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where lnt 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 hypothesis but comes up with a similar conclusion. It assumes that investors have a preference for bonds of one maturity over another, a particular bond maturity (preferred habitat) in which they prefer to invest. Because they prefer bonds of one maturity over another they will be willing to buy bonds that do not have the preferred maturity only if they earn a somewhat higher expected return. Because investors are likely to prefer the habitat of short-term bonds over that of longer-term bonds, they are willing to hold 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 premium that typically rises with maturity.

The relationship between the expectations theory and the liquidity premiums and preferred habitat theories is shown in Figure 5. There we see that because the liquidity 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 yield curve implied by the expectations theory and generally has a steeper slope.

A simple numerical example similar to the one we used for the expectations hypothesis 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 next five years is expected to be 5, 6, 7, 8, and 9%, while investorsÕ preferences for holding short-term bonds means that the liquidity premiums for oneto five-year bonds are 0, 0.25, 0.5, 0.75, and 1.0%, respectively. Equation 3 then indicates that the interest rate on the two-year bond would be:

5% 6% 0.25% 5.75%

2

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 liquidity 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 interest rates.

Liquidity

Premium, lnt

Expectations Theory

Yield Curve

Years to Maturity, n

(a ) Future short-term interest rates expected to rise

(b)Future short-term interest rates expected to stay the same

Term to Maturity

(c)Future short-term interest rates expected to fall moderately

Term to Maturity

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

Evidence on the Term Structure

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

6Robert J. Shiller, John Y. Campbell, and Kermit L. Schoenholtz, ÒForward Rates and Future Policy: Interpreting the Term Structure of Interest Rates,Ó Brookings Papers on Economic Activity 1 (1983): 173Ð217; N. Gregory Mankiw and Lawrence H. Summers, ÒDo Long-Term Interest Rates Overreact to Short-Term Interest Rates?Ó

Brookings Papers on Economic Activity 1 (1984): 223Ð242.

Summary

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 accepted theories of the term structure of interest rates because they explain the major empirical facts about the term structure so well. They combine the features of both the expectations theory and the segmented markets theory by asserting that a long-term interest rate will be the sum of a liquidity (term) premium and the average of the short-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-term interest 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 the future. 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 the same, a flat slope means that short-term rates are expected to fall moderately, and an inverted yield curve means that short-term rates are expected to fall sharply.

Summary

1.Bonds with the same maturity will have different interest rates because of three factors: default risk, liquidity, and tax considerations. The greater a bondÕs default risk, the higher its interest rate relative to other bonds; the greater a bondÕs liquidity, the lower its

interest rate; and bonds with tax-exempt status will have lower interest rates than they otherwise would. The relationship among interest rates on bonds with the same 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 bondÕs 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 the average of future short-term interest rates expected to occur over the life of the bond plus a liquidity premium. These theories allow us to infer the marketÕs expectations about the movement of future short-term interest rates from the yield curve. A steeply upwardsloping curve indicates that future short-term rates are expected to rise, a mildly upward-sloping curve indicates that short-term rates are expected to stay the same, a flat curve indicates that short-term rates are expected to decline slightly, and an inverted yield curve indicates that a substantial decline in short-term rates is expected in the future.

QUIZ Questions and Problems

Questions marked with an asterisk are answered at the end of the book in an appendix, ÒAnswers to Selected Questions and Problems.Ó

1.Which should have the higher risk premium on its interest rates, a corporate bond with a MoodyÕs 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 anticyclical; that is, they decrease during business cycle expansions and increase during recessions. Why is this so?

*4. ÒIf bonds of different maturities are close substitutes, their interest rates are more likely to move together.Ó 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 correct theory of the term structure, calculate the interest rates in the term structure for maturities of one to five years, and plot the resulting yield curves for the following series of one-year interest rates over the next five years:

(a)5%, 7%, 7%, 7%, 7%

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

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

7.Assuming that the expectations theory is the correct theory of the term structure, calculate the interest rates in the term structure for maturities of one to five years, and plot the resulting yield curves for the following path of one-year interest rates over the next five years:

(a)5%, 6%, 7%, 6%, 5%

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

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

140 P A R T I I Financial Markets

*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 marketÕs predictions about the inflation rate in the future?

Yield to

Maturity

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

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

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

Web Exercises

Term to Maturity

(a)

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 marketÕs predictions about the inflation rate in the future?

Yield to

Maturity

*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 corporationÕs bonds if the federal government guarantees 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 lowered in the corporate bond market.

1.The amount of additional interest investors receive due to the various premiums changes over time. Sometimes the risk premiums are much larger than at other times. For example, the default risk premium was very small in the late 1990s when the economy was so healthy business failures were rare. This risk premium increases during recessions.

Go to www.federalreserve.gov/releases/releases/h15 (historical data) and find the interest rate listings for AAA and Baa rated bonds at three points in time, the most recent, June 1, 1995, and June 1, 1992. Prepare a graph that shows these three time periods (see Figure 1 for an example). Are the risk premiums stable or do they change over time?

2.Figure 7 shows a number of yield curves at various points in time. Go to www.bloomberg.com, and click on ÒMarketsÓ at the top of the page. Find the Treasury yield curve. Does the current yield curve fall above or below the most recent one listed in Figure 7? Is the current yield curve flatter or steeper than the most recent one reported in Figure 7?

3.Investment companies attempt to explain to investors the nature of the risk the investor incurs when buying shares in their mutual funds. For example, Vanguard carefully explains interest rate risk and offers alternative funds with different interest rate risks. Go to http://flagship5.vanguard.com/VGApp/hnw /FundsStocksOverview.

a. Select the bond fund you would recommend to an investor who has very low tolerance for risk and a short investment horizon. Justify your answer.

b. Select the bond fund you would recommend to an investor who has very high tolerance for risk and a long investment horizon. Justify your answer.

PREVIEW

Rarely does a day go by that the stock market isnÕt a major news item. We have witnessed huge swings in the stock market in recent years. The 1990s were an extraordinary decade for stocks: the Dow Jones and S&P 500 indexes increased more than 400%, 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 to decline: the NASDAQ crashed, falling by over 50%, while the Dow Jones and S&P 500 indexes fell by 30% through January 2003.

Because so many people invest in the stock market and the price of stocks affects the ability of people to retire comfortably, the market for stocks is undoubtedly the financial 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 of stocks. These theories are critical to understanding the forces that cause the value of stocks to rise and fall minute by minute and day by day. Once we have learned the methods 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 hypothesis. 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 rational expectations is a good starting point for analyzing expectations.

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claims against the firmÕs 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, the stockholder has the right to sell the stock.

One basic principle of finance is that the value of any investment is found by computing 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 Ð expenses) it is projected to have over its useful life. Similarly, we value common stock as the value in todayÕs dollars of all future cash flows. The cash flows a stockholder might earn from stock are dividends, the sales price, or both.

To develop the theory of stock valuation, we begin with the simplest possible scenario: You buy the stock, hold it for one period to get a dividend, then sell the stock. We call this the one-period valuation model.

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 and find that Intel is currently selling for $50 per share and pays $0.16 per year in dividends. 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 accurately reflects the analystÕs forecast. To value the stock today, you need to find the present discounted value of the expected cash flows (future payments) using the formula in Equation 1 of Chapter 4. Note that in this equation, the discount factor used to discount the cash flows is the required return on investments in equity rather than the interest 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 equation computes the current price of the stock:

To see how Equation 1 works, letÕs compute the price of the Intel stock if, after careful consideration, you decide that you would be satisfied to earn a 12% return on the investment. If you have decided that ke = 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:

The Generalized

Dividend

Valuation Model

Based on your analysis, you find that the present value of all cash flows from the stock is $53.71. Because the stock is currently priced at $50 per share, you would choose to buy it. However, you should be aware that the stock may be selling for less than $53.71, because other investors place a different risk on the cash flows or estimate the cash flows to be less than you do.

Using the same concept, the one-period dividend valuation model can be extended to any number of periods: The value of stock is the present value of all future cash flows. The only cash flows that an investor will receive are dividends and a final sales price when the stock is ultimately sold in period n. The generalized multi-period formula for stock valuation can be written as:

The Gordon

Growth Model

If you tried to use Equation 2 to find the value of a share of stock, you would soon realize that you must first estimate the value the stock will have at some point in the future before you can estimate its value today. In other words, you must find Pn in order to find P0. However, if Pn is far in the future, it will not affect P0. For example, the present value of a share of stock that sells for $50 seventy-five years from now using a 12% discount rate is just one cent [$50/(1.1275)=$0.01]. This reasoning implies that the current value of a share of stock can be calculated as simply the present value of the future dividend stream. The generalized dividend model is rewritten in Equation 3 without the final sales price:

Consider the implications of Equation 3 for a moment. The generalized dividend model says that the price of stock is determined only by the present value of the dividends and that nothing else matters. Many stocks do not pay dividends, so how is it that these stocks have value? Buyers of the stock expect that the firm will pay dividends someday. Most of the time a firm institutes dividends as soon as it has completed the rapid growth phase of its life cycle.

The generalized dividend valuation model requires that we compute the present value of an infinite stream of dividends, a process that could be difficult, to say the least. Therefore, simplified models have been developed to make the calculations easier. One such model is the Gordon growth model, which assumes constant dividend growth.

Many firms strive to increase their dividends at a constant rate each year. Equation 4 rewrites Equation 3 to reflect this constant growth in dividends: