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. Yield to Maturity

What is the annualized total return (TR) on a bond bought and held to maturity? The obvious answer is its quoted yield-to-maturity (YTM) at the time of purchase.  But that answer is incorrect except for the special case of a zero-coupon bond.  Even a new issue bond bought and redeemed at par will not return the quoted YTM, except in rare instances.

YTM is a measure that only approximates the true return.  Nevertheless it is useful because it is a quick way of making rough comparisons of the returns on bonds of different coupons and maturities.

Yield-to-Maturity vs Total Return

There are similarities between YTM and TR.  Both are the annualized compound rate of return from purchase to sale.  Both assume that all payouts (interest or dividends) are reinvested.  Both take into account the gain or loss due to the difference between the purchase and redemption price.  However TR is strictly a measure of past performance.  It is often misleading as a prediction of future performance unless one factors in the interest rate history over the period for which the TR is quoted.

YTM, on the other hand, is a projection of future performance.  Since future interest rates are unknown, YTM must assume a reinvestment rate, and it assumes the YTM rate itself.  Thus YTM is an implicit function that can only be evaluated by the method of successive approximations.  Many hand calculators can perform this operation.

Reinvestment Rate

In practice it is virtually impossible to reinvest the interest payments at exactly the YTM rate.  Usually the payments are accumulated in an account at a lower interest rate before being reinvested.  This means that the YTM 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 normally trimmed by a tax bite, making it impossible to reinvest the full amount of each payment.

Zero Coupon Yield

The reason that YTM applies exactly 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, this difference is treated as a capital gain/loss and taxed when sold.  However in a zero coupon bond, that gain is treated as interest income and taxed annually according to the gain in accreted value. Since there are no interest payments to reinvest and therefore none to spend, achieving the quoted YTM is automatic when a zero coupon bond is held to maturity.  Of course this ignores the annual income tax bite.

Bond Equivalent Yield

YTM 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 would be the case for once-a-year reinvested interest payments at the full coupon rate. Thus YTM expressed as bond-equivalent yield slightly understates the YTM when viewed as the annualized compound rate of return.

In the absence of taxes, YTM 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 becomes a poorer measure as the yield curve steepens, or as the purchase price deviates further from par.

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