CHAPTER 7 Risk Structure and Term Structure of...

Risk Structure and Term Structure of Interest Rates

CHAPTER

7On any business day, The Wall Street Journal reports interest rates for various finan-cial instruments. Here is a sample of bond yields reported on July 24, 2003:

Bond Maturity Date Yield

Treasury bond August 2013 2.95%

Household Finance 2013 5.19%

General Motors bond 2013 7.16%

Treasury bill January 2004 0.96%

In Chapter 6, we looked at the way in which interest rates are determined in thebond market, assuming that there was one interest rate that was suitable for all bondstraded. Now we observe that there is more than one “market” interest rate. Does thismean that our analysis was wrong? Not really. The assumptions that we made allowedus to develop a broad picture of market interest rates. When investors enter the bondmarket to purchase a particular security, they are interested in the yield it will return,and many of the same variables that determine interest rates for bonds in general applyequally to individual bonds.

In this chapter, we refine the analysis presented in Chapter 6 to see how qualitiespossessed by an individual bond determine the interest rate it must offer an investor. Inthe first part of the analysis, we look at the risk structure of interest rates, whichexplains differences in yields across securities with similar maturity. In the second partof the chapter, we turn to the term structure of interest rates. We compare bonds withsimilar risk, liquidity, and information-cost characteristics and observe how their yieldsvary according to their time to maturity. Investors use both types of analyses to fore-cast the future movement of individual securities and market interest rates, and wedescribe this process as we study the differences in bonds.

Risk Structure of Interest RatesIf the bonds listed at the start of this chapter have similar maturity (as they do, exceptfor the Treasury bill), we can attribute the difference in interest rates—and in yields—to differences in default risk, liquidity, information costs, and taxation. The risk struc-ture of interest rates summarizes effects of these determinants on yields for a givenmaturity. In this section, we describe how each determinant affects the interest rate ofa credit market instrument and how interest rates can change as savers’ perceptions ofeach determinant change. We also describe how variations in the interest rates reportedin the financial media allow investors to forecast financial and economic trends.

Default Risk

Borrowers differ in their ability to repay in full the principal and interest required by aloan agreement. Savers view promises made by O.K. Used Cars, for example, as being

Web Site Suggestions:http://www.gpoaccess.gov/indicators/index.htmlThe Council ofEconomic Advisers’Economic Indicatorsoffers historical dataon a variety of U.S.interest rates.

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less likely to be fulfilled than those made by IBM. As a result, O.K. Used Cars, andother private companies whose ability to repay their obligations in full is uncertain,must offer investors higher yields to compensate them for the risk they take in buyingtheir bonds or making loans. The risk that a creditor cannot fulfill its promised princi-pal and interest payments is called the default risk.

Measuring default risk. To determine the default risk on a security, we need a yard-stick. U.S. Treasury securities fulfill this need because they are default-risk-free instru-ments. We assume that they have zero risk because the U.S. government guarantees thatall principal and interest will be repaid in nominal terms. The government can makethis guarantee to settle debts. We measure the default risk of a security by comparingit to default-risk-free Treasury securities.✝

The default risk premium on a bond is the difference between its yield and the yieldon a default-risk-free instrument of comparable maturity, and it measures default risk.The default risk premium is the additional yield that a saver requires for holding a riskyinstrument. For example, if the yield on Treasury bonds was 8%, you would demand ahigher interest rate, say 12%, on a corporate bond issued by Worry Free Company,which has a middling credit history. The default risk premium on the Worry Free bondis 12% � 8% � 4%.

The risk premium has two components. First, for the risk-neutral savers who careonly about expected returns and not about the variability of those returns, the interestrate for an instrument that carries default risk must be greater than that for a default-risk-free instrument. The higher rate compensates savers for losses if the bond issuerdefaults on either interest or principal, or both. The default risk premium makes theexpected return on the investment with default risk equal to the certain return from thedefault-risk-free instrument. Second, because savers generally are risk-averse and careabout the variability of returns as well as about expected returns, yields incorporate anextra premium for bearing default risk.

To determine the size of the default risk premium to assign to a bond or loan agree-ment, lenders try to assess the creditworthiness (the ability to repay) of borrowers. Thecost of acquiring information about a borrower’s creditworthiness can be high. Accord-ingly, investors often pay professional analysts to gather and monitor such information.For corporate debt instruments, private firms such as Standard & Poor’s Corporation(S&P) and Moody’s Investors Service assign ratings that are published and updatedperiodically (see Table 7.1). A bond rating is a single statistic summarizing the ratingcompany’s view of the issuer’s net worth, cash flow, and prospects—in short, of theissuer’s likely ability to meet its debt obligations. Because they are less risky, instru-ments with high ratings, such as AAA by S&P, have lower yields than do risky instru-ments with low ratings, such as C by S&P, and this difference in yields is one source ofthe yield variation in risk structure. Both borrowers and lenders are concerned aboutratings. For borrowers, the rating affects their risk premium and hence their cost offunds. Savers look to the rating as a source of information about default risk.

Changes in default risk and the default risk premium. How does a changein default risk affect the interest rate on a particular financial instrument, such as Gen-eral Electric bonds? The default risk premium can fluctuate as new information about

CHAPTER 7 Risk Structure and Term Structure of Interest Rates 131

✝ Nonetheless, the prices of Treasury securities can fluctuate as market interest rates increase or decrease. Forexample, an increase in market interest rates raises yields on Treasury securities, reducing their prices.

a borrower’s creditworthiness becomes available to investors. In other words, shifts inthe market’s perception of default risk can lead to a change in yield.

We can examine the determination of the price (and expected interest rate) for high-default-risk and low-default-risk instruments with the bond market diagram developed inChapter 6. Figure 7.1(a) illustrates determination of the market price of a low-default-riskasset, and Fig. 7.1(b) illustrates determination of the market price of a high-default-riskasset. In both diagrams, the willingness to supply bonds rises with the price of the bonds.The demand curves represent lenders’ willingness to buy bonds, based on returns availablefor other investments. The quantity of bonds demanded falls as the price increases. In Fig.7.1 (and other figures that follow), we focus on the market for bonds and the price ofbonds. Remember that bond prices and yields are inversely related, so a rise in the price ofthe bond is associated with a fall in the yield, and a fall in the price is associated with a risein the yield. This relationship allows us to interpret the changes shown in Fig. 7.1. Thegraph shows changes in bond prices. Thus, once we see that bond prices rise or fall, wecan use this price movement to predict what will happen to bond yields. We demonstratethis change in the default risk premium by working through Fig. 7.1.

If lenders anticipate no changes in the other sources of variation in yields (liquidity,information costs, and tax differences), the yield on a risky security should be greater thanthat on a safe security, and the price of the risky security should be lower than the priceof the safe security. Such is the case in Fig. 7.1: The initial price of the safer security, Psafe0,exceeds that of the riskier security, Prisky0. From the pricing information shown, we can

132 PART 2 Interest Rates

U S I N G T H E N E W S . . .

Using Bond Yieldsto Assess RiskWe can use the bond data at the begin-ning of the chapter and in the accom-panying figure to find the default riskpremiums on the GM and HFC bonds.The GM bond due in 2013 with an8.375% coupon rate has a yield of7.16%, whereas the HFC bond due in2013 with a 4.75% coupon rate has ayield of 5.19%. On the same day, theyield to maturity on a Treasury bonddue in 2020 was about 2.95%. Hencethe risk premium on the HFC bond is5.19% – 2.95% = 2.24%, and therisk premium on the GM bond is 7.16%– 2.95% = 4.21%. Since the bondshave similar tax, liquidity, and informa-tion characteristics and both have along maturity, this difference in riskpremiums reflects investors’ belief thatGM is more likely than HFC to default on interest or principal payments.Investors use these quotes as a guideto bond market participants’ assess-ment of the risk of different bonds.

WBFONBACFAOLLEHGMWBMWDGEGSFONCMCSAFONCOPGMUSA CRDSUICFCAWEDCXHSBCGMAC

5.0008.7503.2507.4507.7004.0008.3753.5004.2505.4504.7508.3755.3006.0006.3507.1254.6253.2508.7504.0504.7506.875

Aug 15, 2015 Mar 15 2032Aug 15, 2008Jul 16, 2031

May 01, 2032Jan 22, 2008Jul 15, 2033

Aug 15, 2008May 15, 2010Jan 15, 2013Jul 15, 2013Mar 15 2012Jan 15, 2014Jan15, 2007Oct 15, 2011Jul 15, 2013Jan 15, 2008

May 21, 2008Mar 01, 2031Jun 04, 2008Jul 15, 2013

Sep 15, 2011

99.549116.82398.86290.350

114.347102.14199.05299.846

100.081104.23197.618

116.895100.240106.712112.58699.728

104.86898.575

122.89797.68896.580

100.551

5.0507.3353.4978.3466.5813.4808.4613.5334.2354.8865.0575.8525.2673.9094.4997.1623.4393.5746.8854.5865.1946.784

Source: The Wall Street Journal, July 24, 2003 pC11. Republished by permission of Dow Jones, Inc. via Copyright Clearance Center, Inc. © 2000 Dow Jones and Company, Inc. All Rights Reserved Worldwide. (Quotes are from July 24, 2003.)

Wednesday, July 23, 2003

Forty most active fixed-coupon corporate bonds

COMPANY MATURITYCOUPONLAST

PRICELAST

YIELD

Corporate Bonds

9422955

33015453

34258137995

1741169839

3054963

184164108268

10305

30305

305

10101010105

101055

305

1010

132,735122,700115,878115,152108,248102,92296,50592,88588,62587,49485,90185,77384,20080,22279,11974,45972,98072,74972,11871,39462,43562,364

*ESTSPREAD

EST $ VOL(000'S)UST†


identify the differences in returns on these bonds. The initial interest rate on the riskiersecurity, irisky0, exceeds that on the safer security, isafe0. The risk premium, irisky0 � isafe0,compensates lenders for the default risk on the riskier security.

Now suppose that market participants believe that the likelihood of default on theriskier instrument has increased because an anticipated recession lowers profits of high-risk firms. Accordingly, lenders are willing to pay less for the high-risk security (that is,they demand a higher expected return) to compensate them for bearing additionaldefault risk. The demand curve in Fig. 7.1(b) shifts to the left, as investors reduce thevolume of funds they channel to that security. The shift in the demand curve reducesthe price of risky bonds (and raises the yield on risky bonds).

When lenders perceive an increase in the default risk on risky instruments, theytend to shift their funds to low-risk instruments. This shift is called a flight to quality.Note in Fig. 7.1(a) that the demand curve in the safer market shifts to the right becauseof greater default risk on the riskier security. From the theory of portfolio allocation,we would predict that the increase in the risk of the higher-risk security would increasethe demand for the safer bonds. In this case, the price of the safer bond rises, while theprice of the riskier bond falls—that is, the default risk premium widens. The yield on a


Reading the Ratings Provided by Moody’s and Standard & Poor’s

Moody’s S&P’s Meaning

Investment-grade bonds Aaa AAA Bonds of the best quality, offering the smallest degree of default risk. Issuers are exceptionally stable and dependable.

Aa AA Bonds of high quality by all standards. Slightly higher degree of long-term default risk.

A A Bonds with many favorable investment attributes.

Baa BBB Bonds of medium-grade quality. Security appears adequate at present but may become unreliable.

Non-investment-grade bonds Ba BB Bonds with speculative returns. Moderate security of payments; not well safeguarded.

B B Cannot be considered a desirable investment. Small long-term assurance of payments.

Caa CCC Bonds of poor standing. Issuers may be in defaultor in danger of default.

Ca CC Bonds of highly speculative quality; often in default.

C C Lowest-rated class of bonds. Very poor prospectsof ever attaining investment standing.

— D In default.

Commercial paper P1 A1 Issues of the highest quality, offering the smallest degree of default risk.

P2 A2 Lower-quality commercial paper.

P3 A3 Lowest investment-grade quality commercial paper.

Unrated

Source: Reprinted with the permission of Simon & Schuster from The Wall Street Journal Guide to Understanding Money and Markets, by Richard SaulWurman, Alan Siegel, and Kenneth M. Morris. Copyright © 1989 by Access Press Ltd., and Siegel & Gale, Inc.

TABLE 7.1

bond with a higher default risk carries a greater default risk premium. An increase inexpected default risk reduces lenders’ willingness to buy riskier instruments andincreases their willingness to buy safer instruments.

In practice, how do changes in default risk work to cause investors to shift fundsfrom one asset to another? Figure 7.2 highlights two shifts in U.S. financial markets. Itshows that, although long-term interest rates generally move together (as do short-termrates), episodes do occur in which risk premiums fluctuate. In the early 1980s, when arecession caused concern about corporations’ ability to repay, investors reallocatedfunds away from risky long-term corporate debt and toward safe government debt.Note the dramatic increase in the yield on medium-quality (Baa) bonds relative to theyield on long-term Treasury securities in the early 1980s. The 1974–1975 recessionraised investors’ concern about default risk in the short-term market. Note the signifi-cant increase in the commercial paper rate, which carries some default risk, relative tothe Treasury bill rate, which does not. These episodes reflect market perceptions of anincrease in default risk, raising the required yield on alternatives to default-risk-freeinstruments. In August 1998, risk premiums rose as worldwide investors, panicked bythe Asian financial crisis, bought up Treasury securities. The period after the Septem-ber 2001 terrorist attacks also led to a flight to quality.

Another flight to quality occurred from 1929 to 1931. As expectations of thedownturn worsened during the Great Depression, savers shifted their funds away


B srisky

B ssafe 0

Bdsafe1

Bdsafe 0

Bdrisky1

Bdrisky 0

Prisky1

Prisky 0P

rice

of

bo

nd

s, P

Psafe1

Psafe 0

Pri

ce o

fb

on

ds,

P

Quantity of low-default-risk bonds Quantity of high-default-risk bonds

3. Default riskpremium in bond prices increases.

1. Lenders shift away from riskierasset.

(b) High-Default-Risk Market (a) Low-Default-Risk Market

2. Lenders shifttoward saferasset.

Default risk premium in bond prices.

Determining Default Risk Premium in YieldsThe initial default risk premium can be seen by comparing yields associated with the prices Psafe and Prisky. Because the price of the saferasset exceeds that of the riskier asset, we can infer that the yield on the riskier asset, irisky, exceeds that on the safer asset, isafe, to compensatesavers for bearing risk.

1. The initial default risk premium, then, is irisky 0 � isafe0, where irisky and isafe are the yields associated with Prisky and Psafe, respectively. Aslenders revise upward the expected default risk in the high-default-risk market, the Bd curve shifts to the left (from Bd

risky0 to Bdrisky1).

2. The rise of default risk in the high-default-risk market causes investors to shift their funds to less risky markets, causing the Bd curve toshift to the right (from Bd

safe0 to Bdsafe1) in the low-default-risk market, raising the price of low-default-risk bonds and reducing the yield on

low-default-risk bonds.

3. Because of the greater gap between prices of low-default-risk and high-default-risk instruments, the premium between the high-default-riskyield and the low-default-risk yield increases to irisky1 � isafe1.

FIGURE 7.1

anim134.html

from risky corporate securities. They shifted their savings to government securities,actually pushing yields close to zero. The spread between Baa and long-term gov-ernment bond rates increased significantly—from 2 percentage points in 1929 to 6percentage points in 1931. Other changes in default risk premiums occurred in theearly 1970s in the commercial paper market. The default of the Penn Central Rail-road in 1970 raised the perceived risk on corporate commercial paper. In the munic-ipal bond market in the early 1980s, the default of the Washington State PublicPower System bonds increased the perceived risk of investments in the municipalbond market.

Liquidity

Differences in liquidity are another reason we observe differences in interest rates.Because investors care about liquidity, they are willing to accept a lower interest rateon more liquid investments than on less liquid—illiquid—investments, all other thingsbeing equal. Hence a less liquid asset must pay a higher yield to compensate savers for


Onset ofrecession:Risk premium rises.

1975 1980 1985 19901960 1965 1970Year

Yie

ld (

%)

1995

= Long-term yields

= Short-term yields

Baacorporatebonds

10-year T-bonds

4–6-month commercial paper

6-month T-bills

18.0

16.0

14.0

12.0

10.0

8.0

6.0

4.0

1.0

2.0

2000 2002

Long-Term and Short-TermYields in the United States,1960–2002In periods when investors areconcerned about the ability ofcorporations to repay, investorsreallocate funds from corporatedebt to safe government debt,seen here in 1974–1975 andagain in the early 1980s.Source: Council of Economic Advisers,Economic Report of the President, vari-ous issues; after 1997, commercial paperdata are for three-month instruments.

FIGURE 7.2

Hitechco, a relatively young technology company, has $10 million in bonds out-standing. You notice in The Wall Street Journal that the firm has been awarded a$30 million settlement in a patent dispute with an electronics conglomerate. Whatwould you predict to be the effect of the settlement on the yield on and price ofHitechco’s bonds? The news of the settlement reduces the default risk on anyHitechco debt. The default risk premium on Hitechco bonds should then fall, reducingthe yield and increasing the bonds’ price. ♦

C H E C K P O I N T

their sacrifice of liquidity. The overall risk premium on an investment includes this liq-uidity premium as well as the default risk premium.

Liquidity premium. The way in which a financial instrument is traded affects itsliquidity. As with default risk, we can use U.S. Treasury securities to compare liquidityamong different financial instruments. Markets for Treasury securities are extremelyliquid, whereas matching buyers and sellers of corporate bonds is more difficult. There-fore corporate bond markets are much less liquid than government bond markets, andso investors require an additional premium in their yields.

Changes in liquidity and the liquidity premium. How does a change in theliquidity of a financial instrument affect its yield? The theory of portfolio allocation tells usthat for any yield, investors prefer to hold more liquid instruments (such as governmentbonds) than illiquid ones. Therefore, if the market for corporate bonds becomes less liquid,the spread between yields on less liquid and more liquid instruments increases.

Figure 7.3 illustrates the effect of a change in liquidity on bond prices. Figure 7.3(a)shows the determination of the market price of securities in a more liquid market (suchas that for U.S. Treasury bonds). Figure 7.3(b) shows the determination of the marketprice of bonds in a less liquid market (such as that for corporate bonds). Because wewant to focus on the consequences of a change in liquidity for the risk premium, forsimplicity we assume that the initial prices in the two markets are equal, or Pilliq0 �

Pliq0; hence the initial yields in the two markets are also equal, or iilliq0 � iliq0.Suppose that the less liquid instrument becomes even more illiquid. Savers then will

require a higher expected return to compensate them for the loss of liquidity; that is, thedemand curve in the illiquid market shifts to the left as the demand for bonds decreasesfrom Bd

illiq0 to Bdilliq1 in Fig. 7.3(b). This shift lowers the price and raises the yield in the

illiquid market. As lenders reallocate their funds toward the more liquid market, thedemand curve in Fig. 7.3(a) shifts to the right from Bd

liq0 to Bdliq1. As a result, the price rises

(from Pliq0 to Pliq1) and the interest rate falls in the more liquid market, while the pricefalls (from Pilliq0 to Pilliq1) and the interest rate rises in the less liquid market. Associatedwith the gap between the prices (Pliq1 � Pilliq1), the liquidity component of the risk pre-mium rises to iilliq1 � iliq1. Lenders are less willing to hold the illiquid instrument andrequire a higher return, and borrowers using that instrument to raise funds will have ahigher cost of funds. An increase in the liquidity of an asset reduces its required return; adecrease in liquidity raises the required return.

Information Costs

The third factor influencing the risk structure of interest rates is the cost of acquiringinformation. The activity of an investor who devotes resources—time and money—toacquire information on an asset reduces the expected return on that financial asset. Thecost of using those resources thus is included in the borrowing cost charged by thelender, just as the cost of labor is included in the price of a sweater. If two assets haveequal default risk and liquidity, investors prefer to hold the asset with lower informationcosts.

Measuring information costs. Government obligations, such as Treasury billsand bonds, have the lowest information costs because all savers know with certaintythat the principal and interest will be repaid (in nominal terms). Rating agencies reduce


the information costs of gathering data on and monitoring well-known borrowers, butsuch costs are higher for loans made to less well-known borrowers. For example, if youwant to start a business of selling customized T-shirts and go to your local bank for aloan, the bank will have to assess your ability to repay on the basis of your income andthe chances that your business will succeed. The cost of collecting this informationleads to higher costs either directly in terms of a higher interest rate on your loan orindirectly through restrictions on your activities that the bank will write into your loancontract. Financial instruments with high interest rates due to higher information costsalso tend to be relatively illiquid. The reason is that without readily available informa-tion, trading these instruments in financial markets is difficult.

Changes in information costs and the risk premium. Figure 7.4 illustrates theeffect of an increase in information costs on the price of a financial instrument and, byinference, on the risk premium for a financial instrument. Figure 7.4(a) shows the deter-mination of the market price of low-information-cost bonds. Figure 7.4(b) shows thedetermination of the market price of high-information-cost bonds. Again, for simplicity,let’s assume that the prices of the two bonds are initially equal, or Phigh0 � Plow0, so theyields are equal, ihigh0 � ihigh1. (In practice, of course, ihigh0 � ilow0. This difference reflectsthe difference in costs that lenders incur to gather information on the two bonds.)

When information costs rise for the high-information-cost market, lenders are lesswilling to invest their funds in the market for that instrument at the going price andyield, shifting the demand curve to the left in Fig. 7.4(b). As the funds are reallocated to


B silliq0B s

liq0

Bdliq0

Bdliq1

Bdilliq1

Bdilliq0

Pilliq1

Pilliq 0

Pri

ce o

fb

on

ds,

P

Pliq1

Pliq 0

Pri

ce o

fb

on

ds,

P

Quantity of bonds in more liquid market Quantity of bonds in less liquid market

1. Lenders decreasedemand for less liquid asset.

(b) Less Liquid Market (a) More Liquid Market

2. Lenders increasedemand for moreliquid asset.

3. Liquiditypremium in bond prices rises.

Effect on the Risk Premium of a Decrease in LiquidityLenders value liquidity. Therefore an instrument traded in a less liquid market will have a lower price and greater required return than aninstrument traded in a more liquid market.1. A decrease in liquidity causes lenders to decrease their demand curve for that asset, shifting the demand curve from Bd

illiq0 to Bdilliq1 .

2. Lenders reallocate their funds from the less liquid market to the more liquid market, shifting the demand curve from Bdliq0 to Bd

liq1.3. The liquidity premium embodied in the change in the spread in bond prices—the difference in the yield on the less liquid instruments—equals iilliq1 � iilliq0.

FIGURE 7.3

the low-information-cost market, the demand curve shifts to the right in the market forthat instrument, as shown in Fig. 7.4(a). As a result, the price rises (from Plow0 to Plow1)and the interest rate falls in the low-information-cost market, while the price falls (fromPhigh0 to Phigh1) and the interest rate rises in the high-information-cost market. Associ-ated with the gap between the prices (Plow1 � Phigh1), the information-cost componentof the risk premium rises to ihigh1 � ilow1. An increase in information costs increases therequired return on a financial instrument. A decrease in information costs decreases therequired return on a financial instrument.

Taxation

Another reason for differences in interest rates across credit market instruments is tax-ation. If returns on all instruments were taxed identically, the differences amonginstruments in terms of default risk, liquidity, and information costs would be the onlysources of variation in the risk structure. Differences in the taxation of returns, how-ever, also create differences in yields among credit market instruments.

Measuring tax differences. When savers project the estimated returns from abond investment, they first determine whether interest payments are taxable and howtaxes reduce their returns. For example, interest received on municipal bonds, which


B shigh 0

B slow 0

Bdlow1

Bdlow 0

Bdhigh1

Bdhigh0

Phigh1

Phigh0

Pri

ce o

fb

on

ds,

P

Plow1

Plow 0

Pri

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fb

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Quantity of low-information-cost bonds Quantity of high-information-cost bonds

2. Lenders increasedemand for assetswith low informationcosts. 1. Lenders

decrease demand for assets with high information costs.

(b) High-Information-Cost Market (a) Low-Information-Cost Market

3. Information costpremium in bondprices rises.

Effect on Risk Premium of an Increase in Information CostsAn increase in information costs in a high-information-cost market causes the price of bonds in that market to fall and the interest rate to rise;the difference in the interest rate on high-information-cost lending and low-information-cost lending rises.

1. An increase in information costs in the initially high-information-cost market causes lenders to decrease their demand for that asset, shift-ing the demand curve for that asset to the left from Bd

high0 to Bdhigh1, reducing the price of bonds and raising the yield.

2. Lenders reallocate their funds toward the low-information-cost market, shifting the demand curve to the right from Bdlow0 to Bd

low1 , raisingthe price of bonds, and reducing the yield.

3. The difference in the bond prices is matched by a difference in the required returns. The gap between ihigh1 and ilow1 is the information-costpremium.

FIGURE 7.4

are obligations of state and local governments, is exempt from federal, state, and localincome taxes. Owing to this exemption, many savers are willing to accept a lower inter-est rate on municipal bonds than on comparable instruments (including some withlower default risk) because the after-tax yield of municipal bonds is greater. To demon-strate, suppose that you are comparing the returns on a $1000 Treasury bond with a9% coupon rate and a $1000 municipal bond paying 7.5% interest. The before-taxyield on the Treasury bond (9%) is greater than that on the municipal bond (7.5%). Ifyour marginal income tax rate is 30%, 30¢ of each additional dollar of interest incomegoes to the government through taxes. An annual coupon payment of $90 on the$1000 taxable Treasury bond provides you with (90)(1 � 0.3) � $63 in after-tax inter-est income. Alternatively, a $1000 municipal bond with a $75 coupon payment and notaxes provides you with $75 in after-tax interest income. Therefore you might be will-ing to hold the municipal bond.

In addition to determining whether interest is taxed, savers must compare differingtax rates on the returns from their investments. Under U.S. law, interest and capitalgains are taxed differently. Interest income is taxed at the same rate as wage and salaryincome. Capital gains carry a lower effective tax rate than interest because capital gainsare taxed when they are realized (when the asset is sold) and not as they accrue; thatis, the taxes are deferred. For example, if you hold shares of Boomco for 20 yearsbefore you sell them and realize a capital gain, you will not be taxed until you sell theshares. The benefit of a deferred tax obligation is that the present value of the tax thatis paid on the gain when it is realized is lower than the present value of the tax pay-ments if you paid the tax incrementally as the gain accrued. At times (including cur-rently), capital gains have been subject to a lower explicit tax rate as well as the implicittax benefit of deferral.

Finally, the exemption of interest returns on U.S. government securities from stateand local taxation provides these obligations with favorable tax treatment relative totaxable corporate securities. Because their returns are taxed, part of the risk premiumbetween commercial paper and Treasury bill yields results from this difference in taxtreatment. If the attributes of default risk, liquidity, and information costs are held con-stant, then shifts in the tax treatment of returns on certain obligations will affectbefore-tax yields. Investors, however, will compare after-tax expected returns in mak-ing their portfolio allocation decisions.

Tax exemption and differences in yields. Figure 7.5 depicts the effect of atax exemption for municipal bond interest on the yields of a U.S. government bond anda municipal bond. For simplicity, suppose that, with no difference in tax treatment, theprices of the two instruments (Ptax-ex0 � Ptax0) are the same, as are the yields (itax-ex0 �

itax0). If yields on municipal bonds become tax-exempt, U.S. government bonds are lessattractive to savers because their yields are taxable. Hence the demand curve shifts tothe left in Fig. 7.5(b). At the same time, lenders will increase their demand for munici-pal bonds, shifting the demand curve to the right in Fig. 7.5(a). As a result, the price ofthe tax-exempt bond rises (from Ptax-ex0 to Ptax-ex1) and its yield falls, while the price ofthe taxable bond falls (from Ptax0 to Ptax1) and its yield rises. Associated with the gapbetween the new equilibrium prices, the tax component of the yield difference rises toitax-ex1� itax1. At this difference in yields, lenders are indifferent between holding thetaxable U.S. government bond and holding the tax-exempt municipal bond.

Table 7.2 summarizes the determinants of the risk structure of interest rates.



Suppose that Congress enacted and the President signed a tax on trading in cor-porate bonds to reduce the federal budget deficit. What should happen to the dif-ference between the yield on corporate bonds and that on Treasury bonds? Thetax on trading raises transactions costs in the corporate bond market relative to theTreasury bond market, reducing the liquidity of corporate bonds relative to Treasurybonds. The liquidity premium in corporate bond yields rises. ♦

C H E C K P O I N T

The Risk Structure of Interest Rates

An increase in an asset’s . . . Causes its yield to . . . Because . . .

default risk rise savers must be compensated for bearing additional risk

liquidity fall savers incur lower costs of exchanging the asset for cash

information costs rise savers must spend more resources toevaluate an asset

tax liability rise savers care about after-tax returns and must be compensated for the tax liability

TABLE 7.2

Bstax 0Bs

tax-ex 0

Bdtax-ex1

Bdtax-ex 0

Bdtax1

Bdtax 0

Ptax1

Ptax 0

Pri

ce o

fb

on

ds,

P

Ptax-ex 1

Ptax-ex 0

Pri

ce o

fb

on

ds,

P

Quantity of tax-exempt bonds Quantity of taxable bonds

3. Tax-exempt bondprice rises relative totaxable bond price.

(b) Taxable Bond Market (a) Tax-Exempt Bond Market

2. Lenders increasedemand for tax-exempt instruments.

1. Lenders decrease demand for taxableinstruments.

Effect of Differences in Tax Treatment on YieldsIf nothing else changes, a decrease in a bond’s tax liability raises its prices and decreases its yield.1. If municipal bonds become tax-exempt, lenders decrease their holdings of taxable U.S. government bonds, and the demand curve shifts tothe left, from Bd

tax0 to Bdtax1 in (b), reducing the price of taxable bonds.

2. Lenders increase their demand for tax-exempt bonds, so that the demand curve shifts from Bdtax-ex0 to Bd

tax-ex1 in (a), raising the price of tax-exempt bonds.3. The difference in the bond prices is matched by a difference in the required returns. The gap between itax1 and itax-ex1 is the tax componentof the difference in yields.

FIGURE 7.5

Using the Risk Structure for Forecasting

Many business and government analysts use financial data for forecasting, or predict-ing, changes in economic variables such as total output of the economy or prices. Busi-nesspeople use forecasts in making investment, production, and employment decisions.Government officials use forecasts to predict future tax revenues and expenditures andto guide policy decisions.

Many commercial forecasting models include changes in the risk structure of interestrates to predict future trends in economic activity. When you think about it, this applica-tion is sensible: Risk premiums reflect the difference between the yields of a corporateinstrument and a Treasury instrument of similar maturity. They also include assessmentsof the underlying risk structure—that is, the contribution of default risk, liquidity, infor-mation costs, and taxation—to the yields required on different types of securities.

For example, increases in risk premiums may reflect market participants’ anticipationof periods of difficulty in servicing debt obligations because of, for example, lowerexpected future profits. Analysts have successfully used increases in the risk premium ofcertain broad classes of securities, such as the Baa bond and Treasury bond yield differen-tial or the commercial paper and Treasury bill yield differential, to forecast business reces-sions (in which the likelihood of default increases). The National Bureau of EconomicResearch, an independent research organization that is responsible for determining theonset of recessions in the United States, uses risk premiums in formulating its leading indi-cators of future economic activity and for forecasting when a recession will begin or end.Private forecasters widely use these measures to advise financial and business clients.

Term Structure of Interest RatesLet’s now turn our attention to variations in yields among instruments with commondefault risk, liquidity, information cost, and taxation characteristics but with differentmaturities. The variation in yield for related instruments that differ in maturity is


Will a Consumption TaxKill Munis’ Allure?In late 1994 and through 1995, talkof tax reform swept through Washing-ton. House Majority Leader DickArmey introduced a flat tax, whichwould replace the current individualincome tax with a flat-rate tax onwage and salary income. SenatorsSam Nunn and Pete Domenici intro-duced a plan to allow individuals anunlimited deduction for funds savedrather than spent. These plans andmany other variants share a commontheme: they are taxes on consump-tion, not income. They exempt fromtaxation returns to savings—interest,dividends, and capital gains.

As serious discussion of the proposalsbegan, financial market participantsconsidered the effects of tax reformon the prices and yields of differenttypes of bonds. Under the income tax,interest income from municipal bondsis exempt from federal, state, andlocal taxation. As a result of thatexemption, yields on municipal bondswere lower than those on comparabletaxable bonds. If all forms of interestincome were exempt from taxation,then munis would lose their relativetax preference. The prices of existinghigher-yield currently taxable bondswould rise—and yields would fall—while muni prices would fall—andyields would rise.

Analysts warned municipal bond buy-ers of this prospect in 1995 and early1996, though investors’ demand formunis remained healthy. What wasgoing on? One possibility is thatinvestors did not believe that thesetax changes would be enacted.

Municipal bond investors worriedagain in 2003 when President GeorgeW. Bush proposed to eliminate fed-eral income taxes that equity in-vestors pay on dividends. That changewould have improved the relativeattractiveness of stocks, therebysomewhat raising required returns onmunicipal bonds.

C O N S I D E R T H I S . . .

known as the term structure of interest rates. Because the risk-structure factors can beheld constant most easily for U.S. government obligations, term structure is usuallydefined with respect to yields on those securities.

To obtain information about investors’ expectations of future credit market condi-tions, market analysts often study the yields to maturity on different default-risk-freeinstruments as a function of maturity. The graph of this relationship is known as a yieldcurve. In principle, yield curves can have three shapes. They can be upward sloping,flat, or downward sloping. An upward-sloping yield curve tells us that long-term yieldsare higher than short-term yields. When a yield curve is flat, short-term and long-termobligations have the same yield. If short-term yields are higher than long-term yields,the yield curve is downward sloping. The yield curve in The Wall Street Journal con-tains valuable information for savers and borrowers.

Since World War II, yield curves for U.S. Treasury securities have exhibited a typi-cal slope and position. First, while not the case for the yield curve shown in “Using theNews . . . ,” the shape of the yield curve is usually upward sloping, showing that long-term yields are generally higher than short-term yields. Second, yields on default-risk-free instruments with different maturities typically move together, increasing ordecreasing collectively. Hence the yield curve typically shifts up or down rather thanchanging its shape. Understanding the patterns and position can help you to use yieldcurves to forecast economic variables such as interest rates and inflation rates.

Economists have advanced three theories to explain the appearance of the yieldcurve: the segmented markets theory, the expectations theory, and the preferred habi-tat theory. How can we judge these theories? Two criteria help. First is logical consis-tency: Does the theory offer an internally consistent model of financial markets thatexplains real-world events? Second is predictive power: How well does the theoryexplain actual data on yield curves?

Segmented Markets Theory

The segmented markets theory holds that the yield on each instrument, from three-month T-bills to two-year notes to 30-year bonds, is determined in a separate market,


Asian Flu for European Bonds?A well-functioning corporate bond mar-ket gives investors information aboutrisk premiums on corporate debtinstruments. Until 1994, very few riskybonds for European companies wereissued and traded. As those bondsbecame more popular in the late1990s, many European firms gainedaccess to public debt markets, fre-quently lowering their cost of capitalrelative to bank loans or new equityissues. Europe’s “non-investment-grade” bond sector picked up steam fortwo reasons—the impending European

monetary union and the low transac-tions costs made possible by activedebt markets.

Beginning in late 1997, the Asian finan-cial crisis reduced the appetite for risktaking by investors around the world.When Russia defaulted on its domesticbond obligations in August 1998,investors fled the debt of risky firms—even in Europe and the United States—as they stampeded to buy U.S. Treasuryobligations. As illustrated in Fig. 7.1, theshift away from European non-investment-grade debt lowered bondprices and raised bond yields and thecost of borrowing for European firms.

The high yields began attracting in-vestors in late 1998 and early 1999, asEurope-based bond funds grew in pop-ularity. Some observers have notedthat getting precise information aboutdifferences in default risk, liquidity, andinformation costs from the risk struc-ture of corporate bond yields in Europeremains difficult. Investors are awaitingmore increased coordination ofaccounting standards and the activitiesof rating agencies in Europe. Asian fluor no, optimists predict greater growthin the European non-investment-gradebond market in the new century’s firstdecade than in the U.S. counterpart.

O T H E R T I M E S , O T H E R P L A C E S . . .

Web Site Suggestions:http://quote.yahoo.com/m1?uhttp://www.federalreserve.gov/releasesOffer data on Treasuryyields.http://stockcharts.com/Charts/YieldCurve.htmlIllustrates the yieldcurve.

web_links142.html

with a separate market demand and supply. An assumption of this theory is that bor-rowers have particular periods for which they want to borrow and that lenders haveparticular holding periods in mind. For example, individuals may want to match matu-rities and holding periods because they are saving for retirement or their children’s edu-cation. By doing so, they know exactly what their nominal return is. Or borrowers mayhave a particular period in mind because they know that a business investment projectwill pay off over 20 years and the business wants to match its debt repayments with itsexpected revenues. Under the segmented markets theory, borrowers and lenders areunwilling to move from one market to another, and therefore obligations with differ-ent maturities are not substitutable.

According to the segmented markets theory, the yield in each market reflects onlydemand and supply in that market. The yield curve is plotted from supply and demandbehavior in each market for a specific type of security, and it represents many smalldemand and supply decisions. An upward-sloping yield curve implies that the demandfor short-term bonds is high relative to that for long-term bonds. As we showed in Chap-ter 4, this demand exerts upward pressure on the price and downward pressure on theyield for short-term bonds. A flat yield curve implies that demand and supply conditionsare similar in the various markets. A downward-sloping yield curve implies a higherdemand for long-term bonds relative to that for short-term bonds.

Does this theory pass the first test of explaining the slope of the yield curve?Because upward-sloping yield curves are most prevalent in post–World War II data forthe United States, the segmented markets theory suggests that investors generally preferto hold short-term bonds rather than long-term bonds. Therefore the theory canexplain upward-sloping yield curves as long as investors prefer short-term instruments.



How to Read the Yield CurveEach day in its “Money and Investing”section, The Wall Street Journal plotsthe yield curve for U.S. Treasury securi-ties. The numbers on the horizontal axisindicate the maturity, ranging fromthree months (Treasury bills) to 30years (Treasury bonds). The numberson the vertical axis indicate yields tomaturity at the end of the previoustrading day. Comparing the current andone-month-ago yield curves, we seethat the general level of yields beyondsix months rose, though more forintermediate-term and long-terminstruments. In addition, there is con-siderable variation in yields by maturity.The yield curve slopes up over therange from six months to 30 years,though it is flat for short maturities.

Should you invest in short-term Trea-sury bills because their yield is higherthan that of long-term Treasury

bonds? We answer this question aswe discuss the term structure of inter-est rates.

Treasury Yield CurveYields to maturity of current bills,notes and bonds.

1.0

0.0

2.0

3.0

4.0

5.0%

31 6 2 5 10 30month(s) years

maturity

Yesterday

1 Month Ago

I Year Ago

Source: The Wall Street Journal, July 24, 2003. Republished by permission of Dow Jones, Inc. viaCopyright Clearance Center, Inc. © 2003 Dow Jones and Company, Inc. All Rights Reserved Worldwide.


Does this theory pass the second test of explaining the data for yield curves? As wejust noted, under the segmented markets theory, demand for a bond typically falls asthe bond’s maturity increases. In equilibrium, the yields on longer-maturity bondsexceed those on shorter-maturity bonds. The yield curve then slopes upward. Ofcourse, preferences for bonds of different maturities shift on occasion. At times,investors become more willing to hold longer-term bonds. When they do, the equilib-rium yields on those bonds fall, causing the yield curve to flatten or slope downward.

However, the segmented markets theory cannot explain the observation that yieldson different instruments tend to move together. Because the theory claims that onlymarket-specific demand and supply determine yields, the curves could move togetheronly by coincidence.✝ Thus the theory does not explain why an investor would turndown potentially higher returns in other markets in order to meet a particular holding-period preference.

Expectations Theory

In contrast to the segmented markets theory, the expectations theory states that investorsview assets of all maturities as perfect substitutes at the same levels of default risk, liquid-ity, information costs, and taxation. According to this theory, a long-term bond rate equalsthe average of short-term rates covering the same investment period. In addition, it sug-gests that the yield curve slope depends on the expected future path of short-term rates.

Let’s begin with an example of how you can infer expectations of future short-termrates from current long-term rates. Suppose that the interest rate on a one-year bond is6%, the interest rate on a two-year bond is 7%, the interest rate on a three-year bondis 8%, and the interest rate on a four-year bond is 9%. Figure 7.6(a) shows thisupward-sloping yield curve. The simple description of the expectations theory tells youhow to infer the (unobservable) expectations of future short-term interest rates from


Maturity (years)

9

8

7

6

5

4

1 2 3 4Maturity (years)

9

8

7

6

5

4

Maturity (years)

1 2 3 4 1 2 3 4

One-year rates are expected to remain constant.

One-year ratesare expected to fall.

One-year ratesare expected to rise.

9

8

7

6

5

4

i (%

)

(a) (b) (c)

i (%

)

i (%

)

Using the Yield Curve to Predict Interest Rates: The Expectations TheoryUnder the expectations theory, the slope of the yield curve shows that future short-term interest rates are expected to (a) rise, (b) remain thesame, or (c) fall relative to current levels.

FIGURE 7.6

✝ Technically, the segmented markets theory can explain the up and down movements in the yield curve ifthere are movements into and out of the bond market at all maturities. This occurrence certainly would becoincidental.

this yield curve. The two-year rate (7%) is an average of the current one-year rate (6%)and the expected future one-year rate,✝ or

The expected future one-year rate then is 2(7%) � 6% � 8%.Similarly, you can infer the expected future one-year rate two periods from now by

looking at the three-year bond rate. That rate should be the average of the current one-year bond rate (6%), the expected one-year rate one year ahead (just calculated to be8%), and the expected one-year rate two years ahead, or

The expected one-year rate two years ahead is 10%. Finally, you can infer the expected one-year rate three years ahead, which is 12%.✝✝ Under the expectationstheory, when short-term rates are expected to rise, the yield curve slopes up.

Figure 7.6(b) shows a flat yield curve, in which the yields on one-year, two-year,three-year, and four-year bonds all are 6%. Thus, under the expectations theory, youcan infer that one-year rates will remain unchanged at 6% for the next three years.Under the expectations theory, when short-term rates are expected to remainunchanged, the yield curve is flat.

Figure 7.6(c) shows a downward-sloping yield curve in which the yields are 6% forthe one-year bond, 5.5% for the two-year bond, 5% for the three-year bond, and 4.5%for the four-year bond. What would you expect future one-year rates to be one, two,and three years from now? The two-year bond rate is an average of the current one-year rate (6%) and the expected future one-year rate, or

The expected one-year rate one year from now is 5%. The expected one-year rate twoyears from now can be found from the following:

Rate on three-year bonds

The one-year rate that you can infer for two years from now is 4%. Using the sameapproach, you can find the expected one-year rate three years from now:

Rate on four-year bonds �

6% � 5% � 4% � Expected one-yearrate three years ahead

4� 4.5%.

�

6% � 5% � Expected one-year ratetwo years ahead

3� 5%.

6% � Expected future one- year rate one year ahead

2� 5.5%.

6% � 8% � Expected one- year rate two years ahead3

� 8%.

6% � Expected future one- year rate one year ahead2

� 7%.


✝ This arithmetic average is an approximation to the more precise answer, which is the geometric mean of thecurrent and expected future rates.✝✝ Here

so the expected one-year rate three years ahead is 12%.

6% � 8% � 10% � Expected one- year rate three years ahead

4� 9%,

The one-year rate that you can infer for three years from now is 3%. Under the expec-tations theory, when short-term rates are expected to fall, the yield curve slopes down.

We can generalize from these examples. The perfect substitutability assumption ofthe expectations theory implies that expected returns for a given holding period must bethe same for bonds of different maturities. Otherwise, investors would change their rela-tive demand for instruments with different maturities to take advantage of differences inyields. In addition, the perfect substitutability assumption implies that the yield on a long-term bond will equal an average of expected short-term yields over the life of the bonds.Why? Take a holding period of, say, 10 years. If all instruments are perfect substitutes,investors should get the same expected return from holding a 10-year bond, a sequenceof five two-year notes, a sequence of 40 three-month bills, and so on. Under this theory,if the long-term yield is higher than the short-term yield, investors should expect short-term rates to increase over the 10-year period.

Let’s further clarify the prediction of the expectations theory about relationshipsamong yields on bonds with different maturities. Suppose that you are considering twostrategies for a two-year investment, where i is the interest rate of the bond:

Buy-and-hold strategy Roll-over strategyBuy a two-year bond and hold it Buy a one-year bond today and hold it until maturity. until maturity. The interest rate The interest rate today is i1t . After the one-year bondtoday is i2t, where t represents matures (t � 1), buy another one-year bond and holdthe time period. it until maturity. The precise interest rate on that bond

is unknown. As of today, we expect that it will be ie1,t �1, where e represents expectation.

What are the expected returns on a $1 investment after two years for each strat-egy? If you buy and hold, your $1 is worth after the first year and

after two years. Under the roll-over strategy, your $1 is worthafter the first year, and as you expect to earn ie

1,t�1 on a one-year bond inthe second year, your initial $1 will be worth the following: .

Under the expectations theory, the two instruments are perfect substitutes. There-fore their expected net returns over the two-year holding period must be equal:

Simplifying, we get

Because the product of the two interest rates is small, we can ignore it. (Note, forexample, that if i � 0.08, then i2 � 0.0064, and the i22t and i1t(i

e1,t�1) terms can be

ignored.) With that approximation, the yield on the two-year bond is an average ofthe expected yields on the two one-year bonds:

(7.1)

More generally, for an n-period bond, a more precise statement of the expectations the-ory is

i2t �i1t � i1, t�1

e

2.

2i2t � i22t � i1t � ie1, t�1 � i1t1ie1, t�12.

11 � i2t2 11 � i2t2 � 1 � 11 � i1t2 11 � ie1, t�12 � 1.

$11 � i1t2 11 � i e1, t�12

$11 � i2t2$11 � i2t2 11 � i2t2

$11 � i2t2


The n-period bond yield is an average of the expected short-term yields over the life ofthe bond.

Unlike the segmented markets theory, the expectations theory attributes the slopeof the yield curve to market expectations, based on the assumption that instrumentswith different maturities are perfect substitutes. A flat yield curve means that marketparticipants expect future short-term rates to be the same as current short-term rates,making current short-term rates and long-term rates (the average of expected futureshort-term rates) equal. A downward-sloping yield curve means that investors believethat short-term rates will decline in the future relative to current levels. Finally, anupward-sloping yield curve reflects expectations that short-term rates will be higher inthe future, thereby increasing long-term rates today.

How successful is this theory at explaining actual patterns in yield curves? In con-trast to the segmented markets theory, the expectations theory offers a logically con-sistent explanation of movement together by interest rates on bonds of differentmaturities. For the post–World War II period, movements in U.S. interest rates havebeen persistent; that is, increases (or decreases) in short-term rates tend to continue formany periods. An increase in short-term rates today increases expected future short-term rates and current long-term rates. Hence the expectations theory can explainmovement together by short-term and long-term interest rates.

However, the expectations theory does not explain well the general pattern of anupward-sloping yield curve. If we interpreted the theory strictly, an upward-slopingyield curve would mean that short-term interest rates are expected to rise always. Thispattern is inconsistent enough with actual experience to warrant skepticism. Nonethe-less, the theory offers a logically consistent foundation for explaining investors’ deci-sions and comovements of interest rates.

Preferred Habitat Theory

Neither the segmented markets theory nor the expectations theory provides a completeexplanation of the yield curve. Essentially, their shortcomings arise from the extremeposition that each takes. Under the segmented markets theory, investors view maturi-ties as completely unsubstitutable; under the expectations theory, investors view matu-rities as perfect substitutes. A third theory, the preferred habitat theory, seeks a middleground and thus is able to explain the shape of the yield curve.

The preferred habitat theory holds that investors care about both expected returnsand maturity; they view instruments having different maturities as substitutes—but not

in, t �i1t � ie1, t�1 � ... � ie1i, t�n�1

n .


Use the expectations theory to answer the following question. Studying The WallStreet Journal, you notice that the yield curve slopes upward: Yields on 10-yearTreasury bonds are greater than those on three-year notes, which are in turngreater than those on six-month bills. As all Treasury securities have the samedefault risk, liquidity, information costs, and tax treatment, should you invest allyour money in the 20-year bonds? No. Under the expectations theory, the long-term bond rate is just the average of the expected future short-term rates. You wouldnot earn a higher expected return by holding long-term rather than intermediate-termor short-term Treasury instruments. ♦

C H E C K P O I N T

perfect substitutes. Specifically, investors prefer shorter to longer maturities, as in thesegmented markets theory. That is, investors have a preferred maturity, called a habi-tat, but they can be induced to purchase other securities. As a result, investors will notbuy a long-term bond if it offers the same yield as a sequence of short-term bonds.Instead, investors require something extra, a term premium, to compensate them forinvesting in a less preferred maturity. An example helps to illustrate this point.

Suppose that one-year bonds currently yield 6% but are expected to yield 8% nextyear. Would investors be just as happy buying a two-year bond yielding 7%? The two-year bond offers the same yield as the average of two one-year bonds. But as investorsprefer to buy one-year bonds, they must be given an even higher yield—say, 7.5%—tolure them into the less desirable two-year maturity. If they are offered only 7%, theywill choose the one-year bonds. The additional 0.5% that is needed to make the two-year bonds competitive is the term premium.

Let’s generalize this example to compare the predictions of the expectations theoryand the preferred habitat theory. Let i represent yields as before, n the number of peri-ods until maturity, and h (habitat) the term premium for the particular maturity. Underthe preferred habitat theory, the interest rate on an n-period bond (approximately)equals the average of expected future one-period yields over the life of the bond plus aterm premium for that maturity. In general, then, the preferred habitat theory predictsthat the yield on an n-period bond is

(7.2)

Under the expectations theory, assets are perfect substitutes; there are no habitats,and h is always zero. The term premium hn,t is not a constant under the preferred habi-tat theory. Data for post–World War II U.S. financial markets reveal, on average, apositive term premium for longer-term securities. Because shorter maturities are pre-ferred to longer maturities, hn,t increases as a bond’s maturity increases. Thus the pre-ferred habitat theory predicts a built-in upward slope in the yield curve, regardless ofthe expected path of short-term rates—an important correction of the strictly inter-preted expectations theory. Thus the shape of the yield curve depends on both theexpected path of short-term rates and the size of the term premium at each maturity.

Under the preferred habitat theory, then, a flat yield curve reflects an expectation ofslightly falling future short-term rates, because of the built-in upward tilt in the yieldcurve. An upward-sloping yield curve reflects a smaller expected increase in future short-term rates than it does under the expectations theory. A downward-sloping yield curvereflects a more significant expected decline in future short-term rates than the expecta-tions theory predicts. As with the expectations theory, the slope of the yield curve underthe preferred habitat theory provides information on market expectations about futureshort-term rates. The preferred habitat theory is logically consistent and explains boththe usual pattern of an upward-sloping yield curve and the movement together by yieldson bonds having different maturities.

Table 7.3 summarizes the segmented markets theory, the expectations theory, andthe preferred habitat theory.

Using the Term Structure for Forecasting

Investors, businesspeople, and policymakers also use information contained in the termstructure of interest rates for forecasting. Under the expectations and preferred habitat

in, t �i1t � ie1, t�1 � . . . � ie

1, t�n�1

n � hn, t .


theories, the slope of the yield curve provides information about market participants’expectations about future short-term nominal interest rates. In addition, if fluctuationsin expected real interest rates are small, the yield curve provides information aboutexpectations of future inflation rates. Suppose that you want the financial markets’ bestguess about the rate of inflation in five years. If the real interest rate is expected toremain constant, you can interpret an upward-sloping yield curve to mean that infla-tion is expected to rise. Indeed, the Fed and many financial market participants use theyield curve to forecast future inflation. Economists and market participants also lookto the slope of the yield curve for information on the likelihood of a recession. Whenshort-term rates are higher than long-term rates, the yield curve is said to be“inverted.” (Remember that the yield curve is generally upward sloping.) CampbellHarvey of Duke University found that, since the mid-1950s, inverted yield curves(specifically, a three-month Treasury bill yield higher than a 10-year Treasury bondyield) have generally predicted recessions four to five quarters hence. More generally,Michael Dotsey of the Federal Reserve Bank of Richmond concluded that the slope ofthe yield curve is a useful leading indicator of economic activity.✝

Figure 7.7 shows three yield curves: one that slopes downward, one that slopesupward slightly, and one that slopes upward steeply. If we apply the preferred habitattheory, these three yield curves—representing three points in time between 1989 and1991—tell a story about financial markets’ expectations and the economy.

The top yield curve characterizes the term structure in the spring of 1989. Thebelief that the Fed would pursue a policy to reduce inflation led market participants toexpect that future short-term rates would be lower than current short-term rates. Thepreferred habitat theory of the term structure suggests that long-term rates should fallrelative to short-term rates. In this case, the yield curve actually is inverted from the normalupward-sloping case.


Theories of the Term Structure

Theory Assumes . . . Predicts . . . Evaluation . . .

Segmented markets Maturities are not Yields on different Explains shapes of the yieldsubstitutable; maturities are determined curve but not why short-shorter maturities are in separate markets term and long-term ratespreferred to longer move togethermaturities

Expectations Maturities are perfect Yield on an n-period bond Explains why short-termsubstitutes equals the average of and long-term rates move

yields on one-period bonds together but not the usualover the next n periods of upward slopethe yield curve

Preferred habitat Maturities are Yield on an n-period bond Explains both the shapes ofsubstitutable but not equals the average of the yield curve and whyperfectly yields on one-period bonds short-term and long-term

over the next n periods rates move togetherplus a term premium

TABLE 7.3

✝ Campbell R. Harvey, “The Real Term Structure and Consumption Growth,” Journal of Financial Eco-nomics 22 (1988). Michael Dotsey, “The Predictive Content of the Interest Rate Term Spread for Future Eco-nomic Growth,” Federal Reserve Bank of Richmond, Economic Quarterly 84 (Summer 1998): 31–52.


Can the Treasury Changethe Shape of the YieldCurve?In January 2000, the U.S. TreasuryDepartment announced that it plannedto decrease the average maturity ofoutstanding U.S. Treasury debt by cur-tailing sales of long-term bonds, partic-ularly 30-year bonds. In May 1993, ithad made a similar announcement,with a larger-than-anticipated reductionin the government’s issuance of long-term bonds being accompanied by anincrease in issuance of short-term debt.The situation in 2000 was somewhatdifferent, as federal budget surplusespermitted the Treasury to retire sub-stantial amounts of debt, something ithad not done in many years.

Following the Treasury Department’sannouncement, market yields onintermediate-term and long-term U.S.Treasury securities—especially the 30-year bond—fell substantially betweenmid-January and late February 2000.Some market participants argued thatthe yield changes reflected supply anddemand. Investors with long-term com-mitments, such as pension funds, buy

long-term U.S. Treasury securities tohedge future liabilities. To the extentthat those investors’ increased pur-chases of securities anticipating lowerfuture supply, long-term bond priceswere expected to rise, trimming yields.

This version of events reflects the pre-ferred habitat theory of the term struc-ture. That approach argues thatinvestors prefer short-term maturities.Thus the interaction of investor prefer-ences and the supply of Treasury debtat different maturities determines theterm premium needed to attractinvestors. If investor preferences forshorter-term maturities are held con-stant, a reduction in the quantity of 30-year bonds supplied would raise theirprice and reduce their yield.

Alternatively, a drop in yields on long-term securities below yields onshort-term securities would reflect ex-pectations of lower economic activityand inflation, as many forecasters pre-dicted at the time. Implicitly, such astory reflects the perspective of theexpectations theory of the term struc-ture. Under this theory, investors viewshort-term and long-term Treasury obli-

gations as perfect substitutes. As aresult, a relatively low long-term bondrate reflects market participants’ expec-tation of lower short-term interest ratesin the future (as would be the case withan economic slowdown and lowerexpected inflation).

Which story is right? We can use theyield spreads between conventionaland inflation-protected Treasury securi-ties (TIPS) to shed light on inflationaryexpectations and to examine reasonsfor the fall in market yields. Looking atlate January and early February, thespread between 30-year conventionalsecurities and TIPS fell substantially,while yield spreads for 5-year and 10-year securities did not. This divergencesuggests that the behavior of Treasurybond prices in January and February2000 was not dominated by changes inexpected inflation. While yields incor-porate market expectations aboutfuture economic activity and inflation,as predicted by the expectations the-ory, market demand and supply factorscan also affect yields in the short run,as predicted by the preferred habitattheory.

C O N S I D E R T H I S . . .

May 1989

September 1990

January 1991

Inverted yield curve: Higher short-term rates and lowerexpected future inflation

Positive yield curve: Normal shapeunder preferred habitat theory

Steep yield curve: Verylow short-term rates and higher long-term yields

1 30

Inte

rest

rate

(%

)

Year

5 10 202 3 4 6 7

10.0

9.5

9.0

8.5

8.0

7.5

7.0

6.5

6.0

Interpreting the Yield CurveModels of term structure, such asthe preferred habitat theory, helpanalysts use data from The WallStreet Journal as a forecastingtool. Understanding the shape ofthe yield curve makes readingThe Wall Street Journal data moremeaningful.

FIGURE 7.7

The upward slope shown in the middle curve is characteristic of a normal yield curveunder the preferred habitat theory. It characterizes the term structure in the fall of 1990,when the economy was experiencing a recession. However, investors expected that, aseconomic activity increased in the future, the demand for credit would increase, causinginterest rates to increase. In other words, investors expected future short-term rates to riseabove current levels.

The bottom yield curve represents the term structure in early 1991, when the Fedcontinued to reduce short-term rates. However, concerns about inflation and gov-ernment budget deficits kept expected future short-term rates—and hence currentlong-term rates—high. The inflation fears added to the normal upward slope of theyield curve predicted by the preferred habitat theory.


KEY TERMS AND CONCEPTS

SUMMARY

1. There are two ways to categorize the differences ininterest rates on different bonds. The risk structure ofinterest rates describes the variation in yields amongfinancial instruments that have the same time to matu-rity but differences in default risk, liquidity, informa-tion costs, and taxation. The term structure of interestrates distinguishes variation in yields between instru-ments with the same risk, liquidity, information costs,and taxation but different maturities.

2. The default risk premium is the additional return thata saver requires to hold a risky instrument rather thana default-risk-free instrument with the same maturity.Although the major component of differences inyields on instruments of similar maturity is defaultrisk, differences in liquidity, information costs, andtaxation are also important components. U.S. gov-ernment securities serve as a benchmark againstwhich to calculate risk premiums because they aredefault-risk-free, are traded in liquid markets, andhave low information costs. Differential taxation ofreturns on credit market instruments affects their riskpremiums.

3. Because government securities are instruments forwhich default risk, liquidity, information costs, andtaxation can be held constant most easily, the termstructure usually refers to the yields on governmentsecurities. A graph of the yields to maturity on

default-risk-free instruments as a function of maturityis known as a yield curve.

4. The yield curves for contemporary U.S. Treasurysecurities have two typical patterns. First, the yieldcurve usually slopes upward because long-term yieldsgenerally are higher than short-term yields. Second,yields on securities that have different maturitiesoften move together.

5. Economists use three theories to explain the two yieldcurve features. The theories differ in the relativeemphasis placed on expected return or maturity.Under the segmented markets theory, borrowers andlenders want only a particular maturity. This theorycan explain upward-sloping yield curves as long asinvestors have a preference for short-term instru-ments, other factors being held constant. It cannotexplain the observation that interest rates tend tomove together. Under the expectations theory, bor-rowers and lenders care only about getting the highestexpected return; instruments with different maturitiesare perfect substitutes. The expectations theoryimplies that the interest rate on a long-term bond is anaverage of expected future short-term rates. Thisapproach can explain comovement of interest rates aslong as increases (or decreases) in short-term ratescontinue for many periods. However, an upward-slop-ing yield curve predicts ever-increasing short-term

Risk structure of interest rates

Bond rating

Default risk

Default-risk-free instruments

Default risk premium

Municipal bonds

Term structure of interest rates

Expectations theory

Preferred habitat theory

Segmented markets theory

Term premium

Yield curve

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The U.S. Treasury willattempt to quash specula-tion that historically lowinterest rates and theprospect of chronically bigdeficits will eventually com-pel the Bush administrationto bring back the 30-yearTreasury bond . . . .

A report laying out acomprehensive financialcase in defence of the deci-sion to end issuance, underreview by Treasury andWhite Houses officials, isexpected before earlyNovember. It will arguethat the administration’sdecision in November2001 to end the long bondremains justified.

“Getting rid of the 30-year bond was the rightthing to do. It was anexpensive form of financ-ing,” said a senior adminis-tration official. “We’ll showthat under any scenario—other than a dramaticincrease in inflation thatwould reduce the real costof the 30-year bond—thegovernment is better off.”

Critics say the govern-ment is trading lower inter-est costs today for greater“rollover risk” tomor-

row—or more exposure tofuture jumps in interestrates. . . .

The Treasury paper willargue that the governmentdoes not try to “time” thefinancial markets; that itsborrowing should be regu-lar and predictable; and thatshorter-term debt has his-torically been cheaper thanlong-term debt.

The report will alsomake clear that the decisionto end the 30-year bond waswidely supported within theTreasury, and will not beaffected by the departure ofPeter Fisher, Treasury under-secretary for domesticfinance. . . .

The administration po-tentially faces disappointingtax revenues and an array ofmassive drains on the Trea-sury. Such expenses includepotentially permanent taxcuts, escalating healthcareand pension costs, expen-sive new prescription drugbenefits, reform of the alter-native-minimum tax, Iraqireconstruction, and the waragainst terrorism.

“We are entering aperiod of chronic budgetdeficits, so it really makes

sense to revisit the 30-yearbond issue,” said Bill Dud-ley, head of economicresearch at Goldman Sachs.. . .

But momentum forreexamining the 30-yearbond is growing.

“If you took the pastprojections of surplusesseriously . . . taking the 30-year bond off the table [in2001] clearly was a veryreasonable [decision],”said Alan Greenspan, Fed-eral Reserve chairman,during a congressionalhearing last week. “Timeshave changed. Presumablythis issue will be revisited.”. . .

“There are lots ofoptions before we get tobringing back the bond,”including more issuance ofshorter-dated debt, saidMarcello Frustaci, govern-ment bond trader atMizuho Securities. . . .

Total new Treasuryissuance is likely to reach$89bn in the third quarter,up 134 per cent on thesame period last year,according to the BondMarket Association.

FINANCIAL TIMES JULY 22, 2003

Bring Back the Long Bond?

a

b

c

M O V I N G F R O M T H E O R Y T O P R A C T I C E . . .M O V I N G F R O M T H E O R Y T O P R A C T I C E . . .


In a surprise move that sent a shock-wave throughout the bond market, theU.S. Treasury Department announcedon October 31, 2001 that it would nolonger sell 30-year bonds, for manyyears the benchmark for the entiremultitrillion-dollar U.S. bond market.Yields on the 30-year bond fell from5.25% to 4.88% over the day, asinvestors bought the now-scarcerbonds; yields on the new benchmark10-year note fell, too. In part, Treasuryofficials argued that the long-term out-look for the federal budget remainsupbeat, and borrowing through 30-year bonds was costly. The Treasury’sdecision, announced by Undersecre-tary Peter Fisher, shocked some mar-ket participants who had bet thathomeland security spending after theSeptember 11 tragedy would lead tomore, rather than less, issuance of the30-year bond. Many economistsargued that the rising price of the“long bond”—the nickname of the 30-year bond—would give a boost tohousing and capital spending, whichwould be less costly with lower yields.

The reaction of the bond market mayhave surprised the Treasury, as theofficial statement had simply notedthat: “The 30-year bond no longermaintains a position of significance inthe financial markets.”

To the extent that the segmentedmarkets theory or preferred

habitat theory of the term structureare the Treasury’s view, officials maybelieve that lower interest rates ondebt maturities of less than 30 yearswould reduce the federal government’sborrowing costs.

But the expectations theory sug-gests that the gap between 30-

year yields and shorter yieldsrepresents higher expected borrowingcosts in the future as the debt is rolledover. The government is substitutinglower interest costs in the present formore substantial rollover risk. An anal-ogy would be a homeowner electing ashorter-term adjustable-rate mortgageover a longer-term fixed-rate mort-gage when interest rates may beincreasing in the future.

With higher federal budgetdeficits and borrowing require-

ments over the next several years,some analysts implicitly urge the Trea-sury to bring back the “long bond” tolock in currently low borrowing costs.To bolster that case, those analystsoften argue that foreign and institu-tional investors would be eager buy-ers, offering a premium for a long-termdefault-risk-free instrument.

For further thought . . .

If the public had expectations of long-term inflation that were persistentlytoo high, would you advise the Trea-sury to reissue the 30-year bond?Explain.

Source: Peronet Despeignes and Jenny Wiggins, “Treasury to DefendDropping Its Long Bond,” Financial Times, July 22, 2003. Copyright© 2003, Financial Times. Reprinted with permission.

a

b

c

A N A L Y Z I N G T H E N E W S . . .A N A L Y Z I N G T H E N E W S . . .


REVIEW QUESTIONS

1. A yield curve shows the relationship between themarket interest rates on bonds that are identicalexcept in what aspect?

2. What is the term structure of interest rates?

3. According to the expectations theory of the termstructure of interest rates, what happens to long-terminterest rates when short-term interest rates areexpected to fall in the future?

4. When does the yield curve slope upward, accordingto the expectations theory? According to the seg-mented markets theory? According to the preferredhabitat theory?

5. Why does the yield curve often slope slightly upward,according to the preferred habitat theory?

6. What theory is being used by analysts who examinethe demand for and supply of funds at differentmaturity levels to predict the term structure of inter-est rates?

7. Why is the interest rate on a U.S. Treasury bond usu-ally less than that on a corporate bond?

8. What factors affect the interest rate that is paid on abond?

9. Does a taxable bond or a tax-free bond pay a higher before-tax interest rate?

10. If the risk premium on a corporate bond increases,does its interest rate necessarily rise? In answeringthis question, be sure to define “risk premium.”

11. At the start of the recession in 1990, interest rates onlower-rated corporate bonds rose relative to the inter-est rate on Treasury bonds. Why did this happen?What is this phenomenon called?

12. Would you expect the yield on a six-month Treasurybill to be higher or lower than that on commercialpaper of comparable maturity? Why?

13. Describe factors that affect the difference between a10-year General Motors bond and a 10-year U.S.Treasury bond. What additional factors would youconsider in explaining the difference between a 10-year junk bond and a 10-year U.S. Treasury bond?

14. Suppose that the risk premiums on new issues of cor-porate bonds and commercial paper increase. Explainhow the shifts would affect your guess about the like-lihood of an economic downturn in the near future.

15. During the late 1970s Michael Milken convincedmany investors that the yields on junk bonds morethan compensated for their higher default risk. Whatdo you think happened to the liquidity of these bondsas a result?

16. Why are credit market instruments with high infor-mation costs often illiquid?

rates, casting doubt on the theory in its simplest form.The third approach is a hybrid of the first two theo-ries and is based on the assumption that investorscare about both maturity and expected returns.Known as the preferred habitat theory, it describesthe interest rate on a long-term bond as an average ofexpected future short-term rates over the life of thebond plus a term premium. The term premium isaffected by demand for and supply of the specificmaturity. With an investor preference for short-terminstruments (all other factors being equal), the yieldcurve slopes upward even if short-term rates are notexpected to rise.

6. The risk and term structures of interest rates containimportant information about expectations of futureeconomic variables and, for that reason, are usefulfor forecasting. Because risk premiums reflect expec-tations about default risk, they are good predictors offuture levels of economic activity and the ability offirms to meet debt obligations. Under the expecta-tions theory and preferred habitat theory, the termstructure includes expectations of future short-termrates in current long-term rates. If real interest ratesare expected to be constant over the long run, theterm structure may contain information aboutexpected future rates of inflation.

QUIZ

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17. Suppose that interest rates for one-year bonds areexpected to follow this pattern: 3% today, 5% oneyear from now, and 7% two years from now. Whatare the current interest rates on two-year and three-year bonds, according to the expectations theory?

18. Suppose that an investor wants to invest for three yearsto get the highest possible return. The investor has threeoptions: (a) roll over three one-year bonds, which payinterest rates of 8% in the first year, 11% in the secondyear, and 7% in the third year; (b) buy a two-year bondpaying 10% today, then roll over the amount receivedwhen that bond matures into a one-year bond paying7%; or (c) buy a three-year bond today paying 8.5%.Assuming annual compounding and no transactionscosts, which option should the investor choose?

19. Suppose that you have $1000 to invest in the bondmarket on January 1, 2004. You could buy a one-year bond paying 4%, a two-year bond paying 5%,a three-year bond paying 5.5%, or a four-year bondpaying 6%. You expect interest rates on one-yearbonds in the future to be 6.5% on January 1, 2005,7% on January 1, 2006, and 9% on January 1,2007. You want to hold your investment until Janu-ary 1, 2008. Which of the following investmentalternatives gives you the highest expected return by2008: (a) buy a four-year bond today; (b) buy athree-year bond today and a one-year bond in 2007;(c) buy a two-year bond today, a one-year bond in2006, and another one-year bond in 2007; or (d) buya one-year bond today and then additional one-yearbonds in 2005, 2006, and 2007?

20. Answer Problem 19 if a $10 transactions cost isadded for every bond you purchase. In other words,if you have $1000 now, you can buy a bond only for$990, as $10 goes for the transactions cost. Which setof bonds should you buy?

21. In June 1981, the yield curve sloped downward, andin June 1984, the yield curve sloped upward. Inter-pret these slopes according to the expectations theory.

22. Suppose that short-term interest rates fall duringrecessions and rise during expansions. What wouldyou expect the slope of the yield curve to be (accord-ing to the expectations theory) when (a) the economyis at a peak and a recession is beginning; (b) the econ-omy is midway between a peak and a trough; (c) theeconomy is in a trough, and an expansion is begin-

ning; and (d) the economy is midway between atrough and a peak?

23. In the spring of 1999 it was unclear whether theJapanese economy was expanding or whether itwould fall into deeper recession. If it began toexpand, then inflation was likely to increase. If it fellinto deeper recession, then government borrowingwas likely to increase. The Wall Street Journal quotedone analyst as arguing: “Either way, the yield curvewill steepen.” Explain his reasoning.

24. Suppose the presidential election in the year 2004 iswon by a candidate who runs on a platform of “soakthe rich.” After being elected he or she persuadesCongress to raise the top marginal tax rate on the fed-eral personal income tax from 35% to 65%. Use onediagram to show the impact of this change in taxrates on the municipal bond market and another dia-gram to show the impact on the market for U.S. Trea-sury bonds.

25. Suppose that, holding yield constant, investors areindifferent as to whether they hold bonds issued bythe federal government or bonds issued by state andlocal governments (that is, they consider them to havethe same degree of default risk and liquidity). Sup-pose that state governments have issued perpetuities(or consols) with $75 coupons and the federal gov-ernment has also issued perpetuities with $75coupons. If the state and federal perpetuities bothhave after-tax yields of 8%, then what are their pre-tax yields? (Assume for purposes of this problem thatthe relevant federal income tax rate is 39.6%.)

26. Suppose that your marginal federal income tax rateis 40%. What is your after-tax rate of return fromholding to maturity a one-year municipal bond withan 8% yield? What is your return from holding tomaturity a one-year corporate bond with a 10%yield? If both securities had the same default risk andliquidity, which would you prefer to own?

27. If you looked at the data on interest rates, you wouldsee less difference between rates on U.S. governmentbonds and municipal bonds in the 1980s than earlier.Why do you think this happened?

28. What happens to the yields on junk bonds as the levelof economic activity rises and falls?

ANALYTICAL PROBLEMSQUIZ

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29. You are considering investing in Fred’s Fine FurnitureFactory. It is an expanding firm with fine prospectswhose future looks fabulous. Based on solid informa-tion, your analysis of Fred’s finances shows that thecompany is sound. You decide that the risk of such aninvestment is small relative to other investments andthat the return looks better than average. What otherfactor might be important to your decision aboutinvesting in Fred’s?

30. Some aspects of an asset’s taxability may cause theyield to maturity to be an inaccurate measure ofreturn. Suppose that Bob’s bond was issued someyears ago and has one year left to maturity; it has ayield to maturity of 7%, with a current yield of 3%and an expected capital gain of 4%. Suppose thatBetty’s bond is newly issued and matures in a year,with a yield to maturity equal to the current yield of8%. If you are an investor with a 33% marginal tax

rate on interest income but a 0% tax rate on capitalgains, whose bond would you prefer to own? Why?

31. The Federal Reserve System holds many U.S. govern-ment bonds. When the yield curve slopes upwardsharply, the Fed could earn a higher return by buyinglong-term bonds instead of short-term bonds. Shouldit do so?

32. Under what conditions can you infer expectationsabout future rates of inflation from the yield curve(according to the expectations theory of the termstructure)? Are these conditions more likely to holdfor short or long time periods?

33. Using the expectations theory, explain why a firm thatis borrowing for two years is unlikely to save money(over the two years) by borrowing short-term (and refi-nancing) instead of borrowing long-term when the cur-rent short-term rate is lower than the long-term rate.

DATA QUESTIONS

34. Look at The Wall Street Journal today or sometimethis week and find a plot of the yield curve. (It is aregular feature in Section C.) Compare this plot withthe yield curves on the same date one, two, and threeyears ago. How do the yield curves compare? Canyou use the theories of the term structure of interestrates to explain why the yield curve has changed overtime?

35. The Council of Economic Advisers’ Economic Indica-tors offers historical data on a variety of U.S. interestrates. Browse the most recent issue at http://www.gpoaccess.gov/indicators/browse.html and look at themost recent data given for interest rate and bondyields. Are short rates lower than long term rates?Why? Is there a difference between 30-year Treasurybonds and New Home Mortgage Yields, which alsohave 30-year terms? If so, why is this the case?

36. An upward-sloping yield curve suggests that long-term yields are higher than short-term yields. Com-pare yield information for 5-year Treasury notes withthat of 13-week Treasury bills for the most recentyear. (A good site to find this information would beYahoo! Finance, at http://quote.yahoo.com/m1?u.)Ceteris paribus, was the yield curve during this timeperiod upward sloping? Explain.

37. StockCharts.com depicts a “dynamic yield curve” thatshows shifts in the yield curve, on a daily basis, for thelast several years. Look at this site (http://stockcharts.com/charts/yieldcurve.html). In what months isthe curve upward sloping, flat, or downward sloping?What happened to the yield curve for shorter-term ratesin the months following September 11, 2001? Giventhat many investors got out of the stock market duringthis time period, explain your answer.

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