Unlike equities or currencies, bonds are often as likely to be priced in terms of a dollar price as in terms of a yield. Thus, we need to differentiate among a few different types of yields that are of relevance for bonds.
The examples provided earlier made rather generic references to “yield.”
To be more precise, when a yield is calculated for the spot (or present) value of a bond, that yield commonly is referred to as yield-to-maturity, bond- equivalent yield,orpresent yield.There are also current yields (the result of dividing a bond’s coupon by its current price), and spot yields(yield on bonds with no cash flows to be made until maturity). Thus, a spot yield could be
Rising uncertainty
Generally when a security is a nongovernmental issue
When a coupon is paid prior to sale or maturity
For any fixed income security
Uncertainty of credit quality Uncertainty of reinvestment
Uncertainty of price
FIGURE 2.7 Layers of uncertainty among various types of bonds.
a yield on a Treasury bill,3a yield on a coupon-bearing bond with no remain- ing coupons to be paid until maturity, or a yield on a zero-coupon bond. In some instances even a yield on a coupon-bearing bond that has a price of par may be said to have a spot yield.4In fact, for a coupon-bearing bond whose price is par, its yield is sometimes called a par bond yield.For all of the yield types cited, annualizing according to U.S. convention is assumed to occur on the basis of a 365-day year (except for a leap year). Finally, when an entire yield curveis comprised of par bond yields, it is referred to as a par bond curve. A yield curve is created when the dots are connected across the yields of a particular issuer (or class of issuers) when its bonds are plot- ted by maturity. Figure 2.8 shows a yield curve of Treasury bonds taken from November 2002.
As shown, the Treasury bond yield curve is upward sloping. That is, longer-maturity yields are higher than shorter-maturity yields. In fact, more
3As a money market instrument (a fixed income security with an original term to maturity of 12 months or less), a Treasury bill also has unique calculations for its yield that are called “rate of discount” and “money market yield.” A rate of discount is calculated as price divided by par and then annualized on the basis of a 360-day year, while a money market yield is calculated as par minus price divided by par and then annualized on the basis of a 360-day year.
4The reason why a coupon-bearing bond priced at par is said to have a yield equivalent to a spot yield is simply a function of algebraic manipulation. Namely, since a bond’s coupon rate is equal to its yield when the bond is priced at par, and since its price and face value are equivalent when yield is equal to coupon rate, lettingC=YandP=Fand multiplying through a generic price/yield equation by 1/F(permissible by the distributive property of multiplication) we get 1 = Y/2/(1 + Y/2)1+Y/2 /(1 + Y/2)2+ ... In short, Cdrops away.
Time (years) Yield
0.5 2 4 6
1 2 5 10 30
FIGURE 2.8 Normal upward-sloping yield curve.
often than not, the Treasury bond yield curve typically reflects such a pos- itive slope.
When a bond is being priced, the same yield value is used to discount (reduce to a present value) every cash flow from the first coupon received in six months’ time to the last coupon and face amount received in 2 or even 30 years’ time. Instead of discounting a bond’s cash flows with a single yield, which would suggest that the market’s yield curve is perfectly flat, why not discount a bond’s cash flows with more representative yields? Figure 2.9 shows how this might be done.
In actuality, many larger bond investors (e.g., bond funds and invest- ment banks) make active use of this approach (or a variation thereof) to pric- ing bonds to perform relative value (the value of Bond A to Bond B) analysis. That is, if a bond’s market price (calculated by market convention with a single yield throughout) was lower than its theoretical value (calcu- lated from an actual yield curve), this would suggest that the bond is actu- ally trading cheap in the marketplace.5
Time (years) Yield
0.5 2 4 6
1 2 5 10 30
Price = C&F + C + C + C = $1,000 (1 + Y/2) (1 + Y/2) (1 + Y/2) (1 + Y/2) 4 3 2 1
FIGURE 2.9 Using actual yields from a yield curve to calculate a bond’s price.
5It is important to note that it is theoretically possible for a given bond to remain
“cheap” (or rich) until the day it matures. A more likely scenario is that a bond’s cheapness and richness will vary over time. Indeed, what many relative value investors look for is a good amount of variability in a bond’s richness and cheapness as a precondition for purchasing it on a relative value basis.
While there is just one spot price in the world of bonds, there can be a variety of yields for bonds. Sometimes these different terms for yield apply to a single value. For example, for a coupon-bearing bond priced at par, its yield-to-maturity, current yield, and par bond yield are all the same value.
As previously stated, a yield spread is the difference between the yield of a nonbenchmark security and a benchmark security, and it is expressed in basis points.
Therefore, any one of the following things might cause a spread to nar- row or become smaller (where the opposite event would cause it to widen or become larger):
A. If the yield of the nonbenchmark (YNB) issue were to . . .
i. . . . decline while the yield of the benchmark (YB) issue were to remain unchanged
ii. . . . rise while the YB rose by more iii. . . . remain unchanged while the YB rose
B. If the yield of the benchmark issue (YB) were to . . .
i. . . . rise while the yield of the nonbenchmark (YNB) issue remained unchanged
ii. . . . decline while the YNB fell by more iii. . . . remain unchanged while the YNB fell
Thus, the driving force(s) behind a change in spread can be attributable to the nonbenchmark, the benchmark, or a combination of both.
Accordingly, investors using spreads to identify relative value must keep these contributory factors in mind.
Regarding spreads generally, while certainly of some value as a single sta- tic measure, they are more typically regarded by fixed income investors as having value in a dynamic context. At the very least, a single spread measure communicates whether the nonbenchmark security is trading rich(at a lower yield) or cheap (at a higher yield) to the benchmark security. Since the bench- mark yield is usually subtracted from the nonbenchmark yield, a positive yield spread suggests that the nonbenchmark is trading cheap to the benchmark security, and a negative yield spread suggests that it is trading rich to the benchmark security. To say much beyond this in a strategy-creation context with the benefit of only one data point (the one spread value) is rather diffi- cult. More could be said with the benefit of additional data points.
For example, if today’s spread value is 50 basis points (bps), and we know that over the past four weeks the spread has ranged between 50 bps Yield of nonbenchmarkYield of benchmarkSpread in basis points
and 82 bps, then we might say that the nonbenchmark security is at the richer (narrower) end of the range of where it has traded relative to the benchmark issue. If today’s spread value were 82 bps, then we might say that the nonbenchmark security is at the cheaper(wider) end of the range of where it has been trading. These types of observations can be of great value to fixed income investors when trying to decipher market trends and potential opportunities. Yet even for a measure as simple as the difference between two yields, some basic analysis might very well be appropriate. A spread might change from day to day for any number of reasons. Many bond fund managers work to know when and how to trade around these various changes.
Spot Equities
Now we can begin listing similarities and differences between equities and bonds. Equities differ from bonds since they have no predetermined matu- rity. Equities are similar to bonds since many equities pay dividends, just as most bonds pay coupons. However, dividends of equities generally tend to be of lower dollar amounts relative to coupons of bonds, and dividend amounts paid may vary over time in line with the company’s profitability and dividend-paying philosophy; the terms of a bond’s coupon payments typ- ically are set from the beginning. And while not typical, a company might choose to skip a dividend payment on its equity and without legal conse- quences, while a skipped coupon payment on a bond is generally sufficient to initiate immediate concerns regarding a company’s ongoing viability.6 Occasionally a company may decide to skip a dividend payment altogether, with the decision having nothing to do with the problems in the company;
there may simply be some accounting incentives for it, for example.
Otherwise, in the United States, bonds typically pay coupons on a semian- nual basis while equities tend to pay dividends on a quarterly basis. Figure 2.10 is tailored to equities.
6Terms and conditions of certain preferred equities may impose strict guidelines on dividend policies that firms are expected to follow.
We need to think not only about probabilities related to the nature and size of future dividends, but also about what to assume for the end price of an equity purchase. At least among the so-called blue chip(stocks of strong and well-established companies with reputations for paying dividends over a variety of market cycles) equities, investors tend to rest pretty comfortably with the assumption that regular and timely dividend payments will be made (just as with the debt instruments issued by blue chip corporations).
How can an investor attempt to divine an end price of an equity? There are formulas available to assist with answering this question, one of which is called the expected growth in dividends formula.As the name implies, a forecast of future dividends is required, and such a forecast typically is made with consideration of expectations of future earnings.
The expected growth in dividends approach to divining a future price for an equity is expressed as
While this formula may provide some rudimentary guidance on future price behavior, it falls short of the world of bonds where at least a final matu- rity price is prespecified.
Perhaps because of the more open-ended matter of determining what an equity’s price ought to be, there tends to be less of a focus on using quanti-
Expected dividend1s2per share
Cost of equity1%2Expected growth rate of dividend1s2 1%2 Expected future price per share
Cash inflow
Cash outflow
0
6 months later Dividend payment 3 months later
Dividend payment
Price at sale 9 months later
Dividend payment
12 months later Dividend payment
Note: Dividend payment amounts may vary from quarter to quarter.
Purchase – Cash flow known
with 100%
certainty
FIGURE 2.10 Cash flows of a typical equity.
tative valuation methods with equities in favor of more qualitative measures.7 For example, some equity analysts assign great value to determining an equity’s book valueand then forecasting an appropriate multiple for that book value. Book value is defined as the current value of assets on a com- pany’s balance sheet according to its accounting conventions, and the term
“multiple” is simply a reference to how many times higher the book value could trade as an actual market price. For an equity with a $10 per share book value that an analyst believes should trade at a multiple of eight within the span of a year, the forecast is for a market value of $80 per share. The decision to assign a multiple of 8 instead of 4 or 20 may stem from any- thing ranging from an analyst’s gut feeling to an extensive analysis of a com- pany’s overall standing relative to peer groups. Other valuation methods might include analysis of an equity’s price relative to its earnings outlook, or even technical analysis, which involves charting an equity’s past price behavior to extrapolate what future price patterns may actually look like.
Investors typically buy bonds for different reasons than why they buy equities. For example, an investor who is predisposed to a Treasury bond is likely to be someone who wants the predictability and safety that the Treasury bond represents. An investor who is predisposed to the equity of a given issuer (as opposed to the debt of that issuer) is likely to be someone who is comfortable with the risk and uncertainty of what its price will be in two years’ time or even two months’ time.
There are some pretty clear expectations about price patterns and behavior of bonds; in the equity arena, price boundaries are less well delin- eated. As two significant implications of this observation, equities tend to experience much greater price action (or volatility) relative to bonds, and the less constrained (and greater potential) for experiencing upside perfor- mance would be more likely linked with equities as opposed to bonds (at least as long as the longer-run economic backdrop is such that the underly- ing economy itself is growing). Both of these expectations hold up rather well on a historical basis.
7I do not mean to detract from the rigor of analysis that often accompanies a qualitative approach. The point is simply that a key forecast (or set of forecasts) is required (often pertaining to the expected behavior of future dividends and/or earnings), and this, by definition, requires cash flow assumptions to be made. This forecasting requirement is in contrast to the cash flow profile of a Treasury note where all expected distributions are known at time of purchase.
Currencies are considerably simpler than either equities or bonds when it comes to spot pricing. From a cash flow perspective, there is a cash outflow when a currency is purchased and a cash inflow when a currency is sold.
There are no intervening cash flows. As with equities, there are no maturity dates, yet since there is typically one currency per country, shaping a view on a currency’s prospects could well become much more involved than what is required for developing an outlook for a single company (as with fore- casting future dividends). Chapter 3 explores important credit quality con- siderations for currencies.