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 coupons every 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:
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:
In this context, nominal yield isn't particularly
informative. 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 scheduled.
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 clean price:
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 to call:
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 intrinsic value 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 option-adjusted yield. 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 conventions—annual compounding, semiannual compounding, continuous 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. Short-term discount instruments, such as T-bills, are generally quoted as discount yields. These may be converted to bond equivalent yields for comparison with yields quoted on coupon-bearing instruments. 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 3.18%.
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