Same Coupon, Different Return: What Changed?
Follow two hypothetical three-year outcomes for the same bond. Separate coupon income, reinvestment and sale gains to see why holding-period return differs from purchase YTM.
01 · The setup
One bond, two possible three-year outcomes
A and B are alternative outcomes for the same purchase, not two people trading in the same market at the same moment. The bond has face value USD 1,000.00, a 4.00% fixed coupon, 10 years to maturity and semiannual payments. The purchase yield is 4.00%, so each outcome starts with a price of USD 1,000.00. The investor plans to sell after 3 years, immediately after collecting a coupon.
At purchase, “a 4% bond” sounds like a complete description of the return. It is not. The coupon specifies contractual income, while a three-year investment ends with a sale of a bond that still has 7 years left. The sale price and what happened to earlier coupons must also enter the account.
02 · Shared assumptions
Separate the assumptions from the promised payments
In outcome A, the exit yield is 3.00% and coupons are reinvested at a nominal annual 2.00%. In B, the exit yield is 6.00% and reinvestment earns 5.00%. These are hypothetical combinations, not forecasts or claims about which rates must move together. The bond pays on time and has no call option; taxes, fees, default and currency movements are excluded.
Each coupon is USD 20.00. Both outcomes collect 6 payments, totalling USD 120.00 before reinvestment. Early coupons earn interest for more half-years than late coupons; the final coupon has no time left to compound. Reinvestment income is only the extra interest on coupons, not those coupons counted a second time.
Outcome A
Outcome B
All bars share one absolute USD scale. Bold amounts are the higher signed value for each component. Dashed bars with a minus sign are losses; they reduce total return.
| Component | A | B |
|---|---|---|
| Coupon income | USD 120.00 | USD 120.00 |
| Reinvestment income | USD 3.04 | USD 7.75 |
| Sale gain / loss | USD 62.72 | USD -112.96 |
| Total gain / loss | USD 185.76 | USD 14.79 |
| Ending wealth | USD 1,185.76 | USD 1,014.79 |
| Holding-period return | 18.58% | 1.48% |
| Effective annualized return | 5.84% | 0.49% |
Bold marks the higher income, signed gain, wealth or return in each row. Equal values stay unmarked; for two losses, the less negative amount is higher. A higher component alone need not produce a higher total return.
03 · Compare the numbers
Coupons do not tell the whole profit story
In A, the remaining bond sells for USD 1,062.72. The sale gain is USD 62.72, and reinvestment adds USD 3.04. Together with coupons, the gain is USD 185.76 and ending wealth is USD 1,185.76. The holding-period return is 18.58%; its effective annualized rate is 5.84%.
In B, the higher exit yield produces a sale price of USD 887.04 and a capital change of USD -112.96. Reinvestment earns USD 7.75, more than in A, yet total gain is USD 14.79 and ending wealth is USD 1,014.79. Its holding-period return is 1.48%, or 0.49% effective annually. Better reinvestment cannot offset the larger price loss in this particular case.
04 · Understand the model
YTM is an internal rate, not a guaranteed wealth path
The original 4.00% YTM is the nominal annual discount rate, compounded semiannually, that prices all scheduled cash flows through maturity. It does not say the investor will sell after three years at a particular price. Nor does computing an IRR require the coupons actually to be reinvested. To turn that IRR into a compound terminal-wealth return, however, reinvestment assumptions become necessary.
If every coupon can be reinvested at that periodic YTM and all payments arrive, holding to maturity reconciles terminal wealth with the YTM compounding convention. Here the investor exits earlier and uses different reinvestment rates. The article's annualized returns are effective annual rates; the purchase YTM is nominal with semiannual compounding. Even unchanged yields therefore imply an effective annual rate of 4.04%, not exactly the quoted nominal rate.
G: total gain; I: coupons; R: extra interest on reinvested coupons; PH: sale price; P0: purchase price. Annualized return compounds ending wealth over the holding years.
Change B, keep A as the reference
The two assumptions can change independently. A and the article's baseline stay fixed.
| Component | A | B |
|---|---|---|
| Coupon income | USD 120.00 | USD 120.00 |
| Reinvestment income | USD 3.04 | USD 7.75 |
| Sale gain / loss | USD 62.72 | USD -112.96 |
| Total gain / loss | USD 185.76 | USD 14.79 |
| Ending wealth | USD 1,185.76 | USD 1,014.79 |
| Holding-period return | 18.58% | 1.48% |
| Effective annualized return | 5.84% | 0.49% |
Bold marks the higher income, signed gain, wealth or return in each row. Equal values stay unmarked; for two losses, the less negative amount is higher. A higher component alone need not produce a higher total return.
05 · Decision conditions
A longer holding period changes the balance of risks
Higher yields can hurt the sale price while improving the return on reinvested coupons. Over a short horizon, the price effect may dominate; over a longer horizon, more coupons have time to accumulate and principal is closer to repayment. The balance depends on duration, the timing and path of rates, and when the money is needed. A change in rates is not universally good or bad for every bond holder.
The model uses one reinvestment rate for all coupons and one flat exit yield. Real reinvestment rates vary through time; actual selling can involve spreads, illiquidity and accrued interest. A bond fund also trades and replaces securities, so it has no single maturity date that matches this example. Compare the three return components in the tool, and ask which assumption matters most over your own horizon.
The sale occurs just after a coupon: the investor receives that coupon, and the sale price values only the remaining payments. Counting the same coupon again in the sale price would overstate wealth. The returned sale proceeds also contain recovered principal; only the difference from the original purchase price is a capital gain or loss.
Further comparison
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The tool lets you change bond terms and inspect the full calculations. Its current inputs are independent of the article.
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