The return if you hold to maturity
A bond bought below face value pays two things: the coupons, and the gap between what you paid and the face value returned at maturity. Yield to maturity folds both into one annual rate, which is the only figure that lets you compare bonds with different prices and coupons.
What goes into it
YTM is the discount rate at which the present value of every future payment equals today's price. There is no closed-form solution; it is solved iteratively.
Worked example: $1,000 face, bought at $950, 5% coupon, 10 years
- Coupon paid: 5% of face = $50 a year, $25 every six months
- Current yield: 50 ÷ 950 = 5.26%
- Yield to maturity: 5.66%
Three different figures describe the same bond. The 5% coupon rate is fixed at issue and never changes. The 5.26% current yield reflects what you paid. The 5.66% YTM adds the $50 capital gain you collect at maturity, spread across ten years.
Why the three diverge
| Bought at | Coupon | Current yield | YTM |
|---|---|---|---|
| $950 (discount) | 5.00% | 5.26% | 5.66% |
| $1,000 (par) | 5.00% | 5.00% | 5.00% |
| $1,050 (premium) | 5.00% | 4.76% | 4.37% |
At par all three are identical. Away from par they fan out, and the further out you go the more misleading the coupon rate becomes.
The assumption most people miss
YTM assumes every coupon is reinvested at the YTM itself. If rates fall and you can only reinvest those $25 payments at 3%, your realised return will be below 5.66%.
This is the same hidden assumption that makes internal rate of return optimistic, and it matters more on long bonds where there are many coupons to reinvest.
What this calculator leaves out
Default risk, tax on coupons, dealer spread on the purchase, and call provisions. A callable bond will be redeemed early if rates fall, which caps your return well below the YTM shown here.
Price and yield move in opposite directions
The coupon is fixed in cash terms. If market rates rise after issue, the only way a 5% bond can compete with new 6% issues is for its price to fall until the yield matches. That is the entire mechanism behind bond price movements.
The size of the move depends on how long the bond has left. A two-year bond barely reacts; a thirty-year bond moves sharply, because the below-market coupon is locked in for three decades. That sensitivity is what duration measures.
Semi-annual coupons and the quoted figure
This bond pays $25 twice a year rather than $50 once. Because the first $25 arrives six months early and can be reinvested, the true annual yield is slightly above the quoted semi-annual figure.
Convention in most markets is to quote the semi-annual figure doubled rather than the compounded equivalent, so the 5.66% shown here is comparable to how other bonds are quoted, not to a savings account APY. Convert both to the same basis before comparing across asset types.
Related calculators
- Yield to call calculator — the return if the issuer redeems early
- Current yield calculator — income against price, ignoring maturity
- Bond price calculator — the same relationship solved for price