Separate Bond Carry, Curve Roll and an Unexpected Exit-Yield Change

Define the counterfactual before naming the return components

FINRA distinguishes yield measures from realized bond return. A one-year result on a longer bond depends on its exit value even when no coupon arrives. To explain that result, an analyst can construct a reference path in which the bond ages while its yield is held constant, then compare that path with other exit-yield assumptions. The resulting components depend on the chosen reference and should be labeled accordingly.

This case uses an invented USD 10,000 zero-coupon claim due in two years. Annual effective yields are used throughout, with no default, fees or accrued coupon. At an initial two-year yield of 5 percent, purchase value is USD 10,000 divided by 1.05 squared, about USD 9,070.29. The full claim still pays only USD 10,000 at maturity if payment occurs; nothing extra is distributed during the first year.

Supporting references: 1. FINRA: Understanding Bond Yield and Return

Measure aging at an unchanged yield

After one year, the claim has one year remaining. If its required annual yield stays at 5 percent, its value is USD 10,000 divided by 1.05, about USD 9,523.81. The USD 453.51 difference from purchase value equals 5 percent of initial capital. Here we call that the unchanged-yield aging component. It is economic accrual expressed through value, not a coupon credited to the cash account.

This definition absorbs the movement toward the maturity payment that follows from shortening the horizon at the same yield. Adding a separate pull-to-par gain on top of that USD 453.51 would count the same mechanism twice. Other attribution systems may use the word carry differently, especially for coupon bonds. The important discipline is to specify the reference valuation and reconcile all components to one total. A positive modeled aging gain also does not create cash for an intervening bill. Before maturity, making that value spendable generally requires a sale or another funding source, with costs and a price that the constant-yield reference has not guaranteed.

Add a stated curve-roll assumption

Suppose the initial one-year yield is 4 percent while the initial two-year yield is 5 percent. An unchanged-curve scenario assumes that one year later the now-one-year claim is priced at 4 percent. Its exit value is then USD 9,615.38. Relative to the constant-5-percent-yield reference value, the extra USD 91.58 is the modeled curve-roll effect. Relative to purchase, the entire gain is USD 545.09.

The phrase unchanged curve describes a scenario, not an observation about the future. It assumes the one-year point on a future date equals today's one-year point. A current upward slope does not ensure that this will happen. Forward rates and future spot rates answer different questions, and the roll scenario should not be interpreted as an arbitrage or an available promised one-year investment return.

Reconcile an unfavorable surprise without losing the reference

Now suppose the actual exit yield after one year is 6 percent. The claim's sale value becomes USD 9,433.96, leaving a USD 363.67 gain relative to purchase before costs. Relative to the unchanged-curve 4 percent scenario, the exit-yield surprise costs USD 181.42. Unchanged-yield aging of USD 453.51 plus curve roll of USD 91.58 minus that surprise of USD 181.42 reconciles to the USD 363.67 realized gain.

The calculation uses exact discounting in this simplified zero-coupon model, rather than adding duration estimates. Small displayed rounding differences can arise because components retain full precision internally. The point is not that rising yields always leave a positive result. It is that one component can be negative while the entire holding-period gain remains positive, depending on the purchase price, passage of time and exit yield.

Find the loss boundary and test beyond it

A one-year exit value equal to the original purchase requires an exit yield of 10.25 percent: USD 10,000 divided by 1.1025 equals the original USD 9,070.29. At a supplied 12 percent exit yield, value is approximately USD 8,928.57 and the investor loses USD 141.72. The zero's eventual face amount has not changed, but selling after one year substitutes a market payment for the later contractual redemption.

That boundary is specific to this two-year purchase and one-year sale. A different starting yield, horizon, credit assumption or fee changes it. It also says nothing about the probability of such an exit yield. For a date-sensitive spending plan, use the boundary to understand which market states produce a shortfall rather than treating today's yield as a forecast of resources available whenever the money is needed.

Carry the attribution into a usable holding-period ledger

TreasuryDirect explains that a STRIPS component has one maturity payment. Such a structure helps isolate valuation timing, although the fictional pricing here is not a Treasury quote or a product recommendation. For a coupon bond, the same ledger would also need each receipt, any reinvestment earnings, beginning and ending accrued interest, and execution costs. A simplified zero-coupon attribution cannot just be copied into that richer schedule.

The decision boundary is whether a claimed return component comes from an actual cash flow, a defined aging counterfactual or an assumed market change. Keep those fields separate, then require their sum to equal total gain. If a presentation counts coupon yield, yield-to-maturity, pull to par and roll as independent additions without a reconciliation, its attractive headline may be arithmetic duplication rather than an economically achievable outcome.

Supporting references: 2. TreasuryDirect: STRIPS

Limits of this analysis

• Attribution terminology varies; this article defines its own constant-yield reference.
• Unchanged-curve roll is a hypothetical assumption, not a forecast or guaranteed gain.
• Exact simple zero discounting omits credit, taxes, financing and execution costs.