
Yield to Maturity

What is the annualized total return
(TR) on
a bond bought
and held to maturity? The obvious answer is its quoted
yieldtomaturity
(YTM) at the time of purchase. But that answer is
incorrect
except
for the special case of a zerocoupon 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.
YieldtoMaturity
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 bondequivalent
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 onceayear
reinvested
interest payments at the full coupon rate. Thus YTM expressed as
bondequivalent
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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