What it means
A bond's coupon rate is fixed at issue, but its market price moves constantly, so the coupon alone tells you nothing useful about what a buyer today will earn. Yield to maturity solves that by folding the purchase price, the coupons and the repayment of face value into one annualised rate.
The relationship with price is inverse and worth remembering. A bond bought below face value has a yield to maturity above its coupon rate, because the buyer collects the coupons and also a gain on repayment, while a bond bought at a premium yields less than its coupon.
Beyond bond investing, yield to maturity is the benchmark cost of debt for corporate finance. When a business calculates its weighted average cost of capital, the debt component is normally the yield to maturity on its own bonds rather than the coupon it happens to be paying.
Mathematically the yield is an internal rate of return, so there is no clean way to solve for it by hand; a spreadsheet or calculator finds it by iteration. The approximation formula below gets within a few basis points and is good enough for a sanity check in a meeting.
The main caveat is the reinvestment assumption. The calculation quietly assumes each coupon can be reinvested at the yield to maturity itself, so in a falling rate market the realised return will be lower than the quoted figure, which is one reason investors also look at duration and yield to worst.
In practice
Real-world examples.
Example
A treasurer compares two corporate bonds, one with a 3% coupon priced at $880 and one with a 6% coupon priced at $1,110. Yield to maturity puts them on the same footing and shows the lower coupon bond is actually the better return.
Example
A finance team calculating its weighted average cost of capital uses the 6.2% yield to maturity on its listed bonds rather than the 4.5% coupon it pays, recognising that 6.2% is what the market would charge to lend to it today.
Example
A charity's investment committee is told its bond portfolio yields 5.4%. The treasurer points out that if rates keep falling, coupons will be reinvested below that level and the realised return over ten years will land nearer 4.9%.
Think of it
“YTM is total return if you hold the bond until it matures-all-in yield.
Formula
Calculation
Exactly, yield to maturity is the discount rate that makes the present value of all remaining coupons plus the face value equal to the current market price. A common approximation is: yield to maturity = [annual coupon + (face value - market price) / years to maturity] / [(face value + market price) / 2].
Consider a $1,000 face value bond with a 5% coupon, so $50 a year, trading at $920 with 6 years left to run. The annual amortisation of the discount = ($1,000 - $920) / 6 = $80 / 6 = $13.33. The average of face value and price = ($1,000 + $920) / 2 = $960.
Yield to maturity = ($50 + $13.33) / $960 = $63.33 / $960 = 6.60%. Solving the full present value equation gives 6.66%, so the approximation is within seven basis points, and either way the answer is comfortably above the 5% coupon because the bond was bought at a discount.Case study
Seen in the real world.
This is an illustrative and fictional example. Alderton Foods, an invented food producer, had $40,000,000 of listed bonds carrying a 4% coupon issued when credit conditions were easy. Its finance team used that 4% as the cost of debt in every investment appraisal.
After a disappointing trading year the bonds fell to $84 per $100 of face value with six years remaining, implying a yield to maturity of roughly 7.4%. The market was saying it would now demand 7.4% to lend to Alderton, while the company was still approving projects that returned barely 6%.
Once the fictional board switched to the market based yield, three of the seven projects in the capital plan no longer cleared the hurdle. Alderton shelved them, used the cash to buy back some of its own discounted bonds instead, and improved returns without spending a dollar on new assets.
Watch out
Common mistakes.
- Using the coupon rate as the cost of debt when the bond's market yield is materially different, which understates the true hurdle for new investment.
- Believing the quoted yield is guaranteed, when it depends on holding to maturity and on reinvesting every coupon at the same rate.
- Comparing bonds on price alone, since a cheaper looking bond may simply have a lower coupon or a longer time to repayment.
Questions
People also ask.
Why does yield to maturity move in the opposite direction to price?
Because the future cash flows are fixed, so paying less for the same stream of payments must produce a higher return, and paying more must produce a lower one.
Does yield to maturity account for the risk of default?
No, it assumes every payment is made in full and on time, which is why riskier issuers show higher yields as compensation rather than as a promise.
How is it different from current yield?
Current yield is just the annual coupon divided by the price and ignores the gain or loss at repayment, so it is a rougher measure.
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