What Is Yield to Maturity? YTM Formula

What is yield to maturity

Yield to maturity (YTM) is the annual rate of return you would earn on a bond if you bought it at today's price, held it until it matures, and received every coupon and the face value on time.

A coupon is the interest a bond pays. The face value (par value) is the amount the issuer repays at maturity. YTM combines both, plus any gain or loss between the price you pay and the face value, into a single annual rate.

A bond with a 5% coupon: when market yields rise, its price falls, and a longer bond moves much more than a short one. Illustrative example: made-up numbers for learning, not real prices or a broker's conditions.

YTM formula

YTM has no simple closed formula. It is the discount rate that makes the present value of all future cash flows equal to the bond's current price:

Price = sum of every coupon, each discounted at rate y over the time until it is paid, plus the face value discounted at rate y over the time to maturity.
YTM is the value of y that makes both sides equal.

Spreadsheets, bond calculators and trading terminals find y by trial and error (iteration). For bonds that pay coupons more than once a year, the result is usually quoted as an annualised figure under a stated convention, such as bond-equivalent yield.

Worked example (hypothetical)

Take a bond with face value F that pays a fixed coupon each year.

Bought below face value (at a discount). You receive the coupons and also gain the difference between your price and F at maturity. The YTM is higher than the coupon rate.
Bought at face value (at par). There is no gain or loss at maturity. The YTM equals the coupon rate.
Bought above face value (at a premium). You lose the difference between your price and F at maturity. The YTM is lower than the coupon rate.

The same rule explains why bond prices and yields move in opposite directions. When the price falls, the YTM rises, and when the price rises, the YTM falls.

Where you see YTM

Bond quotes and platforms. Fixed-income screens show price and yield side by side. The yield shown is usually YTM.
Auction results and reports. Government bond auction results are often reported as cut-off yields.
News. Headlines such as "yields rose by so many basis points" refer to changes in YTM. Central bank decisions are read against these yields. For example, the latest State Bank of Pakistan decision: SBP policy rate raised by 50 bps to 12% with effect from 27.10.2026 (MPC).
Credit comparison. The gap between a corporate bond's YTM and a government bond's YTM is the credit spread.

Formal points and edge cases

Reinvestment assumption. YTM assumes every coupon is reinvested at the same YTM. Your actual return will differ if rates change.
Default risk. YTM assumes every payment is made. If the issuer defaults, the quoted YTM is not what you earn. High YTMs often reflect high credit risk.
Callable bonds. If the issuer can repay the bond early, traders also look at yield to call and yield to worst.
Floating-rate and inflation-linked bonds. Future coupons are unknown, so YTM rests on assumptions about future rates or inflation.
Clean vs dirty price. YTM is calculated on the full price, which includes accrued interest.
Selling before maturity. If you sell early, your return depends on the market price at the time of sale, not on YTM.

If you trade bonds or rate products through leveraged CFDs, yield moves can produce fast losses that are larger than a bond's coupon income.

Frequent questions

What is the difference between yield to maturity and coupon rate?

The coupon rate is fixed against face value. YTM also reflects the price you pay, so it changes as the bond's price moves.

Is YTM the return I will actually get?

Only if you hold the bond to maturity, every payment is made, and you reinvest the coupons at the same rate. Otherwise your return will differ.

Why do yields rise when bond prices fall?

The cash flows are fixed. A lower price for the same cash flows means a higher rate of return, so the YTM rises.

Can YTM be negative?

Yes. If the price is high enough that the coupons plus the face value total less than what you pay, the YTM is below zero.

Yield to maturity (YTM): meaning and formula