Definitions

# Yield to maturity

The Yield to maturity (YTM) or redemption yield is the yield promised to the bondholder on the assumption that the bond or other fixed-interest security such as gilts will be held to maturity, that all coupon and principal payments will be made and coupon payments are reinvested at the bond's promised yield at the same rate as invested. It is a measure of the return of the bond. This technique in theory allows investors to calculate the fair value of different financial instruments. The YTM is almost always given in terms of annual effective rate.

The calculation of YTM is identical to the calculation of internal rate of return.

• If a bond's current yield is less than its YTM, then the bond is selling at a discount.
• If a bond's current yield is more than its YTM, then the bond is selling at a premium.
• If a bond's current yield is equal to its YTM, then the bond is selling at par.

## Variants of Yield to maturity

Given that many bonds have different characteristics, there are some variants of YTM:

• Yield to Call: when a bond is callable (can be repurchased by the issuer before the maturity), the market looks also to the Yield to Call, which is the same calculation of the YTM, but assumes that the bond will be called, so the cashflow is shortened.
• Yield to Put: same as Yield to Call, but when the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date.
• Yield to Worst: when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of Yield to Maturity, Yield to Call, Yield to Put, and others.

## Example

Consider a 30-year zero coupon bond with a face value of \$100. If the bond is priced at a yield-to-maturity 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%.

But what happens in the meantime? Suppose that over the first 10 years of the holding period, interest rates decline, and the yield-to-maturity on the bond falls to 7%. With 20 years remaining to maturity, the price of the bond will be \$25.84. Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the return earned over the first 10 years is 16.26%. This can be found by evaluating (1+i) = (25.84/5.73)0.1 = 1.1626.

Over the remaining 20 years of the bond, the annual rate earned is not 16.26%, but 7%. This can be found by evaluating (1+i) = (100/25.84)0.05 = 1.07. Over the entire 30 year holding period, the original \$5.73 invested matured to \$100, so 10% annually was made, irrespective of interest rate changes in between.