Price = Σ(t=1..n) C / (1 + y/2)^t + F / (1 + y/2)^n — solve iteratively for y (YTM, semi-annual convention); C = coupon paid per period, F = face value, n = periods to maturity
What it is
Yield to maturity (YTM) is the one discount rate that makes the present value of every payment a bond still owes — each remaining coupon, plus the face value repaid at maturity — equal to the bond's price today. It turns a price into an annualized rate, so bonds with different coupons, prices and maturities can be compared on a single scale. YTM is derived from the price rather than fed into it, and because the payments themselves are fixed, price and yield move inversely: a lower price for the same fixed stream of payments implies a higher yield, and a higher price implies a lower one.
Why it matters
A bond's coupon rate on its own says little, because bonds rarely trade at exactly their face value. YTM folds three things — the price paid, the coupons received, and the gain or loss back to face value at maturity — into one comparable number, which is why yield rather than coupon is the figure bonds are usually compared on. It also makes the price-yield seesaw visible: when market yields rise, an existing bond with a lower fixed coupon must fall in price for its YTM to line up with them. And because YTM rests on assumptions — that the bond is held to maturity, that the issuer pays in full and on time, and that coupons are reinvested at that same rate — knowing what it assumes is what tells a beginner where a realized result can differ from the quoted figure.
How it's calculated
Most bonds have no simple closed-form solution, so YTM is found by iteration — testing candidate rates until the discounted payments equal the observed price. A calculator or spreadsheet function does this automatically. The inputs are the market price, the coupon payments, the face value and the time remaining to maturity. Government bonds and most corporate bonds in the US and Canada pay coupons twice a year, so the periodic rate is solved first and then conventionally doubled to give an annual "bond-equivalent" figure. The price input is conventionally the full (dirty) price: the quoted clean price plus the interest accrued since the last coupon date.
Cross-border note. Government of Canada bonds and US Treasuries both pay semi-annual coupons, so YTM in each market is quoted on the same compounding basis (currency and day-count conventions still differ). The other checkable difference is the price input: US corporate bond trades are publicly disseminated via FINRA's TRACE, while Canadian debt trades are reported to CIRO, whose public dissemination is narrower and delayed.
FAQ
Is yield to maturity the same as the coupon rate?
No. On a conventional fixed-rate bond the coupon rate is set at issue as a fixed percentage of face value and does not move with the market. YTM instead depends on the price actually paid. A bond trading below face value has a YTM above its coupon rate, because the holder also collects the difference back at maturity; one trading above face value has a YTM below its coupon rate, because that premium is not repaid. They are equal only when price equals face value.
Why does a bond's yield rise when its price falls?
On a conventional fixed-rate bond the future payments are fixed in dollars. If the price drops, the buyer is paying less for that same unchanged stream, so the rate that reconciles price to payments must be higher. The reverse holds when the price rises. This inverse link is arithmetic, not a market mood — it is built into how YTM is defined.
Does a bond always deliver its quoted yield to maturity?
Not necessarily. YTM is a quoted figure built on assumptions: that the bond is held to maturity, that the issuer pays in full and on time, and that each coupon is reinvested at that same YTM. Selling early makes the outcome depend on the price that day; a callable bond can be redeemed early; a default or missed payment breaks the calculation; and reinvestment rates are not guaranteed to match. YTM measures what the current price implies, not what is assured.