Yield to Maturity

Yield to maturity (YTM) is the single most common way to measure a bond's return. It is the annual rate of return an investor would earn by buying a bond at today's price and holding it to maturity, assuming every coupon is paid on time and reinvested at the same rate. YTM lets investors compare bonds with different prices, coupons and maturities on one scale. It is also the discount rate that makes the present value of a bond's cash flows equal to its price.

The definition#

YTM is the rate y that solves:

price = Σ (coupon / (1 + y/f)^t) + face / (1 + y/f)^n

where f is the number of coupon payments per year and n is the total number of payments. There is no simple closed form; YTM is found by trial and error or with a calculator. See Time Value of Money and the Bond Price, Duration and DV01 Calculator.

Worked example#

A quick approximation#

approximate YTM ≈ [annual coupon + (face - price) / years] / [(face + price) / 2]

For the example: [50 + (1,000 minus 950) / 6] / [(1,000 + 950) / 2] = (50 + 8.33) / 975 ≈ 5.98%. Close to the exact answer.

Related yield measures#

In the example, the current yield is 50 / 950 ≈ 5.26%, below the YTM because it ignores the $50 gain at maturity.

Premium, par and discount bonds#

Assumptions and limitations#

• Held to maturity: if sold earlier, the return depends on the price at sale.
• Coupons reinvested at the YTM: if rates change, actual returns differ. This is reinvestment risk.
• No default: for risky bonds, YTM is a promised yield, not an expected one. See Default Probability and Recovery Rate.
• Flat discount rate: YTM uses one rate for all cash flows, while the yield curve has different rates for different maturities. See Yield Curves.
• Taxes and costs are ignored.

YTM and price sensitivity#

Small changes in YTM move prices. The size of the move depends on the bond's duration. A bond with a duration of 7 loses about 7% of its value for a 1 percentage point rise in yield. See Duration.

Conventions#

US Treasuries and many corporate bonds quote YTM on a semiannual "bond equivalent" basis. Some markets use annual compounding. Comparing yields across markets requires the same convention.

Frequently asked questions#

What is yield to maturity?#

The annual return an investor would earn by buying a bond at its current price and holding it to maturity, assuming all payments are made and reinvested at the same rate.

What is the difference between current yield and yield to maturity?#

Current yield is only the annual coupon divided by the price; yield to maturity also includes the gain or loss as the price moves to par at maturity.

What is yield to worst?#

The lowest yield an investor could receive on a callable bond, considering all possible call dates and maturity.

Next, learn how bond prices respond to yield changes in Duration.