CFA Level I Exam · Interest Rate Risk and Return

Bond Returns and Horizon Yield for CFA Level I

Updated 7 October 2026 · Fact-checked

A bond's return over a holding period comes from three sources: coupon payments, interest earned by reinvesting those coupons, and the capital gain or loss when you sell or the bond matures. Horizon yield is the annualized rate that grows the purchase price into that total future value: (total future value ÷ price)^(1/years) − 1.

Understand Bond Returns and Horizon Yield

A fixed-rate bond pays you in three ways. First, you receive coupon and principal payments. Second, you can earn reinvestment income by investing each coupon until the end of your holding period. Third, if you sell before maturity, you realize a capital gain or loss: the sale price minus the purchase price.

The yield to maturity (YTM) is only a promise under strict conditions: you hold to maturity, the issuer pays in full, and every coupon is reinvested at the YTM. Real returns differ because reinvestment rates and the selling price depend on future interest rates. The horizon yield (also called realized return or horizon return) measures what you actually earn once you state those assumptions.

Interest rates pull the two risky sources in opposite directions. If rates rise, the bond's sale price falls (price risk) but coupons are reinvested at higher rates (more reinvestment income). If rates fall, the price rises but reinvestment income shrinks. Reinvestment risk is the risk that rates fall when you reinvest. Price risk is the risk that rates rise before you sell.

Because the two effects offset, there is a point where they roughly cancel. When your investment horizon equals the bond's Macaulay duration, a one-time parallel yield shift right after purchase leaves the horizon return close to the original YTM. If the horizon is shorter than Macaulay duration, price risk dominates. If it is longer, reinvestment risk dominates.

To compute horizon yield, add up everything you will have at the horizon: coupons, interest on coupons, and the sale price. Divide by the purchase price, then take the root for the number of periods. The result is a compound rate per period, which you annualize.

Key formulas to remember

Sources of return: Total return = coupons received + reinvestment income + (sale price − purchase price); If the bond is held to maturity, the sale price is par and the capital gain or loss is par minus purchase price.
Future value of reinvested coupons: FV of coupons = C × [((1 + r)^n − 1) ÷ r]; C = coupon per period, r = reinvestment rate per period, n = number of coupons received up to the horizon. This includes the coupons themselves plus interest on them.
Sale price at horizon: Price = Σ [C ÷ (1 + y)^t] + FV ÷ (1 + y)^N; Use the yield y expected at the horizon and N = periods remaining after the sale date, not the original maturity.
Total future value at horizon: Total FV = FV of coupons + sale price; Accrued interest at sale, if any, belongs in the total. Exam questions usually avoid it by selling on a coupon date.
Horizon yield per period: Horizon yield = (Total FV ÷ Purchase price)^(1 ÷ n) − 1; n = number of periods held. For semiannual periods, the bond-equivalent annual rate is this value × 2 unless the question asks for an effective annual rate.
Duration matching rule: Horizon = Macaulay duration → price risk ≈ reinvestment risk; This holds approximately for a single parallel yield shift right after purchase. It is not exact.

How to solve Bond Returns and Horizon Yield questions

Use this order for any horizon yield or return decomposition question. Keep the cash flows on a simple timeline.

1Write the purchase price, coupon per period, holding period in periods, and the reinvestment rate per period. Convert annual rates to periodic rates if coupons are semiannual.
2Count how many coupons you receive before and at the horizon date.
3Compute the future value of those coupons at the reinvestment rate using the annuity future value formula.
4Compute the sale price at the horizon: use the horizon yield, the remaining coupons and the remaining periods. If the bond matures at the horizon, the price is par.
5Add the coupon future value and the sale price to get the total future value.
6Divide by the purchase price and raise to 1/n, then subtract 1 to get the periodic horizon yield.
7Annualize as the question asks (multiply by the periods per year for bond-equivalent, or compound for an effective rate).
8Check reasonableness: if rates rose and you reinvested at higher rates, compare the result with the original YTM and see that the direction makes sense.

Quickest way: Calculator route for horizon yield

When to use it: Use this under time pressure when the question gives rates and dates. Skip algebra and use the financial keys.

TI BA II Plus, coupon future value: N = number of coupons, I/Y = reinvestment rate per period, PV = 0, PMT = −coupon, CPT FV.
TI BA II Plus, sale price: N = periods remaining, I/Y = horizon yield per period, PMT = coupon, FV = par, CPT PV. Ignore the sign.
Add the two results to get the total future value.
Horizon yield: N = periods held, PV = −purchase price, PMT = 0, FV = total future value, CPT I/Y. Clear the TVM registers (2nd FV) between steps.
HP 12C: use n, i, PV, PMT, FV in the same pattern, and enter cash outflows as negative numbers.
For options, estimate first. If there is no capital gain and reinvestment is at a rate near the coupon rate, the answer will be near the coupon yield. Eliminate options that are clearly off.

Common mistakes in Bond Returns and Horizon Yield

Treating the YTM as the expected return on a bond that is sold before maturity.
YTM is quoted everywhere, so it feels like the return.
Fix: YTM equals the realized return only if the bond is held to maturity and coupons are reinvested at the YTM. Otherwise compute horizon yield from the cash flows.
Pricing the bond at the horizon using the original maturity.
You carry over N from the purchase date.
Fix: Subtract the holding period from the original term. Use only the remaining periods and the horizon yield.
Leaving out interest on reinvested coupons, or counting the coupons as a plain sum.
Adding coupons is easier than compounding them.
Fix: Use the annuity future value formula at the reinvestment rate. The last coupon at the horizon earns nothing but still counts.
Mixing periodic and annual rates, such as using 6% with 6 semiannual periods.
Semiannual bonds need halved rates and doubled periods.
Fix: Convert rate and periods first and write both beside the formula. Annualize only at the end.
Mixing up which risk dominates when rates change.
Price and reinvestment effects move in opposite directions.
Fix: Rates up: price falls, reinvestment income rises. Rates down: price rises, reinvestment income falls. Short horizon means price risk matters more, long horizon means reinvestment risk matters more, relative to Macaulay duration.
Dividing the total gain by the price and the number of years to annualize.
It looks like a simple average annual return.
Fix: Horizon yield is a compound rate: take the root of the ratio of total future value to price.

Worked examples

Example 1

An investor buys a 5-year, 6% annual-coupon bond at par (100). She holds it for 3 years and reinvests each coupon at 4%. After 3 years the bond has 2 years left and she sells it at a yield of 5%. What is her annualized horizon yield? A. 5.62% B. 6.44% C. 7.10%

Show the solution

Future value of coupons: 6 × (1.04² + 1.04 + 1) = 6 × 3.1216 = 18.7296.
Sale price with 2 years left at 5%: 6 ÷ 1.05 + 106 ÷ 1.05² = 5.7143 + 96.1451 = 101.8594.
Total future value = 18.7296 + 101.8594 = 120.5890.
Horizon yield = (120.5890 ÷ 100)^(1/3) − 1 = 1.20589^(1/3) − 1 ≈ 1.06440 − 1 = 6.44%.
Check: 1.0644³ ≈ 1.2059, which matches the ratio.
Calculator check: N = 3, PV = −100, PMT = 0, FV = 120.589, CPT I/Y ≈ 6.44.

Answer: B. About 6.44% a year.

Example 2

A bond with a par value of 100 is bought for 98. It pays a 5% annual coupon (5 per 100 par), which the investor reinvests at 3%. After 2 years the bond is sold for 99.50 just after the second coupon is paid. What is the annualized horizon yield? A. 5.10% B. 5.78% C. 5.94%

Show the solution

Future value of coupons: the first coupon is reinvested for 1 year at 3% and the second arrives at the horizon, so 5 × 1.03 + 5 = 10.15.
Total future value = 10.15 + 99.50 = 109.65.
Ratio = 109.65 ÷ 98 = 1.11888.
Horizon yield = 1.11888^(1/2) − 1 ≈ 5.78%.
Why not A: 5 ÷ 98 = 5.10% is only the current yield and ignores the gain and reinvestment.
Why not C: dividing the total gain by price and years gives (11.65 ÷ 98) ÷ 2 = 5.94%, which is a simple average, not a compound rate.

Answer: B. About 5.78% a year.

Exam tips

Questions usually give you the reinvestment rate and the horizon yield. Your job is to put them into the right place: reinvestment rate for the coupons, horizon yield for the sale price.
Expect conceptual questions on which risk dominates. Compare the horizon with Macaulay duration before you read the options.
With three options and no penalty, always answer. Sanity-check first: if the bond is sold at a gain, the horizon yield should be above the coupon yield when reinvestment rates are close to it.
Check whether the question asks for a periodic, bond-equivalent or effective annual rate. The wrong convention is a common trap option.
Numeric options are listed smallest to largest. Do your calculation fully, then match it, and discard options that equal a simple-average or coupon-only answer.

Practice questions from Interest Rate Risk and Return

Bond Returns and Horizon Yield: frequently asked questions

What is horizon yield on a bond?

It is the compound annual rate of return you earn on a bond over a chosen holding period. It uses the purchase price, coupons, interest earned on reinvested coupons and the sale price at the horizon. It differs from YTM whenever reinvestment rates or the sale yield differ from the original YTM.

What are the sources of return on a fixed-rate bond?

There are three: coupon and principal payments, reinvestment income from investing the coupons, and the capital gain or loss when the bond is sold before maturity. For a bond held to maturity, the capital gain or loss is simply par minus the purchase price.

What is the difference between reinvestment risk and price risk?

Price risk is the risk that rising yields reduce the bond's sale price. Reinvestment risk is the risk that falling yields reduce the rate at which you can reinvest coupons. They move in opposite directions, so each partly offsets the other.

When do price risk and reinvestment risk offset each other?

They roughly offset when the investment horizon equals the bond's Macaulay duration, for a single parallel yield change right after purchase. If the horizon is shorter than Macaulay duration, price risk dominates. If it is longer, reinvestment risk dominates.