Duration Is a Risk Budget, Not a Forecast
In this essay
A bond can promise a fixed payment and still have a changing price. The promise concerns future cash flows; the price reflects what those cash flows are worth today. Confusing the two makes a supposedly conservative portfolio surprisingly difficult to hold.
Duration helps translate a change in yield into an approximate change in price. It is most useful as a way to budget exposure, before any view about the next central bank meeting enters the discussion.
Start with the price, not the label
Imagine a default-free, non-callable zero-coupon bond that pays $1,000 in five years. With annual compounding and a 4% yield, its price is:
1 | price = 1,000 / 1.04^5 = approximately $821.93 |
If its yield immediately rises to 5%, with no time elapsed, its price becomes approximately $783.53. That is a decline of about 4.67%. Nothing happened to the $1,000 payment in this example. The discount rate changed.
This example deliberately removes coupons and credit risk. It isolates the price effect of discounting, which can otherwise disappear behind the word “income.” The MSRB’s guide to evaluating interest rate risk explains the inverse price-yield relationship and introduces duration and convexity.
Put units into the approximation
For a conventional option-free bond, modified duration gives a first-order estimate:
1 | percentage price change ≈ −modified duration × change in yield |
The yield change must be expressed as a decimal. A 100 basis point move is one percentage point, or 0.01. For a bond with a modified duration of six, a 0.01 increase in yield implies an approximately 6% price decline, all else equal.
For the zero-coupon example, Macaulay duration is five years and modified duration is 5 / 1.04, approximately 4.8077. The estimated price decline for the one percentage point move is 4.81%. The exact decline was 4.67%. The difference reflects curvature: the price-yield relationship is not a straight line.
Macaulay duration, modified duration, and effective duration are related measures, but they should not be substituted without checking the definition. Effective duration is commonly used when cash flows can change as yields move, as with embedded options. A factsheet that says only “duration” needs that additional context.
Separate the risks the number leaves out
A single duration number is a simplification. It cannot tell you what will happen if different parts of the yield curve move in different directions. Key-rate durations can provide a more detailed map of those exposures.
It also does not, by itself, capture default, downgrade, or liquidity risk. A corporate bond may fall because its credit spread widens even while government yields decline. A bond denominated in another currency introduces exchange-rate exposure for an investor measuring wealth in a home currency.
Nor does a short duration guarantee an acceptable outcome. A small price movement can still be too large for money needed immediately. The relevant risk budget starts with the purpose of the capital.
Holding to maturity changes the question
An individual bond held to maturity can deliver its contractual principal and coupons if the issuer pays as promised and the contract is not changed by a call or other provision. This does not remove inflation risk, opportunity cost, or the problem of reinvesting coupons at unknown rates.
A conventional open-ended bond fund generally does not have the same fixed repayment date as one bond. It holds and trades a changing portfolio. Defined-maturity funds have a different structure again, and require reading their actual terms rather than extrapolating from the category name.
Here is the planning distinction: “Can I tolerate a mark-to-market drawdown?” and “Will cash arrive when my obligation is due?” are separate questions. A long-horizon investor and someone paying tuition next spring can rationally evaluate the same bond differently without disagreeing about the yield outlook.
Turn a rate opinion into a scenario table
Before expressing conviction about interest rates, write a small scenario table. For a hypothetical portfolio with modified duration six, instantaneous parallel yield shifts of −0.5, +0.5, and +1.0 percentage points imply approximate price changes of +3%, −3%, and −6% respectively.
Those are price sensitivities, not total-return forecasts. Coupon income, elapsed time, reinvestment, changing duration, and convexity all matter over a real holding period. For credit instruments, spread scenarios should be examined separately.
The table still serves a purpose: it forces the exposure into units that can be compared with a cash need or a tolerable loss. If the adverse scenario is unacceptable, a compelling forecast does not repair the mismatch.
Duration earns its place by making an assumption visible. It is a measuring tool for a decision that remains yours, rather than a prediction disguised as a technical statistic.
Source and calculation notes
The MSRB guide is investor education about municipal bonds; the zero-coupon arithmetic above is a separate generic example. Prices are rounded after calculation, ignore accrued interest and transaction costs, and assume an unchanged maturity for an immediate yield shock.