Yield to maturity
The Yield to maturity (YTM), book yield or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule. Yield to maturity is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the price of the bond. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more usually market convention is followed. In a number of major markets (such as gilts) the convention is to quote annualised yields with semi-annual compounding (see compound interest); thus, for example, an annual effective yield of 10.25% would be quoted as 10.00%, because 1.05 × 1.05 = 1.1025.
The main underlying assumptions used concerning the traditional yield measures are:
As some bonds have different characteristics, there are some variants of YTM:
![\text{Yield to maturity(YTM)} = \sqrt[\text{Time period}]{\dfrac{\text{Face value}}{\text{Present value}}} - 1](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc3966a03b8c8a90491d65dd9a0e9d569cc2365f)
Consider a 30-year zero-coupon bond with a face value of $100. If the bond is priced at an annual YTM of 10%, it will cost $5.73 today (the present value of this cash flow, 100/(1.1)30 = 5.73). Over the coming 30 years, the price will advance to $100, and the annualized return will be 10%.
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