Yield is a financial concept with archaic origins.
Prior to the 20th century, there wasn't the active secondary market for
fixed income securities of today. There also weren't the great
institutional investors—mutual funds and pension plans.
Bonds were mostly owned
by wealthy families or fledgling insurance companies like the Metropolitan
Life Insurance Company or the New York Life Insurance Company. These
investors would buy bonds at par when they issued, clip the
six months, and hold the bonds to maturity. When the issuer returned their
par value—thirty or so years later—they would reinvest it in new bonds. The goal
was preservation of wealth—preservation for the benefit of heirs or
policyholders. Investors looked for two things in a bond:
credit quality, and
Coupons were quoted as yield, which was simply the sum of
a bond's coupons payable in a year divided by the bond's par value. Today,
different metrics of yield have emerged, so we call this original metric
For example, if a bond has a par value of
USD 1,000 and pays a USD
32.50 coupon every six months, its yield would is 6.5%.
During the late nineteenth century, but especially during
the twentieth century, an active secondary market emerged for bonds.
Brokers and dealers—whose profits are proportional to the trading activity
of their clients—promoted the idea that bonds should be actively traded
for the purpose of achieving capital gains. Investors who embraced this
paradigm came to care less about the credit quality of a bond—buying a
bond was no longer a thirty year commitment. Theirs was a trading
attitude, and they were looking for three things in a bond:
for capital gains.
In this context, nominal yield isn't particularly
Suppose two bonds are trading in the secondary market. They have the same
maturity date and similar credit quality, but one has a nominal yield of
4% while the other has one of 8%. All this really tells us is that the two
bonds must have been issued at different times. One was issued when
interest rates were around 4%, while the other was issued when interest
rates were around 8%.
Which is more attractive: an 8% bond trading
above par or a 4% bond trading
below par? The former has higher coupons, but the later will realize a
nice capital gain when it matures at its par value. To distinguish between
such bonds, investors might calculate their internal rates of
A bond's yield to maturity
(YTM) is the internal rate of return an investor would achieve if she
purchased that bond at its current
dirty price and held
it to maturity, assuming all coupon and principal payments are received as
Prior to the age of computers, YTM was difficult to
calculate. An easier
metric to calculate was
current yield, which is the sum of a bond's coupons payable in a
year divided by the bond's
This is a sort of compromise between nominal yield and YTM.
Like nominal yield, it is easy to calculate. It also ignores anticipated
capital gains or losses that will be realized at maturity. Obviously, if a
bond is trading at par, nominal yield, current yield and YTM are equal. If
the bond is trading above par, nominal yield exceeds current yield, which
exceeds YTM. If the bond is trading below par, those inequalities reverse.
Today, computers have resolved the computational issues
with yield to maturity, but there is another problem that affects all yield metrics.
This is embedded options. Many
corporate bonds and
municipal bonds are
callable. If one is trading
near its call price, yield to maturity will be misleading because the bond is likely to be called
long before it matures.
To address this, investors may calculate yield
Callable bonds may be callable on multiple dates or, in other
cases, on any date following the
first call date, so yield to call can be
calculated for different assumed call dates. Usually, it is calculated for
the first date on which the bond may be called. This metric
is called yield to first call.
However, a bond may be callable at different prices on different dates.
Yield to first par call is
calculated assuming the bond is called on the first date on which it is
callable at its par value. Yield to worst is the minimum yield obtainable based on all
possible call dates as well as the possibility that the bond is never
called. Accordingly, yield to worst is always less than or equal to YTM.
Yield to worst would seem the solution for calculating a
meaningful metric of yield for callable bonds, but it is not. The problem
is that it is static. It ignores the likelihood that interest rates will
fluctuate over the life of the bond. A bond's call feature is a
call option in every sense of the
word. It has both an
and a time value.
Seen in this light, yield to worst is the (discounted) intrinsic value of
the call feature. It ignores the time value.
The theoretically most meaningful metric of yield for
bonds with embedded options is
This is widely used for
mortgage-backed securities (MBSs). It is not as widely used for
callable corporate bonds. The problem is not theoretical so much as
practical. The metric must be calculated with a fixed income option
pricing model. Different institutions use different models, and these may
not be easy to calibrate to the market. If inputs, including assumed
implied volatilities, are somewhat arbitrary, then so is the output. An
institutional investor who queries several dealers about the
option-adjusted spread on a particular MBS is likely to receive a broad
range of opinions.
Mathematically, yields are like interest rates. This means
they may be expressed according to different
compounding, etc. This is not much of an issue for nominal yield or
current yield. Based on how they are calculated, they necessarily reflect the
compounding convention of the bond for which they are calculated. For
example, if a bond pays quarterly coupons, the quarterly coupon could be
extracted from the nominal yield by dividing by four and multiplying by
the par value—math that is consistent with quarterly compounding. Since YTM or yield to call is an internal rate of return, they could be quoted
according to any compounding convention. In practice, they are quoted
based on the frequency with which a bond pays coupons—semi-annual
compounding for most bonds.
discount instruments, such as
generally quoted as discount yields. These may be converted to
equivalent yields for comparison with yields quoted on coupon-bearing
Yields are also calculated for
stocks. The formula is
analogous to that for the current yield of a bond. Not surprisingly, it is
also called current yield,
although the name dividend yield is
also used. The formula is
The numerator is calculated as the value of the most
recently declared dividend multiplied by the number of times a dividend is
payable a year. The denominator is simply the stock's current market price.
For example, if a stock currently pays a
USD 1.05 dividend four times
a year, and it last traded at a price of USD 132.00, its current yield is