Effective duration and modified duration both measure how much a bond’s price moves when interest rates change, but they answer that question under different assumptions. Modified duration assumes the bond’s coupon and principal payments are locked in no matter what rates do. Effective duration recalculates the expected cash flows at each rate level, which is what you need whenever a bond carries a call feature, a put feature, or a prepayment option. For a plain non-callable Treasury or bullet corporate, the two numbers come out nearly identical. For anything with embedded optionality, they can diverge sharply.
What Modified Duration Measures
Modified duration tells you the expected percentage price change for a 1% (100 basis point) move in the bond’s own yield to maturity.1Investopedia. Modified Duration – Formula, Calculation, and How to Use It A bond with a modified duration of 6.0 should fall roughly 6% if its yield climbs by one full percentage point, and rise by about the same amount if its yield drops by that much.
The CFA Institute classifies modified duration as a “yield duration” statistic because it references changes in the bond’s own yield to maturity rather than changes in a broader benchmark curve.2CFA Institute. Yield-Based Bond Duration Measures and Properties It is derived mathematically from the price-yield relationship, and it treats every scheduled payment as fixed.
That fixed-cash-flow assumption is accurate for plain vanilla bonds. Every coupon arrives on time, principal is repaid at maturity, and the only variable is the discount rate. The assumption breaks the moment an embedded option enters. A callable bond gives the issuer the right to redeem early if rates fall enough to make refinancing attractive, so future cash flows are no longer fixed. Modified duration ignores the call entirely and overstates the bond’s upside when rates drop, because it implicitly predicts the bond will trade well above its call price rather than being redeemed.
What Effective Duration Measures
Effective duration measures a bond’s price sensitivity to a parallel shift in the benchmark yield curve rather than a change in the bond’s own yield to maturity.3Investopedia. Understanding Effective Duration – Definition, Formula and Examples That distinction matters because bonds with embedded options often don’t have a single well-defined yield to maturity. The expected cash flows depend on the rate path, and modified duration cannot handle that ambiguity.
Rather than taking a mathematical derivative, effective duration uses scenario analysis. You price the bond three times: at today’s curve, at a curve shifted slightly down, and at a curve shifted slightly up. Published examples use shifts anywhere from 10 to 30 basis points or more.3Investopedia. Understanding Effective Duration – Definition, Formula and Examples The formula subtracts the up-shift price from the down-shift price and divides by twice the shift amount times the original price.
What makes it powerful is that the pricing model used at each scenario incorporates the value of the embedded option at that rate level. When the curve shifts down, the model recognizes that a callable bond’s price will be capped near the call price. When the curve shifts up, the model treats the bond much like a standard fixed-rate issue because the call is unlikely to be exercised. The bond’s expected life shortens or lengthens depending on the scenario, and the duration figure reflects that.
Where the Two Numbers Diverge
For a standard non-callable bond, the two metrics land in roughly the same place. The option-adjusted model used for effective duration produces the same price changes as the modified duration formula because there is no option value to adjust for. Modified duration is the simpler and more common choice for risk reporting on these holdings.
The gap opens once optionality is present. Take a 10-year callable corporate trading near par with a call date in three years. Modified duration might come in around 7, reflecting the bond’s stated maturity. Effective duration, factoring in the high probability that the issuer will call if rates fall, might land closer to 3. The practical stakes are large: modified duration would tell you the bond has more than twice the rate exposure it actually carries, and a hedge sized to that number would be far too big.
Mortgage-backed securities show the most dramatic split. Homeowners effectively hold a call option through refinancing. When rates fall, prepayments surge, shortening the security’s average life and compressing its duration. When rates rise, prepayments slow and the security’s duration extends. An MBS pass-through might carry a modified duration of 6 or 7 based on its stated maturity, but a 150 basis point rate decline can compress its effective duration to 2 or 3. This behavior is called contraction risk, and it is the reason MBS investors and portfolio managers use effective duration almost exclusively.4Investopedia. Understanding Negative Convexity
Which One to Use
The choice comes down to whether your bonds have embedded options. If you hold only non-callable Treasuries or bullet corporate bonds, modified duration is accurate and easier to calculate. If your portfolio contains callable corporates, puttable bonds, or any flavor of mortgage-backed security, effective duration is not optional. Using modified duration on those holdings produces a risk profile that looks right on paper and fails badly when rates actually move.
Immunization strategies make this especially consequential. If you are matching a portfolio’s duration to a liability due in eight years, using modified duration on a portfolio full of callable bonds can leave you significantly under-hedged. The portfolio’s effective duration might be closer to five years once call probabilities are factored in, creating a three-year mismatch that turns into real losses when rates shift.
How Duration Numbers Translate to Price Changes
Whichever measure you use, the underlying interpretation is the same. For every 1% change in interest rates, a bond’s price moves approximately 1% in the opposite direction for each year of duration.5BlackRock. Understanding Duration A bond with a duration of 8 will swing roughly twice as much as a bond with a duration of 4 for the same rate move.
Two features push duration higher: a lower coupon and a longer maturity. A low coupon back-loads more of your return toward the final principal payment, stretching the time until you recoup your investment. A longer maturity does the same. Bonds combining both carry the highest duration and the most interest rate risk.6Investopedia. Duration Definition and Its Use in Fixed Income Investing The logic runs through present value: when rates rise, every future coupon and principal payment becomes worth less today, pulling the bond’s price down; when rates fall, those same payments become more valuable and the price rises. Duration is a linear estimate of the size of that move.
What Duration Doesn’t Capture
Duration works well for small rate changes and gets less reliable as the shift grows larger. The actual relationship between a bond’s price and its yield is curved, not linear. Convexity measures that curvature and adjusts the duration estimate for larger moves.
Standard non-callable bonds have positive convexity: their prices rise faster than duration predicts when rates drop and fall more slowly than duration predicts when rates rise. Callable bonds and mortgage-backed securities often exhibit negative convexity once rates decline past a certain threshold. As rates fall and the call option moves deeper into the money, the bond’s price gets capped near the call price instead of continuing to climb.4Investopedia. Understanding Negative Convexity This asymmetric behavior is exactly what effective duration captures and modified duration misses.
Both duration measures also assume the yield curve shifts in parallel, meaning every maturity point moves by the same amount. Real curves rarely cooperate; they steepen, flatten, or twist. Key rate duration addresses that gap by measuring sensitivity to rate changes at specific maturity points while holding all other rates constant.7Investopedia. Key Rate Duration Explained – Sensitivity, Calculation and Formula For large or complex portfolios, effective duration, key rate duration, and convexity work together. No single number covers all the ways rates can move.