What a Bond’s Yield Does—and Does Not—Measure
A bond’s yield to maturity is useful for summarizing the relationship between its price and its promised cash flows. But the word yield can invite an unwarranted conclusion: that the quoted number is the return an investor is certain to earn. It is not. A bond’s yield to maturity is a rate implied by its price and cash-flow schedule under a particular valuation convention. The investor’s realized return can differ when the bond is sold before maturity, coupons are reinvested at another rate, or promised payments are not received in full.
A second frequent source of confusion is treating current yield as if it measured total return. Current yield compares the annual coupon with the bond’s current price. It does not account for a price gain or loss. Finally, a yield quoted for a bond with multiple coupon payments per year must be interpreted using the correct period length: a rate per half-year is not automatically an effective annual rate.
When coupons are paid annually, \(j\) is an annual rate. With \(m\) coupon periods per year, \(j\) is the yield per coupon period. The annual rate quoted on a bond-equivalent basis is \(m j\), while the effective annual rate is \((1+j)^m-1\). These are different ways of expressing a rate, not different estimates of the same number under an identical convention.
Why Yield to Maturity Is Not a Guaranteed Realized Return
The pricing equation defines an internal rate of return for the bond’s promised cash flows. To see the role of reinvestment, suppose an investor holds a default-free bond to maturity, receives every promised payment, and reinvests each coupon at the per-period yield \(j\). The value at period \(n\) of the coupons and principal is then $$ \sum_{t=1}^{n}CF_t(1+j)^{n-t}. $$ Multiplying the yield-to-maturity pricing equation by \((1+j)^n\) gives $$ P_0(1+j)^n=\sum_{t=1}^{n}CF_t(1+j)^{n-t}. $$ Thus, under these conditions, the accumulated payments equal the amount that grows from \(P_0\) at rate \(j\) for \(n\) periods. The reinvestment condition matters: a coupon received before maturity must earn \(j\) for the accumulated value to match this result. If coupons earn another rate, the terminal value changes. If the investor sells early, the sale price also affects the return.
This justification is not a promise that the conditions will occur. A yield-to-maturity calculation uses the bond’s promised payments and a specified period convention. It does not guarantee payment, coupon reinvestment at \(j\), or a particular price if the bond is sold before maturity. Those distinctions are especially important when comparing a quoted yield with an investor’s actual experience.
Worked Example: A Sale Before Maturity Changes the Return
An investor buys a default-free, two-year bond for its fair price. The bond has face value $1,000 and pays a $50 coupon annually. Its yield to maturity at purchase is 6% per year. After one year, immediately after receiving the first coupon, the investor sells it when the market yield on the remaining one-year cash flow is 7%. Find the one-year holding-period return. Assume annual compounding, no taxes or transaction costs, and no coupon reinvestment during the one-year holding period.
Method. First find the initial price from the promised cash flows discounted at the initial yield:
After the first coupon has been paid, only the $1,050 final payment remains. Discounting it for one year at the new 7% market yield gives the sale price:
The investor’s cash received over the year is the $50 coupon plus the sale proceeds. Therefore,
The holding-period return is 5.06% to two decimal places, not the initial 6% yield to maturity. The higher market yield lowered the resale price, and the bond was sold before the promised final payment. The common mistake is to report the purchase-date yield as the return earned regardless of the sale price. The correction is to include both cash payments received and the change in bond price over the actual holding period.
Current Yield Is Not Total Return
For a bond with annual coupon \(C_{\text{annual}}\) and current price \(P_0\), current yield is
It is a coupon-to-price ratio. It excludes any gain or loss from a change in the bond’s price and does not include the timing or reinvestment of coupons beyond the period being considered. By contrast, for a one-period holding with one coupon received, purchase price \(P_0\), and sale price \(P_1\), the holding-period return is
This formula adds the coupon income and the price change, then measures their combined amount relative to the initial investment. It is a realized return for the stated holding period, not a yield-to-maturity calculation.
Worked Example: Separating Coupon Income from a Price Gain
A hypothetical bond has a $1,000 face value, pays an annual coupon of $60, and is purchased for $960 just after a coupon date. One year later, just after the next $60 coupon is paid, it is sold for $980. Assume no taxes, transaction costs, or other cash flows. Calculate its current yield at purchase and its one-year holding-period return.
Current yield. Divide the annual coupon by the purchase price:
Holding-period return. The price gain is \(980-960=$20\). Adding the $60 coupon gives total cash benefit of $80 relative to the $960 investment:
The holding-period return is 8.33% to two decimal places, which is greater than the 6.25% current yield because the bond also produced a $20 price gain. The common mistake is to call the current yield the total return. The correction is to include the price change when calculating the return over a specified holding period.
Do Not Mix Periodic and Annual Rates
A yield is meaningful only with its period and quoting convention stated. If coupon payments occur \(m\) times per year and the yield per coupon period is \(j\), the nominal annual rate under the bond-equivalent convention is \(m j\). The effective annual rate instead accounts for compounding across all \(m\) periods:
The nominal annual quote and the effective annual rate answer different questions. The nominal quote reports a periodic rate multiplied by the number of periods; the effective rate reports the annual accumulation implied by compounding. For \(m>1\) and a positive \(j\), the effective annual rate is greater than the nominal quote because of within-year compounding.
Worked Example: Interpreting a Semiannual Yield Quote
A bond pays coupons twice a year, and its yield to maturity is 2.5% per half-year. Find the nominal annual bond-equivalent quote and the effective annual rate. Assume the 2.5% yield applies in each half-year and compounds.
Method. There are \(m=2\) periods per year, so the nominal annual quote is
The effective annual rate compounds the two half-year periods:
The nominal annual quote is 5.00%, and the effective annual rate is 5.0625%. The common mistake is to treat 2.5% per half-year as 2.5% per year, or to treat the 5.00% nominal quote as an effective annual rate. Keep the period yield attached to its half-year period, then apply the appropriate conversion.
A Price Decomposition Is a Useful Check
The yield-to-maturity equation also gives a practical consistency check: the price equals the present value of the coupon stream plus the present value of principal. Coupon and principal components must use the same yield and payment periods as the full valuation. The components should add back to the quoted price, subject to rounding.
Worked Example: Checking Coupon and Principal Present Values
A hypothetical bond has face value $1,000, pays six annual coupons of $30, and is valued at a 3% annual yield. Find the present value of the coupons and principal separately, then check the total price. Assume the bond pays all six coupons and the principal at the end of year six.
Method. The coupons form a six-payment level annuity, while principal is a single payment at time six. Using the annual yield of 3% for both components:
Adding the rounded components gives
The price is $1,000.00. The check works because the annual coupon rate equals the annual yield and the bond is priced at face value. A common calculation error is to use an annuity factor for the wrong number of coupons or to misstate the coupon and principal components even when their total is intended to equal par. Here there are six coupons, so the annuity factor uses six periods; principal is discounted for those same six years.
Common Misinterpretations to Avoid
| Misinterpretation | Why it fails | Correction |
|---|---|---|
| “The yield to maturity is the return I am guaranteed to earn.” | It does not ensure promised payments, coupon reinvestment at the yield, or a particular early sale price. | State the assumptions and calculate the return over the investor’s actual horizon when that is the question. |
| “Current yield is total return.” | Current yield includes coupon divided by price, but omits capital gain or loss. | Add the price change to coupons received for a holding-period return. |
| “A 2.5% semiannual yield is 2.5% per year.” | The rate applies to a six-month period, not a full year. | Identify the period, then convert to a nominal quote or effective annual rate as requested. |
| “The nominal annual quote is the effective annual rate.” | A nominal quote is the periodic rate multiplied by the number of periods; it does not include compounding within the year. | Use \((1+j)^m-1\) for the effective annual rate when the same periodic rate compounds \(m\) times a year. |
Check Your Understanding
For each problem, state the relevant rate or return and keep the payment period explicit.
- A hypothetical bond has an annual coupon of $72, is purchased for $900, and is sold one year later for $930 just after the coupon is received. Find the purchase-date current yield and the one-year holding-period return, assuming no costs or taxes. (Answer: current yield \(=8.00\%\); holding-period return \(=(72+930-900)/900=11.3333\%\).)
- A bond’s yield is 3% per half-year, with two coupon periods per year. Find its nominal annual bond-equivalent quote and effective annual rate, assuming the same rate compounds in both half-years. (Answer: nominal quote \(=6.00\%\); effective annual rate \(=(1.03)^2-1=6.09\%\).)
- A two-year bond with face value $1,000 pays a $50 coupon annually and sells for $950. Write the yield equation and estimate the annual yield to maturity to three decimal places. Assume all promised payments are used and annual compounding applies. (Answer: \(950=50/(1+y)+1{,}050/(1+y)^2\), giving \(y\approx7.796\%\).)
- A hypothetical three-year bond has face value $1,000 and pays a $40 coupon annually. It is purchased at par when its annual yield is 4%. After one year’s coupon is paid, the market yield for the remaining two years is 6%, and the investor sells immediately. Find the one-year holding-period return, assuming no costs or taxes. (Answer: sale price \(=40/1.06+1{,}040/(1.06)^2\approx$963.33\); return \(=(40+963.33-1{,}000)/1{,}000\approx0.333\%\).)
- A semiannual bond yield is 2% per half-year. Give both the nominal annual bond-equivalent quote and the effective annual rate. Explain why neither should be reported simply as “2% annually.” (Answer: nominal quote \(=4.00\%\); effective annual rate \(=(1.02)^2-1=4.04\%\); 2% is the rate per half-year.)