# Yield to Maturity

Yield to maturity (YTM) is a way to measure the expected rate of return of a fixed-income security.

There are two ways to understand this concept:

• YTM is the internal rate of return earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, that all coupon and principal payments will be made in full when due, and that coupons are reinvested at the original YTM.
• YTM is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the current price of the bond. It is the single interest rate that equates the present value of a bonds cash flows to its price.

YTM is perhaps the most familiar pricing concept in bond markets. To understand this concept, it is important to clarify how YTM is related to spot rates and a bond’s expected and realized returns.

How is the yield to maturity related to spot rates?

In bond markets, most bonds outstanding have coupon payments and many have various options, such as a call provision. The YTM of these bonds with maturity T would not be the same as the spot rate at T. But, the YTM should be mathematically related to the spot curve. Because the principle of no arbitrage shows that a bond’s value is the sum of the present values of payments discounted by their corresponding spot rates, the YTM of the bond should be some weighted average of spot rates used in the valuation of the bond.

The following example addresses the relationship between spot rates and yield to maturity.

Is the yield to maturity the expected return on a bond?

In general, it is not, except under extremely restrictive assumptions. The expected rate of return is the return one anticipates earning on an investment. The YTM is the expected rate of return for a bond that is held until its maturity, assuming that all coupon and principal payments are made in full when due and that coupons are reinvested at the original YTM. However, the assumption regarding reinvestment of coupons at the original yield to maturity typically does not hold. The YTM can provide a poor estimate of expected return if (1) interest rates are volatile; (2) the yield curve is steeply sloped, either upward or downward; (3) there is significant risk of default; or (4) the bond has one or more embedded options (e.g., put, call, or conversion).

If either (1) or (2) is the case, reinvestment of coupons would not be expected to be at the assumed rate (YTM). Case (3) implies that actual cash flows may differ from those assumed in the YTM calculation, and in case (4), the exercise of an embedded option would, in general, result in a holding period that is shorter than the bond’s original maturity.

The realized return is the actual return on the bond during the time an investor holds the bond. It is based on actual reinvestment rates and the yield curve at the end of the holding period. With perfect foresight, the expected bond return would equal the realized bond return.