting in parallel. Effective duration deals with the first problem, and key rate duration deals with the second.

Where This Topic Appears on the Exams

Duration questions appear in the investment vehicles section of the Series 65, usually asking which measure applies to a particular bond or which bond is most sensitive to a rate change. They also appear in client recommendation questions about managing interest rate risk in a portfolio.

FRC’s Series 65 Exam Preparation course covers bond pricing, yields and duration alongside the rest of the fixed income material, and the exam requires no sponsor. The SIE Examination Preparation course introduces interest rate risk and bond pricing for candidates starting out.

Every FRC course can be spread across interest-free monthly payments, so cost is no reason to delay. Duration is one of the topics where a clear method turns a confusing question into a quick mark.

A Quick Recap: Macaulay and Modified Duration

Macaulay duration is the weighted average time, in years, until a bond’s cash flows are received. A zero-coupon bond’s Macaulay duration equals its maturity, because it pays everything at the end.

Modified duration converts Macaulay duration into an estimate of how much the bond’s price will change for a 1% change in yield. A bond with a modified duration of 6 is expected to fall about 6% in price if its yield rises by 1%.

Both measures work well for option-free bonds, where the cash flows are fixed. FRC’s guide to Macaulay duration vs modified duration covers them in full.

What Effective Duration Is

Effective duration estimates a bond’s price sensitivity by actually repricing the bond after a rate change, rather than relying on a formula that assumes fixed cash flows. Analysts shift the yield curve up and down by a small amount, use a pricing model to see how the bond’s value changes, and measure the result.

Because the model allows the cash flows to change, effective duration captures the effect of embedded options. If falling rates make a callable bond more likely to be called, the model reflects that the investor may get their money back early.

That makes effective duration the right measure for callable bonds, putable bonds and mortgage-backed securities. For an option-free bond, effective duration and modified duration are approximately the same.

How to Calculate Effective Duration

The formula is: effective duration equals the price if yields fall minus the price if yields rise, divided by two times the original price times the change in yield. The change in yield is written as a decimal, so 0.5% becomes 0.005.

Take a bond priced at $100. If yields fall by 0.5%, the model prices it at $103.20, and if yields rise by 0.5%, it prices it at $97.00.

Effective duration is $103.20 minus $97.00, which is $6.20, divided by two times $100 times 0.005, which is $1.00. The result is an effective duration of 6.2, meaning the price is expected to change by about 6.2% for a 1% parallel move in rates.

Effective Duration and Callable Bonds

When interest rates fall, an option-free bond keeps rising in price. A callable bond’s price rise is limited, because the issuer is more likely to call the bond and refinance at the lower rate.

That means a callable bond’s effective duration is lower than the modified duration of an otherwise identical option-free bond, especially when rates are near or below the coupon rate. The bond behaves as though it has a shorter life.

This effect is called negative convexity, and it is the main reason modified duration can mislead for callable bonds. FRC’s guides to callable vs non-callable bonds and yield to call vs yield to maturity explain call risk in more detail.

Effective Duration and Mortgage-Backed Securities

Mortgage-backed securities face a similar problem. When rates fall, homeowners refinance, and investors receive their principal back early, just when reinvestment rates are low.

When rates rise, refinancing slows, and the security’s expected life extends just when investors would prefer shorter bonds. Effective duration captures both of these changes, which is why it is the standard measure for mortgage-backed securities.

FRC’s guide to why investors buy asset-backed securities covers prepayment risk and the trade-offs these securities involve.

What Key Rate Duration Is

Key rate duration measures how sensitive a bond or portfolio is to a change in the yield at one specific maturity, such as two, five, 10 or 30 years, while yields at every other maturity stay the same. Each maturity point gives its own key rate duration.

The key rate durations of a bond or portfolio add up approximately to its effective duration. That is why key rate duration is often described as breaking effective duration into pieces along the yield curve.

The value of key rate duration is that it shows where on the curve the risk sits. Two portfolios can have the same effective duration but very different exposure to changes in short-term or long-term rates.

Why Yield Curves Do Not Move in Parallel

In practice, yield curves change shape all the time. A steepening curve means long-term rates rise relative to short-term rates, while a flattening curve means the gap narrows.

A twist happens when short-term and long-term rates move in opposite directions. In each case, a single duration number assumes a parallel move that is not happening.

FRC’s guide to normal vs inverted yield curves explains what different curve shapes signal about the economy. Key rate duration is the tool that turns those shape changes into an estimated price effect.

Comparing the Duration Measures

The table below summarizes how the main duration measures differ.

Worked Example: Key Rate Duration in a Portfolio

A bond portfolio has an effective duration of 6.2. Its key rate durations are 0.5 at the two-year point, 1.5 at the five-year point, 2.5 at the 10-year point and 1.7 at the 30-year point, which add up to 6.2.

If the 10-year yield rises by 0.5% and every other rate stays the same, the estimated price change is 2.5 times 0.5%, a fall of about 1.25%. A manager looking only at effective duration would have no way of seeing that the 10-year point carries the most risk.

Now suppose the curve steepens, with the two-year yield falling 0.25% and the 30-year yield rising 0.25%. The two-year position gains about 0.125%, the 30-year position loses about 0.425%, and the portfolio falls by roughly 0.3%, even though the average change in rates was close to zero.

Worked Example: Comparing Two Portfolios

Portfolio A holds mostly two-year and 30-year bonds, a barbell structure. Portfolio B holds mostly 10-year bonds, a bullet structure, and both have the same effective duration of 6.

If the yield curve flattens, with short-term rates rising and long-term rates falling, the two portfolios react very differently. Key rate durations show that the barbell portfolio is exposed at both ends of the curve, while the bullet portfolio is concentrated in the middle.

This is why portfolio managers use key rate duration to hedge or position for specific curve changes. Effective duration alone would suggest the two portfolios carry the same risk.

Client Scenario: An Income Investor Worried About Rates

An investment adviser representative’s client holds a bond portfolio made up largely of callable corporate bonds and mortgage-backed securities. The client asks how much the portfolio could lose if rates rise by 1%.

Quoting the portfolio’s modified duration would be misleading, because it ignores how the embedded options change the cash flows. Effective duration gives a more realistic estimate, and key rate durations show whether the risk sits mainly in short-term or long-term rates.

If most of the risk sits at the long end and the client is worried about long-term rates rising, the adviser might discuss shortening the portfolio’s maturities or adding floating-rate securities. As a fiduciary, the adviser should explain these risks clearly, and FRC’s guide to fiduciary standard vs suitability standard explains what that duty requires.

Convexity: Why Duration Is Only an Estimate

Duration gives a straight-line estimate of how a bond’s price responds to rate changes, but the real relationship between price and yield is curved. Convexity measures that curve, and it explains why duration estimates become less accurate as rate changes get larger.

An option-free bond has positive convexity, which means its price rises more when rates fall than it drops when rates rise by the same amount. That works in the investor’s favor, because duration slightly overstates losses and understates gains.

A callable bond or mortgage-backed security can show negative convexity when rates fall, because its price rise is capped by the call or by prepayments. That is the same effect that pulls its effective duration down, and it is why investors in these securities usually demand a higher yield.

How Professionals Use These Measures Together

Portfolio managers typically report effective duration as the headline measure of interest rate risk, then use key rate durations to see where that risk sits. They add convexity to judge how reliable the duration estimate will be for larger moves.

An adviser who understands all three can explain to a client not just how much a portfolio might lose if rates rise, but which rate changes would hurt most. That is a far more useful conversation than quoting a single number.

The Exam Traps

The first trap is using modified duration for a callable bond or a mortgage-backed security. Whenever the question mentions an embedded option or prepayment, the right measure is effective duration.

The second trap is assuming effective duration handles non-parallel moves. It does not; it assumes a parallel shift, and key rate duration is the measure for changes at individual maturities.

The third trap is forgetting that key rate durations add up approximately to effective duration. The fourth is assuming two portfolios with the same duration carry the same interest rate risk, when their key rate profiles can be completely different.

For more traps like these across all four sections of the exam, see FRC’s guide to Series 65 exam traps and common mistakes. The Series 65 investment vehicles questions guide covers the fixed income traps in more depth.

A Memory Aid

Remember “effective for options, key rate for shape.” Effective duration handles bonds whose cash flows change, and key rate duration handles curves that change shape.

For the hierarchy, remember that Macaulay measures time, modified measures price for fixed cash flows, effective measures price when cash flows can change, and key rate measures price at one point on the curve.

Practice Questions

Question one: which duration measure is most appropriate for a mortgage-backed security? Effective duration, because prepayments change the security’s cash flows when rates change.

Question two: a bond priced at $100 would be worth $102.40 if yields fell 0.5% and $97.80 if yields rose 0.5%. What is its effective duration? 4.6, found by dividing $4.60 by $1.00.

Question three: a portfolio has key rate durations of 1.0, 2.0 and 3.0 at the two-, 10- and 30-year points. What is its approximate effective duration? 6.0, because key rate durations add up approximately to effective duration.

Question four: using the portfolio in question three, what is the estimated price change if only the 30-year yield rises by 1%? A fall of about 3%.

Question five: how does a callable bond’s effective duration usually compare with the modified duration of an otherwise identical non-callable bond when rates fall? It is lower, because the call feature limits the price rise.

Related Questions

Duration connects closely to several other fixed income topics on the exams. FRC’s guide to what happens when a bond is downgraded covers credit risk, the other major driver of bond prices, and the guide to interest rate swap vs currency swap explains one of the tools institutions use to adjust their duration.

Together, they give you a complete picture of how bond prices respond to rates, credit and the shape of the yield curve.

Get Exam-Ready

Duration questions are among the most dependable marks on the exam once the differences between the measures are clear. The FRC Series 65 playlist linked at the top of this guide covers every exam section, with the traps to look out for in each one.

The FRC dictionary is more than a dictionary. It is a library of explainer videos, written explanations and on-page quizzes covering the FINRA and SEC rules you are tested on, so you can open any term and go deeper whenever a question catches you out.

Study With FRC

FRC’s programs and memberships are open to everyone. Whether you are preparing for the Series 65, the SIE or both, structured exam preparation turns topics like duration into marks you can rely on.

FRC’s Professional Membership adds verified progress and a Digital Profile, so when you apply for roles, employers can see your exam progress and the knowledge you are building, not just read about it on a resume.

Your Next Step

Effective duration measures price sensitivity to a parallel shift in rates while allowing for embedded options. Key rate duration measures sensitivity to a change at one point on the yield curve, and together the key rate durations add up to effective duration.

Remember “effective for options, key rate for shape,” and you will be ready for every version of this question the exam can ask.