Chapter 7: The Risk and Term Structure of Interest Rates

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The Risk Structure of Interest Rates
We've looked at the measurement of interest rates and the overall level of interest rates in chapter 6. However in reality there is not just one interest rate, but many types of rates. For example, consider the following interest rates from September 2007:

Debt security	maturity	yield
Treasury bill	3 months	4.18%
Commercial Paper	3 months	5.23%
Treasury note	10 years	4.51%
Aaa Corporate bond	10 years	5.74%
Baa Corporate bond	10 years	6.57%
conventional mortgage	30 years	6.45%

These differences are due to the different characteristics of these debt instruments such as the payment structure, the maturity, and the issuer. In this chapter we examine how various characteristic lead to interest rate differences.
First a word about measurement: The differences between the interest rates on two bonds is referred to as the spread. The spread is often measured by basis points. 100 basis points is equal to 1 percentage point. For example, in the table above, the difference between the Baa corporate bond and the Treasury note (both 10 year maturities) is
6.57% - 4.51% = 2.06 percentage points or 206 basis points
Here in part one we focus on bonds with the same maturity. The relationship among these bond interest rates is known as the risk structure of interest rates.
Figures 7.2 and 7.3 in your textbook provide a look at different long-term and short-term rates between 1970 and 2003.
Note how U.S. Treasuries tend to have the lowest yields, while corporate Baa bonds have the highest yields. However, the size of the spreads is not constant over time. The spread between Baa bonds and U.S. government bonds is almost 200 basis points 1982, but less than 10 basis points in 1995. We look at two factors that explain the spread we see in figures 7.2 and 7.3: default risk and tax treatment.
Default Risk and Bond Ratings
The default risk on a bond is the probability that the bond issuer will not make the promised interest payments or face value payments on time (or at all). This is known as a default. The default risk on a bond depends on the creditworthiness of the issuer as well as the structure of the bond. One of the most recent well-publicized defaults occurred in 2001 when the utility companies Southern California Edison & Co. and Pacific Gas & Electric were unable to make their bond payments due to skyrocketing wholesale electricity prices (which we later found out was due in part to market manipulations by Enron).
Any debt issued by the U.S. government is considered to have zero default risk, including U.S. Treasury securities. Such debt is said to be backed by "the full faith and credit" of the U.S. government. Since the U.S. government has the power to tax the largest economy in the world, its bonds are considered by credit markets to be default-free.
What about other issuers? Any bonds issued by private corporations or state/local governments is considered to have some default risk. The amount of default risk is very important to pricing a bond (and thus it's interest rate). Because of this, bond issuers pay rating agencies to measure the default risk on a bond and rate that bond. The two largest rating agencies are Moody's Investors Service and Standard and Poor's (they rate about 75% of bond issues). Bond buyers use this rating as an indicator of default risk. The table below describes the rating system used by Moody's and Standard and Poor's. It is a little more detailed than the one in your book. The higher the credit rating, the lower the default risk

Moody's	S & P	Description	Examples (as of August 2005) of Corporations and Municipal GO
Investment Grade Bonds
Aaa	AAA	Highest quality	Missouri General Electric Johnson & Johnson Medical
Aa1 Aa2 Aa3	AA+ AA AA-	High quality	State Farm Life Insurance Co. Wal Mart Co. Microsoft Corp.
A1 A2 A3	A+ A A-	Upper Medium Quality	IBM Syracuse University New York State, New York City
Baa1 Baa2 Baa3	BBB+ BBB BBB-	Medium Grade	Syracuse, NY 7-Eleven, Inc. Big Lots, Inc.
High Yield or Junk Bonds
Ba1 Ba2 Ba3	BB+ BB BB-	Lower medium grade	GM, Ford Xerox India
B1 B2 B3	B+ B B-	Speculative	American Airlines Pakistan
Caa1 Caa2 Caa3	CCC+ CCC CCC- CC	Poor	Microcell Solutions, Inc Silicon Graphics, Inc Venezuela
Ca	C	Highly speculative
C	SD, D	Lowest grade (in default)	Pacific Gas and Electric.

If a company falls on hard times, like California utility companies, its bond rating may be downgraded. If a state like -- oh, I don't know -- New York has fiscally irresponsible legislators in Albany that borrow too much and repeatedly fail to produce on-time budgets, it's debt can be downgraded too. New York State's general obligation bonds have the lowest rating of all fifty states, along with Louisiana. Click here to see a ranking.
The distinction between investment grade and high yield debt is important since certain institutional investors such as pension funds, insurance companies and commerical banks may only be allowed to buy investment grade debt.
Ratings change over time given the fortunes of a company or government. The city of Syracuse's fiscal problems have led to downgrades in its debt rating. GM and Ford recent had their debt downgraded to junk bond territory in the summer of 2005. When bonds are downgraded from investment grade to junk status they are known as fallen angels. Rating upgrades can happen as well, although they are less common.
In additional to bonds, commerical paper is also rated. Commerical paper is short-term zero coupon debt issued by corporations or government. Commerical paper is usually issued by only the most creditworthy companies so most issues are rated at the highest level.
So how does default risk explain spreads? Obviously, default risk is a bad thing, so to make risky bonds attractive to investors, the issuers must offer higher interest rates. Bonds with greater default risk will have higher yields, holding all other factors constant. This spread is known as the default premium. This feature explains the observed positive spread of Baa bonds over Aaa bonds, and of Aaa bonds over Treasury bonds. U.S. Treasury security yields are considered a benchmark yield, with other bonds carrying higher yields depending on their default premium.
As default risk changes, in general or for specific companies, the default premium will change as well. Over the business cycle default risk will change generally. Defaults will be more likely during recessions and less likely during expansions, so a widening spread between the Baa bonds and Treasury debt is an indicator that credit markets expect an economic downturn. This also explains why spreads were so large in the early 1980s during a bad recession, but much smaller in 1995 during the longest economic expansion in U.S. history.
Tax Treatment
Municipal bonds also have greater default risk than Treasury bonds, and yet municipal bonds have a lower yield. How did that happen? The answer lies in the special tax treatment afforded to municipal debt relative to U.S. government debt and corporate debt:

• Interest payments on municipal debt are tax-exempt from federal income taxes, and from state income taxes in the issuing state.
• Interest payments on U.S. government debt are tax-exempt from state income tax.
• Interest payments on corporate debt are fully taxable.

So

• If I buy New York municipal bonds, I keep every $1 of interest.
• If I buy U.S. government bonds, I only keep $1(1-.25) = 75 cents of every $1 of interest. Why? Because I am in a 25% marginal federal tax bracket, so 25 cents of every $1 goes to Uncle Sam.
• If I buy corporate bonds, I only keep $1(1 - .30) = 70 cents of every $1 of interest. This is because I am in the 5% marginal state tax bracket in addition to the federal bracket.

For municipal bonds, the before-tax yield = the after-tax yield.
For corporate and U.S. government bonds, the before-tax yield > the after-tax yield.
Municipal bonds can offer a lower coupon rate (and thus yield) because the payments are tax exempt. The benefit of this tax-exempt status is larger at larger tax rates. This explains why most individuals who own municipal bonds are in the highest marginal federal income tax brackets. This also implies that any change in the tax law will affect the spread between municipal bonds and other types of bonds:

• Any increase in federal tax rates will increase the spread between municipal bonds and other taxable bonds.
• Any decrease in federal tax rates will decrease the spread between municipal bonds and other taxable bonds.

The Term Structure of Interest Rates
In this part we focus on the maturity of a bond, and how that factor alone affects the interest rate of a bond. This relationship is known as the term structure of interest rates. In figure 7.5 (page 160) in your book, a time series of short, intermediate, and long-term bond yields:
Note that the relationship between bond yield and maturity is not consistent: Sometimes long-term bonds have the highest yields (1992), sometimes they have the lowest yields (1981).
The Yield Curve
To focus on maturity alone, we need to examine a set of bonds with identical risk, features, tax treatment, etc. but different maturities. In reality, only Treasury bonds satisfy these criteria. Municipal and private issuers do not issue enough different maturities to allow useful comparison. Treasury securities range in maturity from 3 months to 30 years.
A plot of Treasury bond maturities versus their yields is known as the yield curve. The shape of the yield tells us the relationship between short-term and long-term interest rates. Consider the sample yield curves below:

In curve (A), the yield curve is upward-sloping, so yields rise as maturity increases.
In curve (B), the yield curve is downward-sloping, or inverted, so yields fall as maturity increases.
In curve (C), the yield curve is flat, so yields are identical across all maturities.
In curve (D), the yield curve changes direction, so the short and long-term bonds have the highest yields, but intermediate-term bonds have lower yields.
The yield curve changes shape over time, depending on financial market conditions. However, in looking at historical data on Treasury yields, there are 3 important facts about the yield curve:

1. Interest rates on bonds of different maturities generally move together.
2. Short-term bonds yields are more volatile than long-term bond yields, i.e. short-term yields move up and down more frequently and over a larger range than long term yields.
3. The yield curve usually slopes up, i.e. long term yields tend to be higher than short-term yields.

In addition to describing the current relationship between short and long-term interest rates, the yield curve may also contain valuable information about investor expectations about future interest rates. To understand what a yield curve tells us we need to understand what causes yields to differ across maturities. We look at 2 alternative explanations, or theories of the term structure. We will "test" the usefulness of each theory by comparing the predictions of the theory to the empirical facts about the U.S. Treasury yield curve.
The Expectations Theory
Assume that bond buyers do not have any preference for the maturity of a bond, or in other words bonds of different maturities are perfect substitutes. Given this key assumption, The expectations theory of the term structure states that the yield of a long-term bond will equal the average of the expected short-term interest rates over the same period.
How do we get from the assumption to the implication? First let's reconsider what it means for two goods to be perfect substitutes. If I hold Diet Coke and Diet Pepsi to be perfect substitutes then I really do not care which one I drink. So if Diet Coke costs $1/bottle and Diet Pepsi costs $1.25/bottle I will always pick Diet Coke, because I like it just as well. Thus if I have both Diet Coke and Diet Pepsi in my shopping cart at Wegman's, you can assume that they were the same price. Otherwise, I would only buy the cheaper soda, because they taste the same to me.
Now, consider an investment horizon of 5 years. Under the expectations theory we assume that investors are indifferent between (1) holding a 5-year bond the entire time or (2) holding 5 1-years bonds over each of the next 5 years. Here investors only care about the expected return. So if we observe investors buying both 1-year and 5-year bonds, then it must be the case that they expect the return to be the same. If investors expect one-year bond yields to be 5%, 6%, 7%, 8%, 9% over the next 5 years, then the 5-year bonds yield must solve the equation


Why? Because if the 5-year bond yield return is expected to be larger than 5 1-year bonds, then everyone will hold the 5-year bond. We observe investors holding both 5-year and 1-year bonds, so the expected returns must be equal, IF they are perfect substitutes. The equation above can be APPROXIMATED by

So then the long term bond yield (the 5-year bond) is an average of the expected short-term bond yields over the next 5 years.
Under the expectations theory, the yield curve tells us something about expected future short-term interest rates. If markets expect short term interest rates to rise, like the example above, then the current long-term rate (7%) is greater than the current short-term rate (5%), and the yield curve slopes up. So an upward sloping yield curve, under this theory, tells us that short-term rates are expected to rise.
How does the expectations theory stack up with reality? Let's reconsider the 3 facts about the yield curve, and see if the expectations theory is consistent with these facts.

1. Interest rates on bonds of different maturities generally move together. YES, under this theory we would predict that interest rates move together. If short term interest rates rise, then their average will rise too, pushing up long-term interest rates. If short-term interest rates fall, then their average will fall too, pushing down long-term interest rates.
2. Short-term bonds yields are more volatile than long-term bond yields, i.e. short-term yields move up and down more frequently and over a larger range than long term yields. YES, this is also consistent with the expectations theory. If long-term rates are an average of expected future short-term rates, then long term rates will be smoother. Any change in expected short term rates has a smaller impact on the average.
3. The yield curve usually slopes up. NO, the expectations theory does not predict this result.Under the expectations theory an upward sloping yield curve only occurs when short-term interest rates are expected to rise, or about 50% of the time.

Why the failure? Go back to the key assumption for this theory: bonds of different maturities are perfect substitutes. This is a very strict assumption that is not really realistic. We know from chapter 6 that long-term bonds exhibit greater price volatility which some investors will find unacceptable.
Well, as the great Meatloaf sang, "Two out of Three Ain't Bad." Let's consider alternative theories that build on the expectations theory.
The Liquidity Premium Theory
Recall that longer term bonds carry greater interest-rate risk and greater inflation risk. Given this, let's assume that bonds of different maturities are imperfect substitutes, with investors preferring short-term bonds. This means that investors would choose short-term bonds, all else being equal, but would be willing to hold long-term bonds if given an incentive to do so. Under the liquidity premium theory, long-term bonds yields are an average of expected short-term bond yields during the same period PLUS a liquidity (or term) premium.
To connect the assumption with the implication, think back to the whole Diet Coke/Diet Pepsi debate. Suppose I prefer Diet Coke when prices are the same, but I am willing to buy Diet Pepsi if it is a lot cheaper than Diet Coke. In this case Diet Coke and Diet Pepsi are imperfect substitutes, with my preferences leaning toward Diet Coke. I will only buy Diet Pepsi if I think it is a much better deal.
If investors do not like long-term bonds as well, then they have to be given an incentive, such as a higher expected return, in order to hold them. Consider our earlier numerical example where investors expect one-year bond yields to be 5%, 6%, 7%, 8%, 9% over the next 5 years. Now suppose that in addition, investors demand an extra 1% to hold a 5-year bond instead of 1-year bonds. Then the 5-year bond yield becomes

Under this theory, it is easy to see why the yield curve usually slopes up. If long-term bond yields include a liquidity premium, then they will usually be larger than short-term bond yields. So this theory explains fact #3. Also, since the long-term bond yield is still related to the average of short-term bond yields, this theory also explains facts #1 and 2. So now, by combining parts of two theories we come up with a third, and more realistic theory.
The downside of this theory is that it is more difficult to interpret the yield curve. The slope of the yield curve reflects two things (1) expectations about future short-term interest rates, and (2) the liquidity premium. If we do not know the size of the liquidity premium, we cannot always be sure about what the yield curve is saying about expected future short-term interest rates. An upward-sloping yield curve could be caused by the expectation of rising interest rates or a liquidity premium, or both.
What Do the Default premium and the Yield Curve Tell Us?
Researchers have investigated whether interest rate spreads give us reliable information about

• future interest rates
• future inflation rates
• future business cycles

The results are mixed, but fairly recently (1996) some economists at the Federal Reserve Bank of New York found that a declining spread between the 3 month Tbill and 10-year Tnote increases the probability of a recession within 6 to 12 months after the decline. An inverted yield curve (with a negative slope) predicts an economic slowdown fairly well.
Also, economists find the default premium between U.S. Tbills and commerical paper to be a reliable tool in forecasting business cycles.

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