Yield to Maturity (YTM)

Yield to maturity (YTM) is the annual rate of return an investor earns by buying a bond at its current market price and holding it until maturity. It takes into account every remaining coupon payment, the repayment of face value at the end, and any gain or loss from having paid more or less than face value. Formally, it is the single discount rate that makes the present value of all the bond's future cash flows equal to its price.

YTM is the yield most often quoted in bond markets and the figure behind the yield curve. It is broader than the coupon rate, which only states the interest paid on face value, and broader than current yield, which divides annual coupons by price and ignores the return of principal. The general idea of yield is covered in its own entry.

Imagine buying a used car that comes with a guaranteed buy-back price in five years and pays you a small rent every year in the meantime. To judge the deal, you would ask: counting the rent and the difference between what I pay now and what I get back at the end, what do I earn per year? YTM is that answer for a bond.

If you buy a bond for less than the amount it repays, you earn the interest plus a gain at the end, so your YTM is higher than the coupon. If you pay more than face value, you earn the interest minus a loss at the end, so your YTM is lower.

The exact YTM is the rate $y$ that solves this equation:

• $P$ is the bond's current price.
• $C$ is the coupon paid each period.
• $F$ is the face value repaid at maturity.
• $n$ is the number of periods left, and $y$ is the yield per period.

There is no simple algebraic solution, so YTM is found by trial and error, a financial calculator or a spreadsheet function. A common shortcut gives a close estimate:

Worked example: a bond with a $1,000 face value pays a 5% coupon once a year ($50) and matures in 5 years. It trades at $950. The shortcut gives $(50 + 50 \div 5) \div ((1{,}000 + 950) \div 2) = 60 \div 975$, or about 6.15%. Solving the exact equation gives about 6.19%. Both are above the 5% coupon because the buyer also gains $50 when the bond repays at par. Most US bonds pay coupons twice a year; YTM is then computed per half-year and doubled, which is the bond-equivalent yield convention.

For a zero-coupon bond, such as a Treasury bill or a STRIPS piece, there are no coupons and the equation simplifies to a closed form:

A zero-coupon bond bought for $800 that repays $1,000 in 5 years has a YTM of $(1{,}000 \div 800)^{1/5} - 1$, or about 4.56% a year.

YTM is a clean comparison tool but rests on assumptions that rarely hold exactly:

• Held to maturity. An investor who sells early receives the market price on that day, which may be higher or lower because of interest rate risk.
• Reinvestment at the same rate. The calculation assumes each coupon is reinvested at the YTM itself; if rates fall, the realised return will be lower.
• Every payment arrives. YTM ignores the chance of default, so for junk bonds it is an upper bound rather than an expected return.
• No early redemption. For callable bonds, investors also look at yield to call and yield to worst, the lowest yield across all possible call dates.

Taxes and trading costs are also left out, so YTM is a pre-tax, pre-cost figure.

Because YTM puts bonds with different coupons, prices and maturities on one scale, it is the main tool for comparing issues. The gap between a corporate bond's YTM and that of a government bond of the same maturity is its credit spread, which reflects credit risk and the issuer's credit rating. YTMs on US Treasury securities serve as benchmark rates for mortgages and other loans.

Bond funds report related figures. A fund's average YTM summarises its holdings, and in the US the standardised 30-day SEC yield is built on the yields to maturity of a fund's bonds. Price and YTM move in opposite directions, which is why a bond bought at a premium above par value has a YTM below its coupon. Over a full holding period, the investor's actual result is measured by total return.

• Investor.gov (SEC): Bonds – FAQs