Yield to maturity
From Citizendium, the Citizens' Compendium
Yield to maturity can be simply described as the interest rate required in the market on a bond. If a bond's purchase price is known, the bond-pricing formulas can be used to find the bond's yield. The yield to maturity tells a person what return they will earn on a bond if it is held to maturity. If you sell the bond before maturity, it is the realized yield that tells you what return you will earn from a bond.
You can tell what level a bond is selling at by looking at the yield to maturity. You do this by comparing a bond's current yield with its yield to maturity. If the current yield is lower than its yield to maturity, the bond is being sold at a discounted level. If the current yield is larger than the yield to maturity, the bond is being sold at a premium. When both yields are equal, the bond is being sold at par value.
There are several variations to yield to maturity. These include: Yield to call - when the bond is callable, the cash flow is shortened; assuming the bond will be called. Yield to put - this comes into play when the bond holder has the opportunity to sell the bond back to issuer at a fixed price on a specified date.
In the absence of taxes, yield to maturity would be an accurate measure of return if the yield curve were flat and interest rates remained constant over the life of the bond. It degrades as the yield curve steepens, or as the purchase price strays further from par.
Zero Coupon Yield:
The reason that yield to maturity applies to a zero coupon bond is that there is no interest to be reinvested. The entire return comes from the difference between the purchase price and the face value of the bond. In ordinary bonds, the difference is treated as a capital gain or loss. They are taxed when sold. In a zero coupon bond, that gain is treated as income from interest and taxed annually according to the gain in accrued value. Since there are no interest payments to reinvest, achieving the quoted yield to maturity is automatic when a zero coupon bond is held to maturity. This ignores the annual income tax cut.
Yield to Maturity and the Reinvestment Rate:
It is pretty much impossible to reinvest interest payments at the exact yield to maturity rate. The payments are usually accumulated in an account at a lower interest rate before being reinvested. This means that the yield to maturity almost always overstates the true return. If the interest earnings are spent rather than reinvested, the return will be even lower. It is also important to recognize that the interest payments are usually cut by a tax bite. This makes it impossible to reinvest the full amount of each payment.
Bond-Equivalent Yield:
Yield to maturity is almost always quoted in terms of bond-equivalent yield. This reflects the fact that bond interest payments are normally made twice a year at half the coupon rate. The compounding of the reinvested interest payments twice a year results in a slightly higher annualized return than a once-a-year reinvested interest payment at the full coupon rate. Yield to maturity expressed as bond-equivalent yield slightly understates the yield to maturity when viewed as an annualized compound rate of return.
Calculating the yield to maturity can be closely compared to the way you calculate rate of return. The yield to maturity cannot be found algebraically. It takes a trial and error process unless you are using a financial calculator or spreadsheet program.
Example: If a person purchases a 3 year bond with a 5% coupon that is paid semiannually for the price of $951.90, what is the bond's yield to maturity?
(r) = interest rate
The equation would be:
$951.90 = $25/(1+r/2) + $25/(1+r/2)^2 + ......+ $25+$1000/(1+r/2)^6
- Solve using trial and error
