# Yield to maturity: Wikis

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# Encyclopedia

The Yield to maturity (YTM) 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 actually an estimation of future return, as the rate at which coupon payments can be reinvested when received is unknown.[1] It enables investors to compare the merits of different financial instruments. 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 the convention is to quote yields semi-annually (see compound interest: thus, for example, an annual effective yield of 10.25% would be quoted as 5.00%, because 1.05 x 1.05 = 1.1025).

The yield is usually quoted without making any allowance for tax paid by the investor on the return, and is then known as "gross redemption yield". It also does not make any allowance for the dealing costs incurred by the purchaser (or seller).

• If the yield to maturity for a bond is less than the bond's coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa).
• If a bond's coupon rate is less than its YTM, then the bond is selling at a discounting.
• If a bond's coupon rate is more than its YTM, then the bond is selling at a premium.
• If a bond's coupon rate is equal to its YTM, then the bond is selling at par.

## Variants of Yield to maturity

As some 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 an (annual) 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%.

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 (100/(1.07^20). 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 16.25%. This can be found by evaluating (1+i) = (25.842/5.731)0.1 = 1.1625.

Over the remaining 20 years of the bond, the annual rate earned is not 16.25%, but rather 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 increased to \$100, so 10% per annum was earned, irrespective of any interest rate changes in between.

Here is another example:

You buy ABC Company bond which matures in 1 year and has a 5% interest rate (coupon) and has a par value of \$100. You pay \$90 for the bond.

The running yield is 5.56% (5/90*100).

If you hold the bond until maturity, ABC Company will give you \$5 as interest and \$100 for the matured bond.

Now for your \$90 investment you made \$105 and your yield to maturity is 16.67% (= 105/90-1)