YTM is the rate that makes the bond price fair
Yield to maturity is the discount rate at which the present value of every future coupon plus the face value repaid at the end equals the price you pay today. There is no closed formula, so it is solved by iteration, but the relationship is what matters.
Price and yield move in opposite directions: as the price you pay rises, the yield falls, because the same fixed cash flows are worth less to you. That inverse link is the whole intuition behind bond math.
Price versus face value tells you the yield at a glance
You can read the direction of YTM off the price before computing anything. The gain or loss against the $1,000 you get back at maturity pulls the yield above or below the coupon.
| Price vs face | Name | YTM vs coupon |
|---|---|---|
| Below par (e.g. $950) | Discount | YTM > coupon |
| At par ($1,000) | Par | YTM = coupon |
| Above par (e.g. $1,050) | Premium | YTM < coupon |
A $1,000 bond with a 5% coupon bought for $950 pays $50 a year plus a $50 gain at maturity, so its YTM is about 5.7% — above both the 5% coupon and the 5.26% current yield ($50 ÷ $950).
Three yields that are easy to confuse
- Coupon rate. The annual coupon as a share of face value. Fixed for life; on a $1,000, 5% bond it is always $50 a year.
- Current yield. Annual coupon divided by today price. It reacts to price but ignores the gain or loss you book at maturity.
- Yield to maturity. The full internal rate of return, counting coupons and the capital gain or loss. It is the number to compare bonds on.
Common questions
What is the difference between yield to maturity and the coupon rate?
The coupon rate is fixed when the bond is issued and never changes. Yield to maturity is the return you actually earn from today price to redemption, folding in the coupons and any gain or loss versus what you paid. YTM moves with the market price; the coupon does not.
Why does a bond priced below face value have a higher yield?
If you pay less than the $1,000 you get back at maturity, that discount is an extra capital gain on top of the coupons. It lifts your total return above the coupon rate, so a discount bond always yields more than its coupon.
Does YTM assume I hold the bond to maturity?
Yes. YTM is the return if you buy at today price and keep the bond until it redeems, reinvesting each coupon at that same yield. Sell early at a different price and your actual return will differ.
