What Is Yield to Maturity (YTM)? How It Works and How to Calculate It

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Yield to maturity (YTM) is the annual rate of return a bond earns if you buy it at today’s market price, hold it until it matures, and receive every coupon and the full face value on schedule. Technically, it is the internal rate of return (IRR) of the bond: the single discount rate that makes the present value of all remaining cash flows equal to the bond’s current price. It is also called book yield or redemption yield.

How Yield to Maturity Works

A plain fixed-rate bond promises two kinds of cash flow: periodic coupon payments and the repayment of face value (par) at maturity. The market price is what investors will pay today for that stream. YTM is the rate that links the price to the promised cash flows.

Where the price sits relative to par tells you how YTM compares with the coupon rate:

• Par bond: price equals face value, and YTM equals the coupon rate.
• Discount bond: price is below par, and YTM is higher than the coupon rate, because the buyer also gains the difference between price and par at maturity.
• Premium bond: price is above par, and YTM is lower than the coupon rate, because the buyer loses the premium by maturity.

This is also why YTM fluctuates. Suppose market rates rise after a bond is issued. New bonds pay more, so the older bond’s price falls until its YTM is competitive with them. When rates fall, the price rises and YTM drops.

The YTM Formula

The exact definition is the bond pricing equation, solved for the rate:

Price = C/(1 + r) + C/(1 + r)² + … + C/(1 + r)ⁿ + FV/(1 + r)ⁿ

• C = coupon payment per period
• FV = face value repaid at maturity
• n = number of periods remaining
• r = yield per period (YTM, once annualized)

There is no algebraic way to isolate r when a bond has more than a couple of payments. YTM is therefore found by trial and error (iteration): test a rate, compute the price it implies, and adjust until the computed price matches the market price. Financial calculators, spreadsheet functions such as RATE or YIELD, and online YTM calculators run this search automatically.

For a quick estimate by hand, the approximation formula is widely used:

Approximate YTM = [C + (FV − PV) ÷ t] ÷ [(FV + PV) ÷ 2]

• C = annual coupon payment in dollars
• FV = face value
• PV = current market price
• t = years to maturity

The numerator is the annual coupon plus the price gain (or minus the price loss) spread evenly over the remaining years. The denominator is the average of the price you pay and the amount you receive at maturity. The result lands close to the true YTM for bonds trading near par and drifts further away for deep discounts, deep premiums and long maturities.

How to Calculate YTM: Worked Example

Hypothetical bond: $1,000 face value, 5% coupon paid once a year ($50), three years to maturity, market price $950.

Step 1: Estimate with the approximation

Approximate YTM = [$50 + ($1,000 − $950) ÷ 3] ÷ [($1,000 + $950) ÷ 2] = [$50 + $16.67] ÷ $975 = $66.67 ÷ $975 ≈ 6.84%

Step 2: Solve exactly by iteration

Test rates in the pricing equation:

• At 6.0%: $50/1.06 + $50/1.06² + $1,050/1.06³ ≈ $973.27. That is too high, so the yield must be higher.
• At 7.0%: $46.73 + $43.67 + $857.11 ≈ $947.51. That is slightly too low, so the yield is between 6% and 7%.
• At 6.9%: $46.77 + $43.75 + $859.52 ≈ $950.05. That is very close to $950.

Narrowing further in 0.01% steps puts the exact YTM at about 6.90%. The approximation (6.84%) was close but not exact, which is typical.

Step 3: Compare with the coupon and current yield

• Coupon rate: 5.00% ($50 ÷ $1,000 face value)
• Current yield: 5.26% ($50 ÷ $950 price)
• YTM: about 6.90%

YTM is the highest of the three because it is the only measure that counts the $50 gain from buying at $950 and being repaid $1,000.

Semiannual coupons

Most U.S. Treasury and corporate bonds pay coupons twice a year. In that case, use half the annual coupon as C, count n in half-year periods, and solve for the semiannual rate. The quoted YTM (the bond-equivalent yield) is that semiannual rate multiplied by 2. If you want the effective annual yield with compounding, use (1 + semiannual rate)² − 1, which is slightly higher than the quoted figure. When comparing two quoted YTMs, make sure both use the same compounding convention.

Treasury Bill YTM

Treasury bills pay no coupon. They are sold below face value and redeemed at par, so the entire return is the difference between price and face value. That makes the calculation direct:

YTM = (FV ÷ Price)^(1/t) − 1, where t is years to maturity.

For bills, yields are commonly expressed in two other ways, and they are not interchangeable. Take a hypothetical $10,000 bill bought for $9,800 with 182 days to maturity:

• Bank discount yield uses face value and a 360-day year: ($200 ÷ $10,000) × (360 ÷ 182) ≈ 3.96%.
• Bond-equivalent (investment) yield uses the price paid and a 365-day year: ($200 ÷ $9,800) × (365 ÷ 182) ≈ 4.09%.

The bond-equivalent yield is the one comparable with coupon bond YTMs. The discount yield understates the return because it divides by face value rather than by the amount invested.

YTM vs. Coupon Rate vs. Current Yield

• Coupon rate is the annual interest as a percentage of face value. It is set at issue and does not change for a fixed-rate bond. It tells you the dollar income, not your return.
• Current yield is annual coupon divided by current price. It reflects what you paid but ignores the gain or loss at maturity and the timing of cash flows.
• YTM accounts for price, coupons, face value and time to maturity together. It is the most complete of the three for a bond held to maturity.

YTM is also different from return on investment (ROI), which measures total gain over a holding period without annualizing it, and closer in spirit to CAGR, since both express a multi-year result as one annual rate.

A required rate of return is not the same thing as YTM either. Required return is the yield an investor demands given the bond’s risk. YTM is the yield the market price implies. If an investor’s required return is below a bond’s YTM, the bond looks attractive to that investor at its current price.

Interpreting YTM: Is a Higher Yield Better?

It depends on why the yield is high. Among bonds with similar credit quality and maturity, a higher YTM means you are paid more for the same risk, which can point to a relatively cheap bond. Across different bonds, a higher YTM usually reflects more risk: a weaker issuer, a longer maturity, lower liquidity or features that favor the issuer. A bond with an unusually high YTM may be pricing in a real chance of missed payments.

For someone who already owns a bond, a rise in YTM means the bond’s market price has fallen. That loss is only on paper if the bond is held to maturity and pays as promised, but it is real if the bond is sold early.

YTM is also a nominal figure. Subtracting expected inflation gives a rough real yield.

Variations of YTM

Bonds with embedded options can end before their stated maturity, so related measures adjust the cash flow schedule:

• Yield to call (YTC) assumes the issuer redeems the bond at the first call date and call price. Issuers tend to call when rates have fallen, so YTC is most relevant for premium callable bonds.
• Yield to put (YTP) assumes the holder sells the bond back to the issuer at the put price on the first put date allowed by the bond’s terms.
• Yield to worst (YTW) is the lowest yield among YTM and all call or put scenarios. It is the conservative figure for bonds with several possible redemption dates.

Bond quotes also show bid YTM and ask YTM. Ask YTM is the yield based on the ask price, the price a buyer pays. Because the ask price is higher than the bid, ask YTM is lower than bid YTM.

Limitations of Yield to Maturity

Reinvestment assumption. The IRR math treats every coupon as if it earns the YTM until maturity. If rates fall and coupons are reinvested at lower yields, the realized return comes in below the quoted YTM. If rates rise, it can come in above. This reinvestment risk grows with higher coupons and longer maturities.

Holding to maturity. YTM says nothing reliable about the return if you sell early. The sale price depends on market rates at that time, and longer bonds are more sensitive to rate changes, which is what bond duration measures.

Credit risk. YTM is a promised yield. It assumes every coupon and the principal are paid in full and on time. A default reduces the actual return, sometimes sharply.

Embedded options. For callable or putable bonds, YTM can overstate or understate the likely return because the bond may not survive to maturity, so yield to worst is the safer reference.

Costs and taxes. The standard calculation excludes commissions, markups, fund fees and taxes on coupon income or gains, all of which lower what an investor keeps.

Funds versus individual bonds. A bond fund or bond ETF has no maturity date and keeps buying and selling bonds, so its reported average yield is not a locked-in return like YTM on a single bond held to maturity.

FAQs

The Bottom Line

YTM matters to anyone comparing individual bonds they plan to hold until maturity. It is the most complete single yield measure because it combines price, coupons, face value and time. Treat it as a promised rate, though. Reinvestment rates, early sales, defaults, call features, costs and taxes can all push the actual return away from the quoted figure.