The economics of Money, Banking and Financial Markets Part 3 ppsx

Three theories have been put forward to explain the term structure of interestrates; that is, the relationship among interest rates on bonds of different maturitiesreflected in yield cur

PREVIEW In our supply and demand analysis of interest-rate behavior in Chapter 5, we

exam-ined the determination of just one interest rate Yet we saw earlier that there are mous numbers of bonds on which the interest rates can and do differ In this chapter,

enor-we complete the interest-rate picture by examining the relationship of the variousinterest rates to one another Understanding why they differ from bond to bond canhelp businesses, banks, insurance companies, and private investors decide whichbonds to purchase as investments and which ones to sell

We first look at why bonds with the same term to maturity have different

inter-est rates The relationship among these interinter-est rates is called the risk structure of

interest rates, although risk, liquidity, and income tax rules all play a role in

deter-mining the risk structure A bond’s term to maturity also affects its interest rate, andthe relationship among interest rates on bonds with different terms to maturity is

called the term structure of interest rates In this chapter, we examine the sources

and causes of fluctuations in interest rates relative to one another and look at a ber of theories that explain these fluctuations

num-Risk Structure of Interest Rates

Figure 1 shows the yields to maturity for several categories of long-term bonds from

1919 to 2002 It shows us two important features of interest-rate behavior for bonds

of the same maturity: Interest rates on different categories of bonds differ from oneanother in any given year, and the spread (or difference) between the interest ratesvaries over time The interest rates on municipal bonds, for example, are above those

on U.S government (Treasury) bonds in the late 1930s but lower thereafter In tion, the spread between the interest rates on Baa corporate bonds (riskier than Aaacorporate bonds) and U.S government bonds is very large during the GreatDepression years 1930–1933, is smaller during the 1940s–1960s, and then widensagain afterwards What factors are responsible for these phenomena?

addi-One attribute of a bond that influences its interest rate is its risk of default, which

occurs when the issuer of the bond is unable or unwilling to make interest paymentswhen promised or pay off the face value when the bond matures A corporation suf-fering big losses, such as Chrysler Corporation did in the 1970s, might be more likely

Default Risk

Chap ter

The Risk and Term Structure

of Interest Rates6

to suspend interest payments on its bonds.1 The default risk on its bonds wouldtherefore be quite high By contrast, U.S Treasury bonds have usually been consid-ered to have no default risk because the federal government can always increase taxes

to pay off its obligations Bonds like these with no default risk are called default-free

bonds (However, during the budget negotiations in Congress in 1995 and 1996, the

Republicans threatened to let Treasury bonds default, and this had an impact on thebond market, as one application following this section indicates.) The spread between

the interest rates on bonds with default risk and default-free bonds, called the risk

premium, indicates how much additional interest people must earn in order to be

willing to hold that risky bond Our supply and demand analysis of the bond market

in Chapter 5 can be used to explain why a bond with default risk always has a tive risk premium and why the higher the default risk is, the larger the risk premiumwill be

posi-To examine the effect of default risk on interest rates, let us look at the supply anddemand diagrams for the default-free (U.S Treasury) and corporate long-term bondmarkets in Figure 2 To make the diagrams somewhat easier to read, let’s assume thatinitially corporate bonds have the same default risk as U.S Treasury bonds In thiscase, these two bonds have the same attributes (identical risk and maturity); their

equilibrium prices and interest rates will initially be equal (P c

1 P T and i c

1 i T),

and the risk premium on corporate bonds (i c

1 i T) will be zero

F I G U R E 1 Long-Term Bond Yields, 1919–2002

Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15/data/.

16 14 12 10 8 6 4 2 0

State and Local Government (Municipal)

U.S Government Long-Term Bonds Corporate Baa Bonds

Annual Yield (%)

Corporate Aaa Bonds

1940 1930 1920

The Federal Reserve reports the

returns on different quality

bonds Look at the bottom of

the listing of interest rates for

AAA and BBB rated bonds

Study Guide Two exercises will help you gain a better understanding of the risk structure:

1 Put yourself in the shoes of an investor—see how your purchase decision would

be affected by changes in risk and liquidity

2 Practice drawing the appropriate shifts in the supply and demand curves whenrisk and liquidity change For example, see if you can draw the appropriate shifts

in the supply and demand curves when, in contrast to the examples in the text,

a corporate bond has a decline in default risk or an improvement in its liquidity

If the possibility of a default increases because a corporation begins to suffer largelosses, the default risk on corporate bonds will increase, and the expected return onthese bonds will decrease In addition, the corporate bond’s return will be moreuncertain as well The theory of asset demand predicts that because the expectedreturn on the corporate bond falls relative to the expected return on the default-freeTreasury bond while its relative riskiness rises, the corporate bond is less desirable(holding everything else equal), and demand for it will fall The demand curve for

corporate bonds in panel (a) of Figure 2 then shifts to the left, from D c

1to D c

2

At the same time, the expected return on default-free Treasury bonds increasesrelative to the expected return on corporate bonds, while their relative riskiness

F I G U R E 2 Response to an Increase in Default Risk on Corporate Bonds

An increase in default risk on corporate bonds shifts the demand curve from D c

1to D c

2 Simultaneously, it shifts the demand curve for

Treasury bonds from D T

1to D T

2 The equilibrium price for corporate bonds (left axis) falls from P c

1to P c

2 , and the equilibrium interest rate

on corporate bonds (right axis) rises from i c

1to i c

2 In the Treasury market, the equilibrium bond price rises from P T

1to P T

2 , and the

equilib-rium interest rate falls from i T

we go down the axis.)

Price of Bonds, P

( P increases ↑)

Interest Rate, i (i increases )↑

Interest Rate, i (i increases )↑

Price of Bonds, P ( P increases ↑)

(a ) Corporate bond market (b) Default-free (U.S Treasury) bond market

Risk Premium

Dc2

i c 1

PT2

PT1

i c 2

S T

DT1 D

T 2

iT1

iT2

i T 2

declines The Treasury bonds thus become more desirable, and demand rises, asshown in panel (b) by the rightward shift in the demand curve for these bonds from

D T to D T

As we can see in Figure 2, the equilibrium price for corporate bonds (left axis)

falls from P c

1to P c

2, and since the bond price is negatively related to the interest rate,

the equilibrium interest rate on corporate bonds (right axis) rises from i c

1to i c

2 At the

same time, however, the equilibrium price for the Treasury bonds rises from P T to P T,

and the equilibrium interest rate falls from i T to i T The spread between the interestrates on corporate and default-free bonds—that is, the risk premium on corporate

bonds—has risen from zero to i c

2  i T We can now conclude that a bond with default risk will always have a positive risk premium, and an increase in its default risk will raise the risk premium.

Because default risk is so important to the size of the risk premium, purchasers

of bonds need to know whether a corporation is likely to default on its bonds Twomajor investment advisory firms, Moody’s Investors Service and Standard and Poor’sCorporation, provide default risk information by rating the quality of corporate andmunicipal bonds in terms of the probability of default The ratings and their descrip-tion are contained in Table 1 Bonds with relatively low risk of default are called

investment-grade securities and have a rating of Baa (or BBB) and above Bonds with

Rating

Mobil Oil

Credit Suisse First Boston

Anheuser-Busch,Ford, Household Finance

Weyerhaeuser Co.,Tommy Hilfiger

Six Flags

Table 1 Bond Ratings by Moody’s and Standard and Poor’s

ratings below Baa (or BBB) have higher default risk and have been aptly dubbed

speculative-grade or junk bonds Because these bonds always have higher interest

rates than investment-grade securities, they are also referred to as high-yield bonds.Next let’s look back at Figure 1 and see if we can explain the relationship betweeninterest rates on corporate and U.S Treasury bonds Corporate bonds always havehigher interest rates than U.S Treasury bonds because they always have some risk ofdefault, whereas U.S Treasury bonds do not Because Baa-rated corporate bonds have

a greater default risk than the higher-rated Aaa bonds, their risk premium is greater,and the Baa rate therefore always exceeds the Aaa rate We can use the same analysis

to explain the huge jump in the risk premium on Baa corporate bond rates during theGreat Depression years 1930–1933 and the rise in the risk premium after 1970 (seeFigure 1) The depression period saw a very high rate of business failures and defaults

As we would expect, these factors led to a substantial increase in default risk for bondsissued by vulnerable corporations, and the risk premium for Baa bonds reachedunprecedentedly high levels Since 1970, we have again seen higher levels of businessfailures and defaults, although they were still well below Great Depression levels.Again, as expected, default risks and risk premiums for corporate bonds rose, widen-ing the spread between interest rates on corporate bonds and Treasury bonds

The Enron Bankruptcy and the Baa-Aaa Spread Application

In December 2001, the Enron Corporation, a firm specializing in trading in theenergy market, and once the seventh-largest corporation in the United States,was forced to declare bankruptcy after it became clear that it had used shadyaccounting to hide its financial problems (The Enron bankruptcy, the largestever in the United States, will be discussed further in Chapter 8.) Because of thescale of the bankruptcy and the questions it raised about the quality of the infor-mation in accounting statements, the Enron collapse had a major impact on thecorporate bond market Let’s see how our supply and demand analysis explainsthe behavior of the spread between interest rates on lower quality (Baa-rated) andhighest quality (Aaa-rated) corporate bonds in the aftermath of the Enron failure

As a consequence of the Enron bankruptcy, many investors began todoubt the financial health of corporations with lower credit ratings such asBaa The increase in default risk for Baa bonds made them less desirable atany given interest rate, decreased the quantity demanded, and shifted thedemand curve for Baa bonds to the left As shown in panel (a) of Figure 2,the interest rate on Baa bonds should have risen, which is indeed what hap-pened Interest rates on Baa bonds rose by 24 basis points (0.24 percentagepoints) from 7.81% in November 2001 to 8.05% in December 2001 But theincrease in the perceived default risk for Baa bonds after the Enron bank-ruptcy made the highest quality (Aaa) bonds relatively more attractive andshifted the demand curve for these securities to the right—an outcomedescribed by some analysts as a “flight to quality.” Just as our analysis predicts

in Figure 2, interest rates on Aaa bonds fell by 20 basis points, from 6.97%

in November to 6.77% in December The overall outcome was that thespread between interest rates on Baa and Aaa bonds rose by 44 basis pointsfrom 0.84% before the bankruptcy to 1.28% afterward

Another attribute of a bond that influences its interest rate is its liquidity As welearned in Chapter 4, a liquid asset is one that can be quickly and cheaply convertedinto cash if the need arises The more liquid an asset is, the more desirable it is (hold-ing everything else constant) U.S Treasury bonds are the most liquid of all long-termbonds, because they are so widely traded that they are the easiest to sell quickly andthe cost of selling them is low Corporate bonds are not as liquid, because fewer bondsfor any one corporation are traded; thus it can be costly to sell these bonds in anemergency, because it might be hard to find buyers quickly.

How does the reduced liquidity of the corporate bonds affect their interest ratesrelative to the interest rate on Treasury bonds? We can use supply and demand analy-sis with the same figure that was used to analyze the effect of default risk, Figure 2,

to show that the lower liquidity of corporate bonds relative to Treasury bondsincreases the spread between the interest rates on these two bonds Let us start theanalysis by assuming that initially corporate and Treasury bonds are equally liquidand all their other attributes are the same As shown in Figure 2, their equilibrium

prices and interest rates will initially be equal: P c

1 P T and i c

1 i T If the corporatebond becomes less liquid than the Treasury bond because it is less widely traded, then(as the theory of asset demand indicates) its demand will fall, shifting its demand

curve from D c

1to D c

2as in panel (a) The Treasury bond now becomes relatively moreliquid in comparison with the corporate bond, so its demand curve shifts rightward

from D T to D T as in panel (b) The shifts in the curves in Figure 2 show that the price

of the less liquid corporate bond falls and its interest rate rises, while the price of themore liquid Treasury bond rises and its interest rate falls

The result is that the spread between the interest rates on the two bond types hasrisen Therefore, the differences between interest rates on corporate bonds andTreasury bonds (that is, the risk premiums) reflect not only the corporate bond’sdefault risk but its liquidity, too This is why a risk premium is more accurately a “risk

and liquidity premium,” but convention dictates that it is called a risk premium.

Returning to Figure 1, we are still left with one puzzle—the behavior of municipalbond rates Municipal bonds are certainly not default-free: State and local govern-ments have defaulted on the municipal bonds they have issued in the past, particu-larly during the Great Depression and even more recently in the case of OrangeCounty, California, in 1994 (more on this in Chapter 13) Also, municipal bonds arenot as liquid as U.S Treasury bonds

Why is it, then, that these bonds have had lower interest rates than U.S Treasurybonds for at least 40 years, as indicated in Figure 1? The explanation lies in the factthat interest payments on municipal bonds are exempt from federal income taxes, afactor that has the same effect on the demand for municipal bonds as an increase intheir expected return

Let us imagine that you have a high enough income to put you in the 35% incometax bracket, where for every extra dollar of income you have to pay 35 cents to the gov-ernment If you own a $1,000-face-value U.S Treasury bond that sells for $1,000 andhas a coupon payment of $100, you get to keep only $65 of the payment after taxes.Although the bond has a 10% interest rate, you actually earn only 6.5% after taxes.Suppose, however, that you put your savings into a $1,000-face-value municipalbond that sells for $1,000 and pays only $80 in coupon payments Its interest rate isonly 8%, but because it is a tax-exempt security, you pay no taxes on the $80 couponpayment, so you earn 8% after taxes Clearly, you earn more on the municipal bond

Income Tax

Considerations

Liquidity

after taxes, so you are willing to hold the riskier and less liquid municipal bond eventhough it has a lower interest rate than the U.S Treasury bond (This was not truebefore World War II, when the tax-exempt status of municipal bonds did not conveymuch of an advantage because income tax rates were extremely low.)

Another way of understanding why municipal bonds have lower interest rates thanTreasury bonds is to use the supply and demand analysis displayed in Figure 3 Weassume that municipal and Treasury bonds have identical attributes and so have the

same bond prices and interest rates as drawn in the figure: P m

1 P T and i m

1 i T Oncethe municipal bonds are given a tax advantage that raises their after-tax expected returnrelative to Treasury bonds and makes them more desirable, demand for them rises, and

their demand curve shifts to the right, from D m

1to D m

2 The result is that their

equilib-rium bond price rises from P m

1to P m

2, and their equilibrium interest rate falls from i m

1to

i m

2 By contrast, Treasury bonds have now become less desirable relative to municipal

bonds; demand for Treasury bonds decreases, and D T shifts to D T The Treasury bond

price falls from P T to P T , and the interest rate rises from i T to i T The resulting lowerinterest rates for municipal bonds and higher interest rates for Treasury bonds explainswhy municipal bonds can have interest rates below those of Treasury bonds.2

F I G U R E 3 Interest Rates on Municipal and Treasury Bonds

When the municipal bond is given tax-free status, demand for the municipal bond shifts rightward from D m

2, while the equilibrium price of the Treasury bond falls from P T to P T and

its interest rate rises from i T to i T The result is that municipal bonds end up with lower interest rates than those on Treasury

bonds (Note: P and i increase in opposite directions P on the left vertical axis increases as we go up the axis, while i on the

right vertical axis increases as we go down the axis.)

Quantity of Treasury Bonds Quantity of Municipal Bonds

Price of Bonds, P

(P increases ↑)

Interest Rate, i (i increases )↑

Price of Bonds, P ( P increases ↑)

(a) Market for municipal bonds ( b) Market for Treasury bonds

Interest Rate, i (i increases )↑

i m 1

im2

D m 2

P T 2

P T 1

ST

D T 1

D T 2

analy-The risk structure of interest rates (the relationship among interest rates on bondswith the same maturity) is explained by three factors: default risk, liquidity, and theincome tax treatment of the bond’s interest payments As a bond’s default riskincreases, the risk premium on that bond (the spread between its interest rate and theinterest rate on a default-free Treasury bond) rises The greater liquidity of Treasurybonds also explains why their interest rates are lower than interest rates on less liquidbonds If a bond has a favorable tax treatment, as do municipal bonds, whose inter-est payments are exempt from federal income taxes, its interest rate will be lower.

Summary

Term Structure of Interest Rates

We have seen how risk, liquidity, and tax considerations (collectively embedded in therisk structure) can influence interest rates Another factor that influences the interestrate on a bond is its term to maturity: Bonds with identical risk, liquidity, and taxcharacteristics may have different interest rates because the time remaining to matu-rity is different A plot of the yields on bonds with differing terms to maturity but the

same risk, liquidity, and tax considerations is called a yield curve, and it describes the

term structure of interest rates for particular types of bonds, such as governmentbonds The “Following the Financial News” box shows several yield curves for

Treasury securities that were published in the Wall Street Journal Yield curves can be

classified as upward-sloping, flat, and downward-sloping (the last sort is often

referred to as an inverted yield curve) When yield curves slope upward, as in the

“Following the Financial News” box, the long-term interest rates are above the term interest rates; when yield curves are flat, short- and long-term interest rates arethe same; and when yield curves are inverted, long-term interest rates are belowshort-term interest rates Yield curves can also have more complicated shapes inwhich they first slope up and then down, or vice versa Why do we usually see

short-Effects of the Bush Tax Cut on Bond Interest Rates Application

The Bush tax cut passed in 2001 scheduled a reduction of the top income taxbracket from 39% to 35% over a ten-year period What is the effect of thisincome tax decrease on interest rates in the municipal bond market relative

to those in the Treasury bond market?

Our supply and demand analysis provides the answer A decreased incometax rate for rich people means that the after-tax expected return on tax-freemunicipal bonds relative to that on Treasury bonds is lower, because theinterest on Treasury bonds is now taxed at a lower rate Because municipalbonds now become less desirable, their demand decreases, shifting thedemand curve to the left, which lowers their price and raises their interestrate Conversely, the lower income tax rate makes Treasury bonds more desir-able; this change shifts their demand curve to the right, raises their price, andlowers their interest rates

Our analysis thus shows that the Bush tax cut raises the interest rates onmunicipal bonds relative to interest rates on Treasury bonds

upward slopes of the yield curve as in the “Following the Financial News” box butsometimes other shapes?

Besides explaining why yield curves take on different shapes at different times, agood theory of the term structure of interest rates must explain the following threeimportant empirical facts:

1 As we see in Figure 4, interest rates on bonds of different maturities movetogether over time

2 When short-term interest rates are low, yield curves are more likely to have anupward slope; when short-term interest rates are high, yield curves are morelikely to slope downward and be inverted

3 Yield curves almost always slope upward, as in the “Following the FinancialNews” box

Three theories have been put forward to explain the term structure of interestrates; that is, the relationship among interest rates on bonds of different maturitiesreflected in yield curve patterns: (1) the expectations theory, (2) the segmented mar-kets theory, and (3) the liquidity premium theory, each of which is described in thefollowing sections The expectations theory does a good job of explaining the first twofacts on our list, but not the third The segmented markets theory can explain fact 3but not the other two facts, which are well explained by the expectations theory.Because each theory explains facts that the other cannot, a natural way to seek a bet-ter understanding of the term structure is to combine features of both theories, whichleads us to the liquidity premium theory, which can explain all three facts

If the liquidity premium theory does a better job of explaining the facts and ishence the most widely accepted theory, why do we spend time discussing the othertwo theories? There are two reasons First, the ideas in these two theories provide the

Following the Financial News

The Wall Street Journal publishes a daily plot of the yield

curves for Treasury securities, an example of which is

presented here It is typically found on page 2 of the

“Money and Investing” section

The numbers on the vertical axis indicate the interest

rate for the Treasury security, with the maturity given by

the numbers on the horizontal axis For example, the

yield curve marked “Yesterday” indicates that the interest

rate on the three-month Treasury bill yesterday was

1.25%, while the one-year bill had an interest rate of

1.35% and the ten-year bond had an interest rate of

4.0% As you can see, the yield curves in the plot have the

typical upward slope

Source: Wall Street Journal, Wednesday, January 22, 2003, p C2.

Yield Curves

www.ratecurve.com/yc2.html

Check out today’s yield curve.

Treasury Yield Curve

Yield to maturity of current bills, notes and bonds.

Source: Reuters

1 1.0 2.0 3.0 4.0 5.0%

groundwork for the liquidity premium theory Second, it is important to see howeconomists modify theories to improve them when they find that the predicted resultsare inconsistent with the empirical evidence.

The expectations theory of the term structure states the following commonsense

proposition: The interest rate on a long-term bond will equal an average of short-terminterest rates that people expect to occur over the life of the long-term bond Forexample, if people expect that short-term interest rates will be 10% on average overthe coming five years, the expectations theory predicts that the interest rate on bondswith five years to maturity will be 10% too If short-term interest rates were expected

to rise even higher after this five-year period so that the average short-term interestrate over the coming 20 years is 11%, then the interest rate on 20-year bonds wouldequal 11% and would be higher than the interest rate on five-year bonds We can seethat the explanation provided by the expectations theory for why interest rates onbonds of different maturities differ is that short-term interest rates are expected tohave different values at future dates

The key assumption behind this theory is that buyers of bonds do not preferbonds of one maturity over another, so they will not hold any quantity of a bond ifits expected return is less than that of another bond with a different maturity Bonds

that have this characteristic are said to be perfect substitutes What this means in

prac-tice is that if bonds with different maturities are perfect substitutes, the expectedreturn on these bonds must be equal

Expectations

Theory

F I G U R E 4 Movements over Time of Interest Rates on U.S Government Bonds with Different Maturities

Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15

Three-Month Bills (Short-Term)

Three-to Five-Year Averages

Interest

Rate (%)

To see how the assumption that bonds with different maturities are perfect stitutes leads to the expectations theory, let us consider the following two investmentstrategies:

sub-1 Purchase a one-year bond, and when it matures in one year, purchase anotherone-year bond

2 Purchase a two-year bond and hold it until maturity

Because both strategies must have the same expected return if people are holdingboth one- and two-year bonds, the interest rate on the two-year bond must equal theaverage of the two one-year interest rates For example, let’s say that the current interestrate on the one-year bond is 9% and you expect the interest rate on the one-year bondnext year to be 11% If you pursue the first strategy of buying the two one-year bonds,the expected return over the two years will average out to be (9%  11%)/2  10% peryear You will be willing to hold both the one- and two-year bonds only if the expectedreturn per year of the two-year bond equals this Therefore, the interest rate on the two-year bond must equal 10%, the average interest rate on the two one-year bonds

We can make this argument more general For an investment of $1, consider thechoice of holding, for two periods, a two-period bond or two one-period bonds.Using the definitions

i t  today’s (time t) interest rate on a one-period bond

ie

t1  interest rate on a one-period bond expected for next period (time t  1)

i 2t  today’s (time t) interest rate on the two-period bond

the expected return over the two periods from investing $1 in the two-period bondand holding it for the two periods can be calculated as:

(1  i2t)(1  i2t) 1  1  2i 2t  (i 2t)2 1 = 2i 2t  (i 2t)2After the second period, the $1 investment is worth (1  i2 t)(1  i2 t) Subtractingthe $1 initial investment from this amount and dividing by the initial $1 investment

gives the rate of return calculated in the previous equation Because (i 2 t)2is extremely

small—if i 2 t  10%  0.10, then (i 2 t)2 0.01—we can simplify the expected returnfor holding the two-period bond for the two periods to

yielding an amount (1  it)(1  ie

t1) Then subtracting the $1 initial investmentfrom this amount and dividing by the initial investment of $1 gives the expectedreturn for the strategy of holding one-period bonds for the two periods Because

2i 2t  i t  ie

t1

Solving for i 2tin terms of the one-period rates, we have:

(1)which tells us that the two-period rate must equal the average of the two one-periodrates Graphically, this can be shown as:

We can conduct the same steps for bonds with a longer maturity so that we can ine the whole term structure of interest rates Doing so, we will find that the interest

exam-rate of i nt on an n-period bond must equal:

(2)

Equation 2 states that the n-period interest rate equals the average of the period interest rates expected to occur over the n-period life of the bond This is a

one-restatement of the expectations theory in more precise terms.3

A simple numerical example might clarify what the expectations theory inEquation 2 is saying If the one-year interest rate over the next five years is expected

to be 5, 6, 7, 8, and 9%, Equation 2 indicates that the interest rate on the two-yearbond would be:

while for the five-year bond it would be:

Doing a similar calculation for the one-, three-, and four-year interest rates, youshould be able to verify that the one- to five-year interest rates are 5.0, 5.5, 6.0, 6.5,and 7.0%, respectively Thus we see that the rising trend in expected short-term inter-est rates produces an upward-sloping yield curve along which interest rates rise asmaturity lengthens

The expectations theory is an elegant theory that provides an explanation of whythe term structure of interest rates (as represented by yield curves) changes at differ-ent times When the yield curve is upward-sloping, the expectations theory suggeststhat short-term interest rates are expected to rise in the future, as we have seen in ournumerical example In this situation, in which the long-term rate is currently abovethe short-term rate, the average of future short-term rates is expected to be higherthan the current short-term rate, which can occur only if short-term interest rates areexpected to rise This is what we see in our numerical example When the yield curve

is inverted (slopes downward), the average of future short-term interest rates is

Today

0

Year1

Year2

expected to be below the current short-term rate, implying that short-term interestrates are expected to fall, on average, in the future Only when the yield curve is flatdoes the expectations theory suggest that short-term interest rates are not expected tochange, on average, in the future.

The expectations theory also explains fact 1 that interest rates on bonds with ferent maturities move together over time Historically, short-term interest rates havehad the characteristic that if they increase today, they will tend to be higher in thefuture Hence a rise in short-term rates will raise people’s expectations of future short-term rates Because long-term rates are the average of expected future short-termrates, a rise in short-term rates will also raise long-term rates, causing short- and long-term rates to move together

dif-The expectations theory also explains fact 2 that yield curves tend to have anupward slope when short-term interest rates are low and are inverted when short-term rates are high When short-term rates are low, people generally expect them torise to some normal level in the future, and the average of future expected short-termrates is high relative to the current short-term rate Therefore, long-term interest rateswill be substantially above current short-term rates, and the yield curve would thenhave an upward slope Conversely, if short-term rates are high, people usually expectthem to come back down Long-term rates would then drop below short-term ratesbecause the average of expected future short-term rates would be below current short-term rates and the yield curve would slope downward and become inverted.4The expectations theory is an attractive theory because it provides a simple expla-nation of the behavior of the term structure, but unfortunately it has a major short-coming: It cannot explain fact 3, which says that yield curves usually slope upward.The typical upward slope of yield curves implies that short-term interest rates are usu-ally expected to rise in the future In practice, short-term interest rates are just aslikely to fall as they are to rise, and so the expectations theory suggests that the typi-cal yield curve should be flat rather than upward-sloping

As the name suggests, the segmented markets theory of the term structure sees

mar-kets for different-maturity bonds as completely separate and segmented The interestrate for each bond with a different maturity is then determined by the supply of anddemand for that bond with no effects from expected returns on other bonds withother maturities

The key assumption in the segmented markets theory is that bonds of differentmaturities are not substitutes at all, so the expected return from holding a bond of onematurity has no effect on the demand for a bond of another maturity This theory ofthe term structure is at the opposite extreme to the expectations theory, whichassumes that bonds of different maturities are perfect substitutes

The argument for why bonds of different maturities are not substitutes is thatinvestors have strong preferences for bonds of one maturity but not for another, sothey will be concerned with the expected returns only for bonds of the maturity theyprefer This might occur because they have a particular holding period in mind, and

est rates are mean-reverting—that is, if they tend to head back down after they are at unusually high levels or go

back up when they are at unusually low levels—then an average of these short-term rates must necessarily have lower volatility than the short-term rates themselves Because the expectations theory suggests that the long-term rate will be an average of future short-term rates, it implies that the long-term rate will have lower volatility than short-term rates.

if they match the maturity of the bond to the desired holding period, they can obtain

a certain return with no risk at all.5(We have seen in Chapter 4 that if the term tomaturity equals the holding period, the return is known for certain because it equalsthe yield exactly, and there is no interest-rate risk.) For example, people who have ashort holding period would prefer to hold short-term bonds Conversely, if you wereputting funds away for your young child to go to college, your desired holding periodmight be much longer, and you would want to hold longer-term bonds

In the segmented markets theory, differing yield curve patterns are accounted for

by supply and demand differences associated with bonds of different maturities If, asseems sensible, investors have short desired holding periods and generally preferbonds with shorter maturities that have less interest-rate risk, the segmented marketstheory can explain fact 3 that yield curves typically slope upward Because in the typ-ical situation the demand for long-term bonds is relatively lower than that for short-term bonds, long-term bonds will have lower prices and higher interest rates, andhence the yield curve will typically slope upward

Although the segmented markets theory can explain why yield curves usuallytend to slope upward, it has a major flaw in that it cannot explain facts 1 and 2.Because it views the market for bonds of different maturities as completely segmented,there is no reason for a rise in interest rates on a bond of one maturity to affect theinterest rate on a bond of another maturity Therefore, it cannot explain why interestrates on bonds of different maturities tend to move together (fact 1) Second, because

it is not clear how demand and supply for short- versus long-term bonds change withthe level of short-term interest rates, the theory cannot explain why yield curves tend

to slope upward when short-term interest rates are low and to be inverted whenshort-term interest rates are high (fact 2)

Because each of our two theories explains empirical facts that the other cannot, alogical step is to combine the theories, which leads us to the liquidity premium theory

The liquidity premium theory of the term structure states that the interest rate on a

long-term bond will equal an average of short-term interest rates expected to occurover the life of the long-term bond plus a liquidity premium (also referred to as a termpremium) that responds to supply and demand conditions for that bond

The liquidity premium theory’s key assumption is that bonds of different

maturi-ties are substitutes, which means that the expected return on one bond does influence

the expected return on a bond of a different maturity, but it allows investors to preferone bond maturity over another In other words, bonds of different maturities areassumed to be substitutes but not perfect substitutes Investors tend to prefer shorter-term bonds because these bonds bear less interest-rate risk For these reasons,investors must be offered a positive liquidity premium to induce them to hold longer-term bonds Such an outcome would modify the expectations theory by adding a pos-itive liquidity premium to the equation that describes the relationship between long-and short-term interest rates The liquidity premium theory is thus written as:

where l nt  the liquidity (term) premium for the n-period bond at time t, which is always positive and rises with the term to maturity of the bond, n

Closely related to the liquidity premium theory is the preferred habitat theory,

which takes a somewhat less direct approach to modifying the expectations sis but comes up with a similar conclusion It assumes that investors have a prefer-ence for bonds of one maturity over another, a particular bond maturity (preferredhabitat) in which they prefer to invest Because they prefer bonds of one maturity overanother they will be willing to buy bonds that do not have the preferred maturity only

hypothe-if they earn a somewhat higher expected return Because investors are likely to preferthe habitat of short-term bonds over that of longer-term bonds, they are willing tohold long-term bonds only if they have higher expected returns This reasoning leads

to the same Equation 3 implied by the liquidity premium theory with a term premiumthat typically rises with maturity

The relationship between the expectations theory and the liquidity premiums andpreferred habitat theories is shown in Figure 5 There we see that because the liquid-ity premium is always positive and typically grows as the term to maturity increases,the yield curve implied by the liquidity premium theory is always above the yieldcurve implied by the expectations theory and generally has a steeper slope

A simple numerical example similar to the one we used for the expectationshypothesis further clarifies what the liquidity premium and preferred habitat theories

in Equation 3 are saying Again suppose that the one-year interest rate over the nextfive years is expected to be 5, 6, 7, 8, and 9%, while investors’ preferences for hold-ing short-term bonds means that the liquidity premiums for one- to five-year bondsare 0, 0.25, 0.5, 0.75, and 1.0%, respectively Equation 3 then indicates that the inter-est rate on the two-year bond would be:

http://stockcharts.com/charts

/YieldCurve.html

This site lets you look at the

dynamic yield curve at any

point in time since 1995.

F I G U R E 5 The Relationship

Between the Liquidity Premium

(Preferred Habitat) and Expectations

Theory

Because the liquidity premium is

always positive and grows as the

term to maturity increases, the

yield curve implied by the

liquid-ity premium and preferred habitat

theories is always above the yield

curve implied by the expectations

theory and has a steeper slope.

Note that the yield curve implied

by the expectations theory is

drawn under the scenario of

unchanging future one-year

inter-est rates.

30 25

20 15

10 5

0

Years to Maturity, n

Interest Rate, int

Expectations Theory Yield Curve

Liquidity Premium, lnt

Liquidity Premium (Preferred Habitat) Theory

Yield Curve

while for the five-year bond it would be:

Doing a similar calculation for the one-, three-, and four-year interest rates, youshould be able to verify that the one- to five-year interest rates are 5.0, 5.75, 6.5, 7.25,and 8.0%, respectively Comparing these findings with those for the expectations the-ory, we see that the liquidity premium and preferred habitat theories produce yieldcurves that slope more steeply upward because of investors’ preferences for short-term bonds

Let’s see if the liquidity premium and preferred habitat theories are consistentwith all three empirical facts we have discussed They explain fact 1 that interest rates

on different-maturity bonds move together over time: A rise in short-term interestrates indicates that short-term interest rates will, on average, be higher in the future,and the first term in Equation 3 then implies that long-term interest rates will risealong with them

They also explain why yield curves tend to have an especially steep upwardslope when short-term interest rates are low and to be inverted when short-termrates are high (fact 2) Because investors generally expect short-term interest rates

to rise to some normal level when they are low, the average of future expected term rates will be high relative to the current short-term rate With the additionalboost of a positive liquidity premium, long-term interest rates will be substantiallyabove current short-term rates, and the yield curve would then have a steep upwardslope Conversely, if short-term rates are high, people usually expect them to comeback down Long-term rates would then drop below short-term rates because theaverage of expected future short-term rates would be so far below current short-term rates that despite positive liquidity premiums, the yield curve would slopedownward

short-The liquidity premium and preferred habitat theories explain fact 3 that yieldcurves typically slope upward by recognizing that the liquidity premium rises with abond’s maturity because of investors’ preferences for short-term bonds Even if short-term interest rates are expected to stay the same on average in the future, long-terminterest rates will be above short-term interest rates, and yield curves will typicallyslope upward

How can the liquidity premium and preferred habitat theories explain the sional appearance of inverted yield curves if the liquidity premium is positive? It must

occa-be that at times short-term interest rates are expected to fall so much in the future thatthe average of the expected short-term rates is well below the current short-term rate.Even when the positive liquidity premium is added to this average, the resulting long-term rate will still be below the current short-term interest rate

As our discussion indicates, a particularly attractive feature of the liquidity mium and preferred habitat theories is that they tell you what the market is predict-ing about future short-term interest rates just from the slope of the yield curve Asteeply rising yield curve, as in panel (a) of Figure 6, indicates that short-term inter-est rates are expected to rise in the future A moderately steep yield curve, as in panel(b), indicates that short-term interest rates are not expected to rise or fall much in thefuture A flat yield curve, as in panel (c), indicates that short-term rates are expected

pre-to fall moderately in the future Finally, an inverted yield curve, as in panel (d), cates that short-term interest rates are expected to fall sharply in the future

In the 1980s, researchers examining the term structure of interest rates questionedwhether the slope of the yield curve provides information about movements of futureshort-term interest rates.6They found that the spread between long- and short-terminterest rates does not always help predict future short-term interest rates, a findingthat may stem from substantial fluctuations in the liquidity (term) premium for long-term bonds More recent research using more discriminating tests now favors a dif-ferent view It shows that the term structure contains quite a bit of information for thevery short run (over the next several months) and the long run (over several years)

Evidence on the

Term Structure

6

Robert J Shiller, John Y Campbell, and Kermit L Schoenholtz, “Forward Rates and Future Policy: Interpreting

the Term Structure of Interest Rates,” Brookings Papers on Economic Activity 1 (1983): 173–217; N Gregory

Mankiw and Lawrence H Summers, “Do Long-Term Interest Rates Overreact to Short-Term Interest Rates?”

Brookings Papers on Economic Activity 1 (1984): 223–242.

F I G U R E 6 Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates According to the Liquidity Premium Theory

(c) Future short-term interest rates

expected to fall moderately

(d) Future short-term interest rates expected to fall sharply

Yield to Maturity

but is unreliable at predicting movements in interest rates over the intermediate term(the time in between).7

The liquidity premium and preferred habitat theories are the most widely acceptedtheories of the term structure of interest rates because they explain the major empir-ical facts about the term structure so well They combine the features of both theexpectations theory and the segmented markets theory by asserting that a long-terminterest rate will be the sum of a liquidity (term) premium and the average of theshort-term interest rates that are expected to occur over the life of the bond

The liquidity premium and preferred habitat theories explain the following facts:(1) Interest rates on bonds of different maturities tend to move together over time, (2)yield curves usually slope upward, and (3) when short-term interest rates are low,yield curves are more likely to have a steep upward slope, whereas when short-terminterest rates are high, yield curves are more likely to be inverted

The theories also help us predict the movement of short-term interest rates in thefuture A steep upward slope of the yield curve means that short-term rates are expected

to rise, a mild upward slope means that short-term rates are expected to remain thesame, a flat slope means that short-term rates are expected to fall moderately, and aninverted yield curve means that short-term rates are expected to fall sharply

Summary

7

Eugene Fama, “The Information in the Term Structure,” Journal of Financial Economics 13 (1984): 509–528; Eugene Fama and Robert Bliss, “The Information in Long-Maturity Forward Rates,” American Economic Review 77

(1987): 680–692; John Y Campbell and Robert J Shiller, “Cointegration and Tests of the Present Value Models,”

Journal of Political Economy 95 (1987): 1062–1088; John Y Campbell and Robert J Shiller, “Yield Spreads and

Interest Rate Movements: A Bird’s Eye View,” Review of Economic Studies 58 (1991): 495–514.

Interpreting Yield Curves, 1980–2003 Application

Figure 7 illustrates several yield curves that have appeared for U.S ment bonds in recent years What do these yield curves tell us about the pub-lic’s expectations of future movements of short-term interest rates?

govern-Study Guide Try to answer the preceding question before reading further in the text If you

have trouble answering it with the liquidity premium and preferred habitattheories, first try answering it with the expectations theory (which is simplerbecause you don’t have to worry about the liquidity premium) When youunderstand what the expectations of future interest rates are in this case,modify your analysis by taking the liquidity premium into account

The steep inverted yield curve that occurred on January 15, 1981, cated that short-term interest rates were expected to decline sharply in thefuture In order for longer-term interest rates with their positive liquiditypremium to be well below the short-term interest rate, short-term interestrates must be expected to decline so sharply that their average is far belowthe current short-term rate Indeed, the public’s expectations of sharply lowershort-term interest rates evident in the yield curve were realized soon afterJanuary 15; by March, three-month Treasury bill rates had declined from the16% level to 13%

indi-The steep upward-sloping yield curves on March 28, 1985, and January

23, 2003, indicated that short-term interest rates would climb in the future

The long-term interest rate is above the term interest rate when term interest rates are expected to rise because their average plus the liquid-ity premium will be above the current short-term rate The moderatelyupward-sloping yield curves on May 16, 1980, and March 3, 1997, indicatedthat short-term interest rates were expected neither to rise nor to fall in thenear future In this case, their average remains the same as the current short-term rate, and the positive liquidity premium for longer-term bonds explainsthe moderate upward slope of the yield curve

short-F I G U R E 7 Yield Curves for U.S Government Bonds

Sources: Federal Reserve Bank of St Louis; U.S Financial Data, various issues; Wall Street Journal, various dates.

6 8 10 12 14 16

Terms to Maturity (Years)

Interest Rate (%)

May 16, 1980 March 28, 1985 January 15, 1981

1.Bonds with the same maturity will have different

interest rates because of three factors: default risk,

liquidity, and tax considerations The greater a bond’s

default risk, the higher its interest rate relative to other

bonds; the greater a bond’s liquidity, the lower its

interest rate; and bonds with tax-exempt status willhave lower interest rates than they otherwise would.The relationship among interest rates on bonds with thesame maturity that arise because of these three factors is

known as the risk structure of interest rates.

2. Four theories of the term structure provide

explanations of how interest rates on bonds with

different terms to maturity are related The expectations

theory views long-term interest rates as equaling the

average of future short-term interest rates expected to

occur over the life of the bond; by contrast, the

segmented markets theory treats the determination of

interest rates for each bond’s maturity as the outcome of

supply and demand in that market only Neither of

these theories by itself can explain the fact that interest

rates on bonds of different maturities move together

over time and that yield curves usually slope upward

3. The liquidity premium and preferred habitat theories

combine the features of the other two theories, and by

so doing are able to explain the facts just mentioned.They view long-term interest rates as equaling theaverage of future short-term interest rates expected tooccur over the life of the bond plus a liquiditypremium These theories allow us to infer the market’sexpectations about the movement of future short-terminterest rates from the yield curve A steeply upward-sloping curve indicates that future short-term rates areexpected to rise, a mildly upward-sloping curveindicates that short-term rates are expected to stay thesame, a flat curve indicates that short-term rates areexpected to decline slightly, and an inverted yield curveindicates that a substantial decline in short-term rates isexpected in the future

risk structure of interest rates, p 120segmented markets theory, p 132term structure of interest rates, p 120yield curve, p 127

Questions and Problems

Questions marked with an asterisk are answered at the end

of the book in an appendix, “Answers to Selected Questions

and Problems.”

1.Which should have the higher risk premium on its

interest rates, a corporate bond with a Moody’s Baa

rating or a corporate bond with a C rating? Why?

*2.Why do U.S Treasury bills have lower interest rates

than large-denomination negotiable bank CDs?

3.Risk premiums on corporate bonds are usually

anticycli-cal; that is, they decrease during business cycle

expan-sions and increase during recesexpan-sions Why is this so?

*4.“If bonds of different maturities are close substitutes, their

interest rates are more likely to move together.” Is this

statement true, false, or uncertain? Explain your answer

5.If yield curves, on average, were flat, what would this

say about the liquidity (term) premiums in the term

structure? Would you be more or less willing to accept

the expectations theory?

*6. Assuming that the expectations theory is the correcttheory of the term structure, calculate the interestrates in the term structure for maturities of one to fiveyears, and plot the resulting yield curves for the fol-lowing series of one-year interest rates over the nextfive years:

(b) 5%, 4%, 3%, 4%, 5%

How would your yield curves change if people ferred shorter-term bonds over longer-term bonds?

pre-QUIZ

*8. If a yield curve looks like the one shown in figure (a)

in this section, what is the market predicting about

the movement of future short-term interest rates?

What might the yield curve indicate about the

mar-ket’s predictions about the inflation rate in the future?

9. If a yield curve looks like the one shown in (b), what

is the market predicting about the movement of future

short-term interest rates? What might the yield curve

indicate about the market’s predictions about the

infla-tion rate in the future?

*10.What effect would reducing income tax rates have on

the interest rates of municipal bonds? Would interest

rates of Treasury securities be affected, and if so, how?

Using Economic Analysis

to Predict the Future

11. Predict what will happen to interest rates on a

corporation’s bonds if the federal government

guaran-tees today that it will pay creditors if the corporation

goes bankrupt in the future What will happen to the

interest rates on Treasury securities?

*12.Predict what would happen to the risk premiums on

corporate bonds if brokerage commissions were

low-ered in the corporate bond market

13. If the income tax exemption on municipal bonds wereabolished, what would happen to the interest rates onthese bonds? What effect would the change have oninterest rates on U.S Treasury securities?

*14. If the yield curve suddenly becomes steeper, howwould you revise your predictions of interest rates inthe future?

15. If expectations of future short-term interest rates denly fall, what would happen to the slope of theyield curve?

sud-Web Exercises

1. The amount of additional interest investors receivedue to the various premiums changes over time.Sometimes the risk premiums are much larger than atother times For example, the default risk premiumwas very small in the late 1990s when the economywas so healthy business failures were rare This riskpremium increases during recessions

Go to www.federalreserve.gov/releases/releases/h15(historical data) and find the interest rate listings forAAA and Baa rated bonds at three points in time, themost recent, June 1, 1995, and June 1, 1992 Prepare

a graph that shows these three time periods (seeFigure 1 for an example) Are the risk premiums sta-ble or do they change over time?

2.Figure 7 shows a number of yield curves at variouspoints in time Go to www.bloomberg.com, and click

on “Markets” at the top of the page Find the Treasuryyield curve Does the current yield curve fall above orbelow the most recent one listed in Figure 7? Is thecurrent yield curve flatter or steeper than the mostrecent one reported in Figure 7?

3. Investment companies attempt to explain to investorsthe nature of the risk the investor incurs when buyingshares in their mutual funds For example, Vanguardcarefully explains interest rate risk and offers alterna-tive funds with different interest rate risks Go tohttp://flagship5.vanguard.com/VGApp/hnw/FundsStocksOverview

a Select the bond fund you would recommend to aninvestor who has very low tolerance for risk and ashort investment horizon Justify your answer

b Select the bond fund you would recommend to aninvestor who has very high tolerance for risk and along investment horizon Justify your answer

Yield to

Maturity

Term to Maturity (a)

Yield to

Maturity

Term to Maturity (b)

PREVIEW Rarely does a day go by that the stock market isn’t a major news item We have

wit-nessed huge swings in the stock market in recent years The 1990s were an dinary decade for stocks: the Dow Jones and S&P 500 indexes increased more than400%, while the tech-laden NASDAQ index rose more than 1,000% By early 2000,both indexes had reached record highs Unfortunately, the good times did not last,and many investors lost their shirts Starting in early 2000, the stock market began todecline: the NASDAQ crashed, falling by over 50%, while the Dow Jones and S&P

extraor-500 indexes fell by 30% through January 2003

Because so many people invest in the stock market and the price of stocks affectsthe ability of people to retire comfortably, the market for stocks is undoubtedly thefinancial market that receives the most attention and scrutiny In this chapter, we look

at how this important market works

We begin by discussing the fundamental theories that underlie the valuation ofstocks These theories are critical to understanding the forces that cause the value ofstocks to rise and fall minute by minute and day by day Once we have learned themethods for stock valuation, we need to explore how expectations about the market

affect its behavior We do so by examining the theory of rational expectations When this theory is applied to financial markets, the outcome is the efficient market hypoth- esis The theory of rational expectations is also central to debates about the conduct

of monetary policy, to be discussed in Chapter 28

Theoretically, the theory of rational expectations should be a powerful tool for

analyzing behavior But to establish that it is in reality a useful tool, we must compare

the outcomes predicted by the theory with empirical evidence Although the evidence

is mixed and controversial, it indicates that for many purposes, the theory of rationalexpectations is a good starting point for analyzing expectations

Computing the Price of Common Stock

Common stock is the principal way that corporations raise equity capital Holders of

common stock own an interest in the corporation consistent with the percentage of

outstanding shares owned This ownership interest gives stockholders—those who

hold stock in a corporation—a bundle of rights The most important are the right to

vote and to be the residual claimant of all funds flowing into the firm (known as

cash flows), meaning that the stockholder receives whatever remains after all other

141

Rational Expectations, and the Efficient Market Hypothesis7

claims against the firm’s assets have been satisfied Stockholders are paid dividends

from the net earnings of the corporation Dividends are payments made periodically,

usually every quarter, to stockholders The board of directors of the firm sets the level

of the dividend, usually upon the recommendation of management In addition, thestockholder has the right to sell the stock

One basic principle of finance is that the value of any investment is found bycomputing the value today of all cash flows the investment will generate over its life.For example, a commercial building will sell for a price that reflects the net cash flows(rents – expenses) it is projected to have over its useful life Similarly, we value com-mon stock as the value in today’s dollars of all future cash flows The cash flows astockholder might earn from stock are dividends, the sales price, or both

To develop the theory of stock valuation, we begin with the simplest possible nario: You buy the stock, hold it for one period to get a dividend, then sell the stock

sce-We call this the one-period valuation model.

Suppose that you have some extra money to invest for one year After a year, you will

need to sell your investment to pay tuition After watching CNBC or Wall Street Week

on TV, you decide that you want to buy Intel Corp stock You call your broker andfind that Intel is currently selling for $50 per share and pays $0.16 per year in divi-

dends The analyst on Wall Street Week predicts that the stock will be selling for $60

in one year Should you buy this stock?

To answer this question, you need to determine whether the current price rately reflects the analyst’s forecast To value the stock today, you need to find the pres-ent discounted value of the expected cash flows (future payments) using the formula

accu-in Equation 1 of Chapter 4 Note that accu-in this equation, the discount factor used to count the cash flows is the required return on investments in equity rather than theinterest rate The cash flows consist of one dividend payment plus a final sales price.When these cash flows are discounted back to the present, the following equationcomputes the current price of the stock:

dis-(1)

where P0=the current price of the stock The zero subscript refers to

time period zero, or the present

Div1=the dividend paid at the end of year 1

k e=the required return on investments in equity

P1=the price at the end of the first period; the assumed salesprice of the stock

To see how Equation 1 works, let’s compute the price of the Intel stock if, aftercareful consideration, you decide that you would be satisfied to earn a 12% return on

the investment If you have decided that k e= 0.12, are told that Intel pays $0.16 per

year in dividends (Div1= 0.16), and forecast the share price of $60 for next year (P1

= $60), you get the following from Equation 1:

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