Modified duration and effective duration both estimate 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 cash flows are locked in and measures sensitivity to the bond’s own yield to maturity. Effective duration re-prices the bond under shifted yield curves and lets the expected cash flows change with rates, which is what you need for any bond with an embedded option. For a non-callable Treasury or bullet corporate, the two numbers land in nearly the same place. For callable bonds, puttable bonds, and mortgage-backed securities, they can diverge sharply, and using the wrong one produces a risk figure that fails the moment rates actually move.
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 jumps by one full percentage point and rise roughly 6% if its yield drops by the same amount.
The measure is a “yield duration” statistic in the CFA Institute’s terminology because it references the bond’s own yield to maturity rather than a broader benchmark curve.2CFA Institute. Yield-Based Bond Duration Measures and Properties It is built on Macaulay duration, the weighted-average time until the bond’s cash flows arrive, adjusted by dividing by one plus the yield per compounding period.1Investopedia. Modified Duration – Formula, Calculation, and How to Use It
The Fixed Cash Flow Assumption
Modified duration assumes coupon payments and principal repayment arrive exactly on schedule regardless of what happens to interest rates. For plain vanilla bonds like non-callable corporates or standard Treasuries, that assumption is accurate. Every scheduled payment is contractually fixed, so the only variable affecting price is the discount rate applied to those payments.
The assumption breaks the moment an embedded option enters the picture. A callable bond gives the issuer the right to redeem early if rates fall far enough to make refinancing attractive. When that call is in play, future cash flows are not fixed. Modified duration ignores the call entirely, so it overstates the bond’s upside price sensitivity when rates decline. It effectively predicts the bond will trade well above its call price when rates drop, but the issuer prevents that by exercising the option. Any bond whose cash flows might change with interest rates needs a different tool.
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 shift in reference point matters. Bonds with embedded options often don’t have a single clean yield to maturity, because their expected cash flows depend on the rate path. Modified duration can’t handle that ambiguity. Effective duration works around it by asking what happens to price when the whole curve moves.
How the Calculation Works
Rather than taking a mathematical derivative of a price-yield function, effective duration uses scenario analysis. You price the bond three ways: under today’s curve, under a curve shifted slightly down, and under a curve shifted slightly up. Published examples use shifts ranging from 10 basis points to 30 basis points or more.3Investopedia. Understanding Effective Duration – Definition, Formula and Examples The formula takes the down-shift price, subtracts the up-shift price, and divides by twice the shift amount times the original price.
What makes the approach powerful is that the pricing model used in each scenario incorporates the value of any embedded option at that rate level. When the curve shifts down, the model recognizes a callable bond’s price will cap near the call price because the issuer is likely to redeem. When the curve shifts up, the model treats the bond like a standard fixed-rate issue because the call is unlikely to be exercised.
Why It Captures Optionality
The scenario approach forces expected maturity and cash flows to change at each rate level. If rates fall substantially, the model assumes the issuer will call, shortening the bond’s effective life and reducing its duration. If rates rise, the call becomes irrelevant and the bond’s duration stretches toward that of a comparable non-callable issue. This asymmetric behavior is exactly what modified duration misses.
The same logic applies to mortgage-backed securities. Homeowners hold what amounts to a call option through refinancing. When rates drop, prepayments surge, the security’s average life shortens, and its duration compresses. When rates rise, prepayments slow and duration extends. Effective duration captures this because it re-prices the security under each rate scenario using a prepayment model. Modified duration, which assumes every mortgage payment arrives on its original schedule, produces a badly misleading number.
Where the Two Numbers Actually Diverge
For a standard non-callable bond, the two measures produce nearly identical results. The option-adjusted pricing model behind effective duration returns the same price changes as the simpler modified duration formula because there is no option value to adjust for. In these cases, modified duration is the more common choice for risk reporting simply because it’s easier to calculate.
The gap opens once optionality is present. Consider a 10-year callable corporate bond trading near par with a call date in three years. Modified duration might produce a figure around 7, reflecting the bond’s stated maturity. Effective duration, incorporating the high probability that the issuer calls if rates fall, might come in closer to 3. The practical difference is enormous. Modified duration says the bond carries roughly twice the rate exposure it actually has, which would lead you to over-hedge if you relied on it.
Mortgage-backed securities show perhaps the most dramatic divergence. An MBS pass-through might report a modified duration of 6 or 7 based on stated maturity. When rates drop 150 basis points, the wave of refinancing activity can compress its effective duration to 2 or 3. This is contraction risk, and it’s the reason MBS investors and portfolio managers use effective duration almost exclusively.4Investopedia. Understanding Negative Convexity
Choosing Between Them
The decision comes down to whether your bonds carry embedded options. If you hold only non-callable Treasuries or bullet corporate bonds, modified duration is accurate and easier to compute. If your portfolio contains callable corporates, puttable bonds, or any flavor of mortgage-backed security, effective duration is not optional. Applying modified duration to those holdings produces a risk profile that looks reasonable on paper and fails when rates actually move.
Immunization strategies raise the stakes. If you’re matching a portfolio’s duration to a liability due in eight years, using the wrong duration measure on a portfolio heavy in callable bonds can leave you under-hedged by a wide margin. The portfolio’s effective duration might be closer to five years once call probabilities are factored in, creating a three-year mismatch that translates into real losses when rates shift.
How Duration Fits With Convexity
Duration, in either form, gives you a straight-line estimate of price changes. The actual relationship between a bond’s price and its yield is curved. For small rate moves of less than 50 basis points, the straight-line approximation is close enough. For larger moves, it systematically underestimates how much a bond’s price rises when rates fall and overestimates how much it falls when rates rise. Convexity measures that curvature and works alongside whichever duration measure applies to your bond.
Standard non-callable bonds have positive convexity: prices rise faster than duration predicts when rates drop and fall more slowly than duration predicts when rates rise. The more convexity a bond has, the better it performs in volatile rate environments.
Callable bonds and mortgage-backed securities often exhibit negative convexity when rates decline below 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. The price-yield curve bends the wrong way: gains slow dramatically as rates drop further, and losses can steepen as rates rise.4Investopedia. Understanding Negative Convexity This is the same asymmetric behavior that separates effective duration from modified duration in the first place, viewed through a different lens.
For stress testing or scenario analysis involving moves of 100 basis points or more, combining duration with a convexity adjustment produces a more accurate estimate than duration alone. For day-to-day risk management with small rate shifts, duration by itself is usually sufficient, provided you’re using the right kind of duration for the bonds you actually hold.