Reinvestment and Roll-Down: Two Different Return Assumptions

Keep payment receipts and terminal wealth separate

Coupon and principal payments are cash-flow events. Terminal wealth additionally depends on what happens to earlier receipts before the chosen horizon. Cash might be spent, retained without interest or reinvested at a stated rate. Those choices produce different wealth measures even when the bond makes every promised payment. A useful explanation therefore states the treatment of interim cash before presenting a compounded realized return.

CFA Institute's interest-rate-risk reading distinguishes payments, reinvestment and sale-price effects as sources of bond return. A yield-to-maturity calculation itself is an internal-rate-of-return calculation on a specified schedule; it does not operate a reinvestment account. Realizing that yield as a compounded terminal-wealth rate requires additional conditions about receipt timing and reinvestment. The formula and the subsequent use of cash answer related but different questions.

Verify a two-year reinvestment illustration

Assume a hypothetical two-year annual-coupon bond with USD 1,000 face value, 4% coupon and purchase price USD 1,000 immediately after a coupon date. All promised payments arrive and there are no costs or taxes. The first USD 40 coupon arrives after one year. Suppose it earns an explicitly assumed 2% for the remaining year, becoming USD 40.80 at the final horizon.

At maturity, the bond pays USD 1,040 including the final coupon, giving terminal wealth USD 1,080.80. Independently, add USD 1,000 principal, USD 80 coupons and USD 0.80 reinvestment interest. The annualized terminal-wealth return is (1,080.80 / 1,000)^(1/2) - 1, approximately 3.961531%. It is below the original 4% yield because the early coupon was reinvested at a lower rate under this isolated scenario.

Interpret the example without overstating the convention

If the first coupon were spent, the bond's contractual payments would be unchanged, but a terminal-wealth calculation excluding that spending would measure something different. It would be incorrect to infer that the spent cash vanished economically. The reporting definition must decide whether to measure investment cash-flow return, ending wealth or resources consumed along the way. Mixing these definitions can make equivalent payment histories appear inconsistent.

The exercise also does not establish that the future reinvestment rate will be 2%. That rate was supplied to expose a dependency. A more elaborate path of reinvestment rates would require more assumptions and a separate model. The parent fixed-coupon tools do not provide that simulation. Their present-value result should not be described as an assurance that coupons can actually be reinvested at the entered discount yield.

Define roll-down using an explicit future-yield assumption

Roll-down asks how a bond might reprice when it occupies a shorter remaining maturity on a specified yield schedule. An unchanged upward-sloping schedule can assign a lower yield to the aged bond, producing a favorable price effect. CFA Institute discusses roll-down within yield-curve strategies. The operative word is unchanged: this is a scenario assumption about the future schedule, not a consequence that today's curve guarantees.

Also distinguish roll-down from the passage of time at a constant bond yield. A discount or premium bond can move toward its redemption value as maturity approaches even without a change in its own yield. Comparing an aged bond at two different assumed yields isolates a different effect. A return explanation should state its baseline, otherwise ordinary aging and a favorable maturity-related yield change may be counted twice.

Calculate an aged-bond price separately from its coupon

Use a second hypothetical bond with USD 100 face, a 4% annual coupon, two years remaining and an initial 4% annual yield, so its coupon-date price is USD 100. After one year, immediately after receiving the USD 4 coupon, assume the remaining one-year payment is discounted at 3%. Its ex-coupon price is 104 / 1.03 = USD 100.970874, rounded to six decimals.

With no costs and no time for reinvestment of the coupon paid at the horizon, the one-year holding-period return is (4 + 100.970874 - 100) / 100, approximately 4.970874%. The same aged payment discounted at the original 4% yield would be worth USD 100. Thus USD 0.970874 of the scenario's price benefit comes from the assumed lower terminal yield, separately from the USD 4 coupon.

Do not treat a static curve as a forecast

The roll-down example imposes a future one-year yield. It does not derive that future yield from a promise embedded in the current two-year bond. A forward rate inferred from today's discount factors is another conditional construct and need not equal the future observed short rate. Distinguishing these ideas prevents an unchanged-curve illustration from being advertised as a return available without uncertainty or a rule for selecting maturities.

An adverse change in the curve can offset the illustrated benefit, as can a spread change or transaction cost outside the example. A useful comparison keeps the same starting bond and horizon while changing the terminal-yield assumption. It should not change the coupon treatment or switch between clean and full prices halfway through the calculation. Consistent boundaries make the source of each difference visible without requiring a market prediction.

Keep an honest holding-period ledger

A complete educational holding-period ledger lists starting outflow, interim receipts, interest on those receipts and ending value or redemption. Each line needs a date and a statement of whether it is contractual or assumed. Summing those components avoids attributing all improvement to roll-down when part came from coupon income. It also prevents a principal redemption from being counted once as terminal value and again as a separate gain.

These examples extend the interpretation of regular bonds without expanding the parent tools' capabilities. Their supported calculations remain coupon-date valuations of noncallable fixed-coupon bullet schedules using annual nominal yields and matching payment-frequency compounding. Reinvestment paths, future curves, accrued interest and settlement effects are outside that scope. The appropriate takeaway is to identify the assumptions behind a proposed return calculation, not to infer a strategy recommendation from a favorable illustration.

Primary references

1. CFA Institute: Interest Rate Risk and Return
2. CFA Institute: Yield Curve Strategies