Asset Prices and Interest Rates

Transcription

1 C H A P T E R 16 Asset Prices and Interest Rates Notes to the Instructor Chapter Summary This chapter develops the theory of how asset prices are determined using the standard model of valuing income streams that assets pay over time. The chapter also discusses the phenomenon of bubbles in which asset prices rise simply because investors expect them to continue to rise. A key element of the chapter is the connection between asset prices and interest rates, providing a role for monetary policy to influence asset prices through its effects on interest rates. The chapter concludes with a discussion of the term structure of interest rates, which relates long-term rates to short-term rates. Comments The material presented in this chapter may be new to most students and so likely requires several classes to cover. In particular, the sections on valuing income streams, classical theory of asset prices, and measuring interest rates and asset returns require working through mathematical examples. The case studies accompanying the material on asset-price bubbles and asset-price crashes provide good applications of the analysis and are likely to be of keen interest to students. Use of the Dismal Scientist Web Site Go to the Dismal Scientist Web site and download monthly data on the Dow Jones Index and the NASDAQ Index from 2000 to present. Graph these two series and discuss the similarities and differences in their movement over this period of time. Would you agree that the technology-heavy NASDAQ Index appears to have experienced a far larger bubble in the early 2000s than the Dow Jones Index, which consists of very large, established firms? Relate your answer to the discussion of how asset prices should reflect the valuation of income streams. Chapter Supplements This chapter includes the following supplements: 16-1 The Stock Market and Consumer Spending 16-2 A Different View of the Stock Exchange 16-3 The Importance of Asset Pricing for Macroeconomics 16-4 Stock Prices and Efficient Markets 16-5 Bond Prices and the Term Structure of Interest Rates 16-6 Bubbles, Excess Volatility, and Fads 16-7 The Capital-Asset Pricing Model 16-8 Animal Spirits 16-9 Taxes, Babies, and Housing Additional Readings 385

2 386 CHAPTER 16 Asset Prices and Interest Rates Lecture Notes Introduction Supplement 16-1, The Stock Market and Consumer Spending and Supplement 16-3 The Importance of Asset Pricing for Macroeconomics Prices of stocks and bonds fluctuate every day that the markets are open, sometimes moving sharply in a very short period of time. These fluctuations in asset prices affect people s wealth, and thereby the overall economy, through changes in consumer spending. This chapter discusses factors influencing the movement of asset prices, focusing on the valuation of the income streams that assets pay to investors. The experience of asset-price bubbles and asset-price crashes, as occurred during the early 2000s and more recently, is highlighted. Finally, the chapter considers the term structure of interest rates Valuing Income Streams A financial asset provides a stream of income in the future to its owner. To determine the value of an asset, we need to determine the value of these income streams. An important principle in making such valuations is the timing of when the income is received. Economists use the concept of present value to develop these valuations. Future Value The value in the future of an investment of one dollar today is known as the investment s future value. For example, if you deposit a dollar in a bank today that pays 4 percent interest per year, you will receive $1.04 in a year. In two years, you will receive $1.04 x $1.04 $ Likewise, after 3 years, you would receive $1.13 $(1.04) 3. And, after n years, you would receive $(1.04) n. More generally, for an interest rate of i (expressed in decimal form), you would receive (1 i) n. Present Value The present value of a future dollar is the amount an investor is willing to pay today in order to receive in the future a payment of one dollar. A dollar n years from now is worth 1/(1 i) n dollars today. An increase in the interest rate will lower the present value of future money. When the future payment is not a single one but is instead a series of payments over a number of years, the present value is given by: Present Value $X 1 /(1 i 1 ) $X 2 /(1 i 2 ) 2 $X 3 /(1 i 3 ) 3... $X T /(1 i T ) T And when payments continue forever (so that there is no end period T), we can derive a simple formula for the present value if the payments each year are the same amount: Present Value $Z/(1 i 1 ) $Z/(1 i 2 ) 2 $Z/(1 i 3 ) 3... $Z/(1 i T ) T... $Z/i Another type of perpetual income stream is one where the income paid each year grows at a fixed rate. For example, suppose that the payment, $Z, grows at a rate of g each year. The present value of this type of stream also has a simple formula: Present Value $Z/(1 i 1 ) $Z(1 g)/(1 i 2 ) 2 $Z(1 g) 2 /(1 i 3 ) 3... $Z(1 g) T 1 /(1 i T ) T... $Z/(i g)

3 Lecture Notes 387 Table 16-1 As for the previous constant perpetual income stream, the present value here depends positively on the initial payment and negatively on the interest rate. But it now also depends positively on the growth rate of the payment The Classical Theory of Asset Prices Economists rely on the classical theory of asset prices to assess the factors determining the price of an asset. This theory is based on the concept of present value. The Present Value of Income According to the classical theory of asset prices, the price of an asset equals the present value of the stream of income that people expect the asset to pay. People purchase an asset because of the income stream that it yields. The present value of the income stream is the measure of how much we expect it to be worth in today s dollars. This should also be the price that an investor is willing to pay today to receive the income stream over the future. If the price of an asset happened to be below the present value of its expected income stream, then buyers would demand more of it, bidding the price up. If the price of an asset happened to be above the present value of its expected income stream, then sellers of the asset would try to sell more of it, pushing the price down. Applying the classical theory to bonds gives the following relationship between the price of the bond today, its future coupon payment (C), its term to maturity (T), the interest rate (i), and its face value (F): Bond Price C/(1 i) C/(1 i) 2... C/(1 i) T 1 (C F)/(1 i) T, where we assume no risk of default so that bondholders expect to receive all payments. Applying the classical theory to stocks gives the following relationship between the price of the stock today, its expected future dividend payments (D t ), and the interest rate: Supplement 16-4, Stock Prices and Efficient Markets Table 16-2 Stock Price D 1 /(1 i) D 2 /(1 i) 2... D 3 /(1 i) 3... Dividends are paid out of a firm s earnings, and so will vary from year to year. And in some years, a firm may opt to not pay any dividend and instead use its earnings to finance investment projects. But over the long run, dividends are closely related to earnings since a firm that invests its earnings today will be one that has greater future returns and thus is expected to pay higher dividends in the future. Accordingly, a firm s earnings performance will have a strong influence on its stock price. What Determines Expectations? The classical theory assumes that people form rational expectations (discussed in Chapter 12), in that they use all available information to predict future variables such as income flows or earnings of a firm. Rational expectations are not always accurate, but represent the best possible forecast using available information. Unpredictable events will cause actual income flows to differ from what was expected, but under rational expectations this difference will be as small as possible.

4 388 CHAPTER 16 Asset Prices and Interest Rates Supplement 16-7, The Capital-Asset Pricing Model What Is the Relevant Interest Rate? Asset prices depend not only on expectations of earnings, but also on interest rates, which are used to determine the present value of asset income. The relevant interest rate depends on the riskiness of the asset. When an asset has a greater degree of uncertainty regarding its income stream, and is therefore riskier, the interest rate is higher. Taking the interest rate on a safe bank account to be the safe or risk-free interest rate (i safe ), interest rates on other risky assets will equal this safe interest rate plus a risk premium, i safe ϕ. This is known as the riskadjusted interest rate. An increase in the risk premium will raise the risk-adjusted interest rate and lower the present value of an expected income stream, lowering the price of an asset. The Gordon Growth Model of Stock Prices Myron Gordon noted that many firms increase the value of their dividend payment at a fairly steady rate. To derive a simple model of stock prices, he assumed that expected dividends grow at a constant rate of g. In this case, using our relationship for the present value of an income stream that grows at a constant rate, the stock price is given by: Stock Price D 1 (1 g)/(1 i) D 1 (1 g) 2 /(1 i) 2... D 1 (1 g) 3 /(1 i) 3... Table 16-1 Stock Price D 1 /(i g) where i is the risk-adjusted interest rate for the stock Fluctuations in Asset Prices Asset prices fluctuate significantly on a day-to-day basis. Here we assess the main reasons for such movements in asset prices. Why Do Asset Prices Change? Because the price of an asset is equal to the present value of its expected income stream, changes in either expected income or interest rates will affect its price. Stock prices change often as a result of changes in expected income when there is news about a firm s business prospects. Bond prices are much less affected by such news because bonds pay a fixed amount of income as long as the issuing firms do not default. Changes in interest rates, by contrast, have important effects on the prices of both stocks and bonds. An increase in interest rates lowers asset prices because it lowers the present value of the stream of income paid by the asset. Interest rates can change either because the safe interest rate changes or because the risk premium changes. Case Study: The Fed and the Stock Market Monetary policy can affect asset prices. As discussed in Chapter 11, the Federal Reserve implements monetary policy by setting a target for the federal funds rate, the interest rate that banks charge for overnight loans. Because these loans are unlikely to be defaulted upon, the federal funds rate is a safe interest rate. When the Fed moves to tighten monetary policy, it will raise the target for the federal funds rate. This increase affects stock prices in several ways. First, this increase in the safe rate directly reduces the present value of dividend payments received by shareholders, lowering stock prices. Second, as discussed in earlier chapters, the higher interest rate reduces spending by consumers and firms, lowering aggregate output for the economy. The reduction in output leads to lower expected earnings for many companies. In turn, lower expected earnings are reflected in lower expected dividend payments, lowering

5 Lecture Notes 389 Figure 16-1 Table 16-3 stock prices. Third, the reduction in output raises uncertainty because it is difficult to know how badly companies will perform. This increase in uncertainty is associated with a higher risk-adjusted interest rate, which lowers the present value of dividends and thereby stock prices. Changes in the federal funds rate will have effects only when they are unexpected. If people knew in advance of a change in monetary policy, stock prices would adjust in advance and no change would occur when the policy was actually implemented. Federal Reserve Chairman Ben Bernanke and economist Kenneth Kuttner studied the response of the stock market to surprise announcements of changes in the Fed s target for the federal funds rate. They found that a quarterpoint increase in the target was associated with a sudden drop in stock prices of 1 percent. A decrease in the target rate had the opposite effect. Which Asset Prices Are Most Volatile? Some asset prices fluctuate more than others. Long-term bond prices change more than short-term bond prices when interest rates change because the present value of payments is affected by more when the payments come in the distant future than in the near future. Stock prices fluctuate more than prices for bonds, including long-term bonds. One reason stock prices are very volatile is that dividend payments continue indefinitely into the future, so that the income stream is very long and changes in interest rates will have large effects on the present value of this stream. Another reason is that news about firms and the economy affect expectations of future earnings and dividends, leading to changes in stock prices Asset-Price Bubbles Supplement 16-6 Bubbles, Excess Volatility, and Fads The classical theory states that the price of an asset equals the present value of expected income from that asset over time. Many economists, however, believe that asset prices can fluctuate for reasons apart from the classical theory. Asset price increases, for example, may be part of an asset-price bubble a situation where asset prices rise rapidly even though there has been no change in expected income or interest rates to support such an increase. How Bubbles Work A bubble occurs when an asset price rises only because people expect it to rise. Demand for the asset increases in response to people expecting its price to rise. This pushes up the price, validating expectations. Once the bubble has begun, it feeds on itself, with people expecting the price to continue rising, demand for the asset continuing to increase, and the price rising in response. Bubbles eventually pop. The asset price eventually reaches a level where people begin to doubt whether the price will continue to rise. At this point, demand for the asset falls and supply of the asset increases as people rush to sell their holdings, causing the price to fall toward the level supported by the classical theory. In addition to the stock market, bubbles can arise in many kinds of asset prices. For example, the average price of a house in the United States experienced an increase of 71 percent from early 2002 through mid Many people bought second homes or rental properties in the belief that prices would continue to rise and give them a big profit when they finally sold their property. Increased availability of home mortgage loans also helped fuel demand for housing and house prices. The bubble in housing finally collapsed, with prices falling by 33 percent

6 390 CHAPTER 16 Asset Prices and Interest Rates Supplement 16-8, Animal Spirits Figure 16-2 Figure 16-3 Supplement 16-9, Taxes, Babies, and Housing from mid-2006 through early Bubbles have also occurred in the prices of bonds, foreign currencies, precious metals, and commodities. A famous bubble occurred in Holland during the 1630s when the prices of tulip bulbs increased enormously before abruptly crashing. Looking for Bubbles One approach to assessing whether a bubble is occurring in stock prices is to look at the price-earnings (P/E) ratio. Using recent earnings, economists compute P/E ratios for individual companies and for the market as a whole. High P/E ratios are sometimes interpreted as evidence of bubbles. The reason for this is that the classical theory sets the price of a stock equal to the present value of expected dividends per share. Since dividends depend on expected earnings, the price of the stock relative to earnings could be a useful gauge of whether a bubble is occurring. But this will only be true if recent earnings are a good predictor of future earnings. If instead future earnings are expected to grow very rapidly, then recent earnings will not be very useful in predicting future earnings and so a high P/E ratio would not be evidence of a bubble. Research by John Campbell and Robert Shiller in a 1997 paper attempts to determine whether high P/E ratios are evidence of bubbles or the expectation of rapid future earnings growth. Using data for the S&P 500, Campbell and Shiller found that high P/E ratios are associated with subsequent declines in stock prices, supporting the view that high P/E ratios are evidence of bubbles. Case Study: The U.S. Stock Market, The performance of the U.S. stock market over the past two decades provides episodes where the price of stocks seems to have been driven by bubbles and episodes where they seem to have moved in line with companies earnings prospects. From 1990 to 2000, the P/E ratio for the Dow Jones Index rose to 40, well above its average of 15 from 1960 to Some economists argued that this was evidence of a bubble in stock prices. Others argued that the ratio was in line with the classical theory because computers and the Internet would raise productivity and reduce costs, leading to rapid future growth in companies earnings. Prices reached a high in 2000 and then dropped sharply over the next three years. Again, some economists argued this was evidence of a bubble bursting. But others claimed that bad news including the terrorist attacks of 2001, accounting scandals at Enron and other companies, and the recession of 2001 led to a decline in future earnings prospects and stock prices. Over the period 2003 to mid-2007, the Dow rose steadily, peaking above 14,000. At first, the rise was spurred by low interest rates, as the Federal Reserve pushed rates down in 2003 because the economic recovery was sluggish. By 2004, the recovery was strengthening and the Fed started to raise rates. Stock prices continued to rise as a result of improving prospects for companies earnings. In late 2007, stock prices began to fall as the housing market declined and disrupted financial markets generally. Stock prices fell further in the aftermath of the financial crisis of September 2008 for two reasons. First, the crisis directly reduced expected earnings for financial firms and indirectly reduced expected earnings for non-financial firms as the crisis spread. Second, the crisis increased risk premiums for companies stock. Even though the Fed lowered the federal funds rate to nearly zero, the increase in risk premiums more than offset the decline in the safe interest rate, and so risk-adjusted interest rates generally increased, lowering the present value of future income. Stock prices began to rise in March

7 Lecture Notes , as people believed the worst of the crisis was past. Expectations of future income increased and risk-adjusted interest rates declined, pushing stock prices upward over the next year Asset-Price Crashes Bubbles eventually come to an end when prices fall. This may happen gradually over months or years. But sometimes it happens very rapidly even in a single day and is known as an asset-price crash. How Crashes Work Crashes are difficult to explain using the classical theory since under that theory prices will fall only if there is a large drop in expected future income or a rise in interest rates. Often crashes occur without any news about expected earnings or dividends, or changes in interest rates. A crash is easier to explain if it follows an asset-price bubble. During a bubble, some people eventually become nervous about whether asset prices will continue to increase and so they start selling their assets. Others see this happening and begin to sell their assets as well. Prices start to fall and the decline accelerates as pessimism become self-fulfilling. Once prices have fallen by enough to make the assets attractive again, panicked selling dries up and prices stabilize. Case Study: The Two Big Crashes The crashes of October 1929 and October 1987 were similar in that they followed rapid increases in stock prices during the preceding years. And each had a singleday decline that was enormous the Dow Jones Index declined 13 percent on October 28, 1929 and 23 percent on October 19, 1987 along with smaller declines over a period of several weeks. But the aftermaths of the crashes differed markedly. In 1929, the Great Depression followed the crash and the Dow didn t reach its earlier peak again until By contrast, in 1987 the economy kept growing strongly and the Dow reached its previous peak again in less than two years and kept climbing throughout the 1990s. And the Federal Reserve responded to the 1987 crash by lending money to financial institutions, whereas in 1929 it responded only passively. Crash Prevention Two important rules have been adopted in the aftermath of the stock-market crashes of 1929 and 1987 that are intended to limit the potential for future crashes. The Federal Reserve, using authority granted by the Congress, instituted margin requirements in the 1930s. This rule limits the amount people can borrow to buy stock. The exact amount has varied over the years and has been 50 percent recently. Margin requirements constrain the ability of people to bid stocks upward on the basis of borrowed money alone and thereby help prevent bubbles that precede crashes. Following the 1987 crash, the securities exchanges established circuit breakers that require trading to be halted temporarily if prices fall sharply. Circuit breakers are intended to slow down self-fulfilling panicked selling and price decline by giving traders time to think things over. Current rules at the New York Stock Exchange require a trading halt if prices fall 10 percent during a day. The length of the suspension depends on the size of the decline and the time of day when the decline occurs, with longer suspensions for larger declines and those happening later in the day.

8 392 CHAPTER 16 Asset Prices and Interest Rates 16-6 Measuring Interest Rates and Asset Returns Two concepts that are central in determining what assets people hold or a company issues are closely related to asset prices. This section discusses a bond s yield to maturity and the rate of return on a stock or bond. Yield to Maturity The price of a bond is equal to the present value of its stream of coupon payments including its face value paid when the bond matures. The interest rate (i) that solves this relationship is known as the yield to maturity: Bond Price C/(1 i) C/(1 i) 2... C/(1 i) T 1 (C F)/(1 i) T To solve for i requires using trial and error, as this equation does not allow for an easy solution. The yield to maturity moves inversely with the price of the bond, just as the classical theory implies for asset prices and interest rates in general. The Rate of Return The return that a person gains from holding a stock or bond includes both the income it pays directly (coupon on a bond and dividend on a stock) and any change in the price of the security. If the price of the security rises, a person s wealth increases through a capital gain. And if the price of a security falls, a person s wealth decreases through a capital loss. Thus, the total return on a security is given as: Return (P 1 P 0 ) X where P 0 is the initial price of the security, P 1 is the price after the security is held for a year, and X is the direct payment of the security. The rate of return is the return on a security expressed as a percentage of the initial price: Rate of Return Return/P 0 (P 1 P 0 )/P 0 X/P 0 Figure 16-4 Returns on Stocks and Bonds Stock returns are more volatile than bond returns. The main reason is that stock prices fluctuate more than bond prices. But, while returns on stocks are more volatile, the average rate of return is higher for stocks, which is necessary to compensate savers for holding an asset with a more uncertain return. Rate of Return Versus Yield to Maturity When buying a bond, whether one considers the rate of return or the yield to maturity depends on how long the person plans to hold the bond. If a person holds a bond to maturity, then the yield to maturity is what the person receives. Alternatively, if a person sells the bond before maturity, then fluctuations in the bond s price and hence the rate of return will determine what the person receives. Note that the yield to maturity and rate of return can move in opposite ways when the price of the bond changes The Term Structure of Interest Rates Figure 16-5 Bonds vary in the interest rates that they pay. This occurs in part because of differences in credit risk and taxes. But it also occurs because of differences in the maturity, or term, of the bonds. Longer-term bonds usually pay higher interest rates than shorter-term bonds. The term structure of interest rates describes the relationship among interest rates on bonds with different maturities.

9 Lecture Notes 393 The Term Structure Under Certainty When future interest rates are known with certainty, the interest rate on an n- period bond will equal the average of one-period interest rates over the next n periods: i n (t) (1/n)[ i 1 (t) i 1 (t 1)... i 1 (t n 1)] The intuition is that someone saving for n periods can buy an n-period bond or a series of n one-period bonds. Both approaches must provide the same earnings if savers willingly purchase both types of bonds. The Expectations Theory of the Term Structure According to the expectations theory of the term structure, savers choose among bonds of different maturities based on their rational expectation about future interest rates. Bonds of different maturities must produce the same expected earnings. By replacing future interest rates with the expectation of future interest rates, we obtain: i n (t) (1/n)[ I 1 (t) EI 1 (t 1)... EI 1 (t n 1)]. Supplement 16-5 Bond Prices and the Term Structure of Interest Rates Figure 16-6 Figure 16-7 Figure 16-8 Accounting for Risk As discussed earlier, long-term bonds are riskier than short-term bonds because their prices are subject to greater volatility when interest rates change. This difference in risk implies that long-term bonds should have higher expected earnings than short-term bonds. To capture the risk, the term structure of expectations must be modified to include a term premium (τ n ) for long-term interest rates: i n (t) (1/n)[ I 1 (t) EI 1 (t 1)... EI 1 (t n 1)] τ. Term premiums will be greater for bonds of longer maturity compared with those of shorter maturity. The Yield Curve The term structure of interest rates can be represented by a yield curve, which shows the interest rates on bonds of different maturities in a given time period. Depending on expectations about future interest rates, the yield curve can take on different shapes. Generally, the yield curve is upward sloping since term premiums are larger on long-term bonds compared with short-term bonds. But when people expect shortterm interest rates to rise, the yield curve is even steeper, and when people expect short-term interest rates to fall, the yield curve is flat. An inverted yield curve can occur if people expect a very large fall in short-term interest rates. Because the expected path of short-term interest rates determines the shape of the yield curve, we can use the yield curve to forecast future interest rates. A very steep yield curve means that short-term rates are expected to rise. An inverted yield curve implies that short-term rates are expected to fall sharply. Case Study: Inverted Yield Curves Historically, most inverted yield curves have occurred at times when the Federal Reserve was tightening monetary policy, raising short-term interest rates to quell inflation. The increase in short-term interest rates is temporary and people expect short-term rates to decline in the future once inflation is dampened. In most cases, people expect short-term interest rates to end up lower than before the Fed started to tighten policy because lower inflation will reduce interest rates through the Fisher effect. The expected decline in short-term interest rates is often large enough to produce an inverted yield curve. An example of an inverted yield curve

10 394 CHAPTER 16 Asset Prices and Interest Rates Figure 16-8 that accompanied monetary tightening occurred during 1981 when inflation was running near 10 percent and the Federal Reserve had tightened policy to reduce inflation. The 3-month Treasury bill rate rose to 15 percent and the yield curve inverted because people expected short-term interest rates to fall sharply in subsequent years. By 1983, the T-bill rate was 8 percent and by 1986 it was 6 percent Conclusion Changes in asset prices have important effects on the economy because they lead to changes in wealth that affect consumer spending and output. Economists use the classical theory of asset prices to explain asset-price movements. But the theory sometimes fails to explain changes in asset prices, particularly during bubbles and crashes. Unlike earlier chapters that emphasized the interest rate for the economy, this chapter considers how the economy has many interest rates and describes the relationship between short- and long-term interest rates.

11 LECTURE SUPPLEMENT 16-1 The Stock Market and Consumer Spending As the stock market soared in the late 1990s, an important issue for policymakers was determining how large an effect the gain in wealth might have on consumer spending. Federal Reserve Chairman Alan Greenspan, testifying before Congress in February 2000, expressed his belief that the wealth effect was an important factor in the surging U.S. economy: Historical evidence suggests that perhaps three to four cents out of every additional dollar of stock market wealth eventually is reflected in increased consumer purchases. The sharp rise in the amount of consumer outlays relative to disposable incomes in recent years, and the corresponding fall in the saving rate, has been consistent with this so-called wealth effect on household purchases.outlays prompted by capital gains in excess of increases in income, as best we can judge, have added about 1 percentage point to annual growth of gross domestic purchases, on average, over the past five years. 1 Greenspan s view is consistent with well-accepted models, that relate a household s consumption to its wealth. But a key additional question is whether the gains in the stock market were large enough to offset the fact that holdings of equities remain highly concentrated among a very small set of households. Even though more than half of all U.S. households now hold some equities (mainly through 401k retirement accounts), the distribution is still highly skewed, with the richest 5 percent of households owning 75 percent of equity wealth and the richest 20 percent owning 95 percent of equity wealth. Some recent evidence suggests that the largest effects on spending were indeed seen among the very wealthy, and were big enough to be consistent with the view that gains in the stock market had a direct effect on spending for the economy as a whole. 2 But another possibility is that indirect effects were also important, whereby households who did not own equities (or owned relatively few) still increased their spending because a rising stock market made them feel more confident about the future. 3 As the stock market fell sharply during , many analysts speculated that the drop in wealth (which was the first outright decline in annual nominal household net worth since at least 1945) would lead to a pullback in consumer spending and a deepening of the recession. Consumer spending, however, remained relatively buoyant during 2001 and into 2002 suggesting either that other factors had come into play or perhaps that the link between wealth and consumption is more complicated than we thought. 1 Testimony of Chairman Alan Greenspan before the Committee on Banking and Financial Services, U.S. House of Representatives, February 17, See K. E. Dynan and D. M. Maki, "Does Stock Market Wealth Matter for Consumption?" Federal Reserve Board Finance and Economics Discussion Paper , May 2001; and D. M. Maki and M. G. Palumbo, "Disentangling the Wealth Effect: A Cohort Analysis of Household Saving in the 1990s" Federal Reserve Board Finance and Economics Discussion Paper , April See J. M. Poterba, "Stock Market Wealth and Consumption," Journal of Economic Perspectives 14, no. 2 (Spring 2000):

12 LECTURE SUPPLEMENT 16-2 A Different View of the Stock Exchange Not everyone views the stock exchange as mainstream economists typically do 1 : The Stock Exchange was founded in 1792 by a group of brokers, who met under a buttonwood (sycamore) tree and agreed on this friendly price-fixing deal: We the subscribers, brokers for the purchase and sale of public stock, do hereby solemnly promise and pledge ourselves that we will not buy or sell from this day, from any person whatsoever, any kind of public stock at a less rate than onequarter percent commission on the special value, and that we will give a prefer - ence to each other in our negotiations. Visitors are treated to a tedious display that instructs us on the virtue of people s capitalism while congratulating us on the power of the great corporations. Hours are 10 A.M. to 4 P.M. on business days naturally. Admission is free, unlike a seat on the Exchange. As we near the nerve center of the Exchange, the tone darkens: No cameras allowed. Visitors gallery partitioned from trading floor by bulletproof 1 1/16-inch thick glass. Here is the story behind these extraordinary precautions. The visitors gallery was always an open balcony overlooking the floor of the Exchange. In 1966 a group from Youth Against War and Fascism made use of this easy access and bombarded the brokers with leaflets condemning the Vietnam War and its corporate supporters. A year later the Yippies floated dollar bills over the balcony, causing a mad scramble on the floor that thoroughly disrupted trade. Unnerved by the prospects of further attacks on its dignity and steadfastness, the Stock Exchange sealed itself off. 1 From T. Glickman and G. Glickman, The New York Red Pages: A Radical Tourist Guide (New York: Praeger, 1984), 26. Glickman and Glickman cite the quoted passage on the founding of the Exchange as coming from Frederick Collins, Moneytown. 396

13 ADVANCED TOPIC 16-3 The Importance of Asset Pricing for Macroeconomics One important area of macroeconomic study is that of asset pricing, that is, trying to explain the equilibrium prices of various economic assets, such as stocks and bonds or houses. This involves the study of financial markets and turns out to present a number of problems and puzzles that have not yet been fully resolved. Yet it is an important area of macroeconomic inquiry because financial markets bring together savers and investors in the economy. Our hope is that financial markets do a good job of directing available loanable funds to those activities that are most profitable. Many economists do indeed believe that financial markets operate efficiently and are an important aid to the smooth functioning of the economy. Others are less sanguine and believe that irrational behavior in such markets may be a source of shocks that disrupt the economy. Robert Shiller, an economist who suspects that asset prices change in large measure because of capricious behavior of investors, explains why this behavior matters as follows 1 : That prices change for no good reason is of great importance for many purposes. Prices of speculative assets guide very many economic activities in our society. When an asset is underpriced, incentives are created to neglect or abuse it. When it is overpriced, incentives are created to invest too much in it. The possibility that these prices may show repeated tendencies to move for no sensible reason matters greatly not only to those managing financial portfolios, but also to regulators, legislators, lawyers, corporate managers, builders, homeowners, collectors, conservators and others. A better understanding of the importance of such price changes may ultimately set the stage for people to take actions that will reduce their impact. Much work on asset pricing focuses on the stock market. Macroeconomists are particularly interested in the stock market for a number of reasons. First, movements in the stock market seem to be linked to movements in aggregate economic activity. Second, as noted previously, the stock market brings together savers and investors and thus helps guide the allocation of loanable funds to investment projects. Third, the stock market, if it functions efficiently, provides information about investors expectations concerning future economic performance. Macroeconomists are thus concerned by the fact that there is evidence of inefficiency in the stock market. 2 One observation suggests that lack of efficiency in the stock market actually might not be so serious. Most trading in the stock market is of existing shares, not new issues, and so has a less direct influence on the allocation of resources. Even if stock market prices do change for no good reason, these fluctuations in relative stock prices might then simply redistribute wealth from one set of gamblers to another, and the consequences for the macroeconomy might not be that large. Aggregate movements in the stock market still matter, however, because they represent changes in wealth, and wealth is a determinant of consumer spending. 3 1 R. Shiller, Market Volatility (Cambridge, Mass.: MIT Press, 1989) and R. Shiller, Irrational Exuberance (Princeton: Princeton University Press, 2000). Shiller s theories are discussed further in Supplement 16-6, Bubbles, Excess Volatility, and Fads. 2 See Supplements 16-4, Stock Prices and Efficient Markets, 16-5, Bond Prices and the Term Structure of Interest Rates, and 16-6, Bubbles, Excess Volatility, and Fads. 3 See Supplement 16-1, The Stock Market and Consumer Spending. 397

14 ADVANCED TOPIC 16-4 Stock Prices and Efficient Markets We discuss here some basic ideas about the pricing of a risky asset, focusing on the stock market. Consider a situation in which investors can invest in a riskless asset, which pays a certain (real) rate of return equal to r, or a stock, which pays an uncertain return. 1 Ownership of a stock entitles the investor to a stream of dividends. Dollars received in the future, however, are worth less than dollars today, because dollars today can be invested at the interest rate r. An individual will be indifferent between a dollar today and 1/(1 + r) dollars tomorrow; this is the present value (that is, the value today) of $1 tomorrow. Similarly, we can write the present value of a stream of dividends as PDV r d d t 1 t r 1 r dt 3 dt 4..., 1 r where d t denotes the dividend at time t. Since the present value tells us what the stream of dividends is worth today, we should expect it to equal the price of the stock today. To see how this works in more detail, suppose that h t is the holding return on the stock between period t and t + 1. The return on the stock consists of two components: the dividend that it will pay and any capital gain or loss that arises because of a change in its price. Thus, if p t is the price of the stock and d t+1 is the dividend, then d t+1 h t = + p p t+1 t ; p t Return = Dividend + Capital Gain. The return is uncertain because, at time t, investors do not know the price that the stock will command at t + 1 or the dividend that it will pay. For simplicity, however, let us suppose for the moment that investors have perfect foresight and so know the future dividend and the future price of the stock. In this case, arbitrage between the risky stock and the riskless asset will ensure that both earn the same return. This gives p t h t = d t+1 + p t+1 p t = rp t d t+1 + p t+1 p t p t p t = r p t (1 + r) = d t+1 + p t+1 p t = 1 (d t+1 + p t+1 ). 1 r This is the basic equation for the pricing of a stock. It tells us that the price of a stock today depends upon the dividend it will pay next period and the price of the stock next period. An analogous equation will hold for the price of the stock next period: p t+1 = 1 (d t+2 + p t+2 ). 1 r Substituting this into the previous equation, we can therefore write 1 2 p t = d t (d t+2 + p t+2 ). 1 r 1 r 1 For simplicity, we suppose that the interest rate is constant. 398

15 Chapter Supplements 399 By repeated substitution of this kind, we can ultimately write the current price of the stock solely in terms of the future dividends: 2 1 Pt r d = t d + r t r dt d r t..., 3 4 The price of the stock is indeed just given by the present discounted value of the stream of dividends that the stock will pay. Investors don t know future dividends with certainty, so the price of a stock actually depends upon their expectations of these dividends. If investors are risk neutral, meaning that they care only about average return and do not worry about risk, then arbitrage will imply that the expected holding return on the stock will equal the interest rate. 2 The price of the stock is then the present discounted value of expected future dividends. If the market is efficient, then investors will be making the best possible forecast that they can of future dividends, given the information that is available to them. In this case, the price of the stock will reflect all the information available in the market about the likely profitability of the company. 3 An important implication of this is that changes in stock prices should come about only as a result of new information. Thus, changes in stock prices should not be predictable on the basis of any currently available information, for if they were, arbitragers would be able to make profits. 4 The overall value of the stock market, by extension, should reflect investors best predictions about the future profitability of all firms (and hence, among other things, about the future state of the U.S. economy). Economists who are skeptical about the efficiency of the stock market point to the stock market crashes of 1929 and 1987 as evidence of inefficiency. The Dow Jones index fell 23 percent in one day in October Although large fluctuations in stock prices are not themselves necessarily inconsistent with stock market efficiency, there was no obvious new information that could have led investors to revise their opinion about the probable future profitability of U.S. firms to such a dramatic extent. 5 Others have pointed out that information may be transmitted imperfectly within the market, so stock prices may change as a result of the transmission of news in the market. The market may rationally revise its view of the fundamentals even when no new outside news arrives. 6 2 Supplement 16-7, The Capital-Asset Pricing Model, considers how riskiness affects asset prices. 3 Different definitions of market efficiency are sometimes used depending upon exactly what information is reflected in the price of the stock. 4 This idea is sometimes loosely referred to as the random-walk theory: stock prices should follow a random walk. See S. LeRoy, Efficient Capital Markets and Martingales, Journal of Economic Literature 27 (December 1989) (particularly Section III) for a good discussion. 5 See Supplement 16-6, Bubbles, Excess Volatility, and Fads, for more discussion of stock market efficiency. 6 See, for example, D. Romer, Rational Asset-Price Movement Without News, American Economic Review 83, no. 5 (December 1993):

16 ADVANCED TOPIC 16-5 Bond Prices and the Term Structure of Interest Rates The textbook often speaks of the interest rate. Yet we know that in the real world there are many different interest rates. An important first observation is that the simplifying assumption of a single interest rate is not badly misleading for much macroeconomic analysis, because different interest rates, broadly speaking, tend to move together in practice. Macroeconomists, however, do concern themselves with explaining why different assets yield different returns. Over the period , the real interest rate on U.S. Treasury bills averaged 0.5 percent. Other assets yielded much higher returns. Over the same period, the real return on long-term government bonds was 1.7 percent; the real return on long-term corporate bonds was 2.3 percent; the real return on common stocks was 8.8 percent; and the real return on small-company stocks was 14.2 percent. 1 Such substantial differences in returns are naturally of interest to macroeconomists and financial economists. The returns on assets differ for two reasons: first, because different assets have different risk characteristics and, second, because different assets have different terms to maturity. Explaining how the risk characteristics of assets affect their return is a topic that has given rise to a great deal of work in financial economics, and though much is understood, many puzzles also remain. 2 The way in which the return on assets depends upon their term to maturity is known as the term structure of interest rates. As a preliminary to this, consider the basic principles discussed in the text, behind the pricing of a bond. A bond is an asset that is described in terms of three basic characteristics: its term to maturity; the coupon that it pays out each year; and its face value, which is the amount that it pays at maturity. 3 Various assets exist that are special cases: zero-coupon bonds, as the name suggests, pay only at maturity; perpetuities (or consols) have an infinite term to maturity, or in other words, they simply pay a coupon every year, forever. The pricing of a bond in some ways resembles the pricing of a stock. 4 Whereas the price of a stock is the present value of the stream of dividends that it pays, the price of a bond is the present value of the coupon payments and the face value. For simplicity, consider the case of a consol, in which case the price of the bond is given by PDV r C 1 1 C C 1 1 r 1 r r 1 r 1 r.. C, where C is the coupon payment. The sum of the infinite series in parentheses is simply 1/r, so we have C PDV =. r 1 Stocks, Bonds, Bills, and Inflation 1988 Yearbook (Chicago: Ibbotson Associates, 1988), See Supplement 16-7, The Capital-Asset Pricing Model. 3 Bonds may, and often do, pay coupons more frequently than annually; for ease of presentation we here take the relevant time period for analysis to be a year. 4 See Supplement 16-4, Stock Prices and Efficient Markets. 5 More generally, if a bond comes to maturity M periods from now, we can write 1 PDV = ( ) ( ) C C + ( ) 3 C ( ) M (C + F), 1 + r 1 + r 1 + r 1 + r where C is the coupon payment, F is the face value, and r is an appropriate interest rate. 400

17 Chapter Supplements 401 Equally, just as the holding return on a stock at time t depends upon the dividend that it pays next period and the change in the price (capital gain or loss) between this period and next period, so the holding return on a bond depends upon the coupon payment and the change in the price. The coupon payment, however, does not vary over time and so does not need to be predicted. Letting p t be the price of the bond and h t be the return on the bond, we have C p t+1 p t h t = +. p t If we set this return to be constant between now and the time of maturity (that is, set h t = r for every year), we can calculate the yield to maturity (r) of the bond. When people speak of the interest rate on a bond, they usually are referring to the yield to maturity. We have rp t = C + p t+1 p t 1 p t = (C + p t+1 ). 1 r An equation like this holds for every period. By repeated substitution we can write the price of a bond at time t as Pt = 1 r C 1 1 C C r + + r p t = C/r, confirming that the price of the consol is indeed simply the coupon divided by the interest rate. The important conclusion from this analysis is that bond prices and interest rates are inversely related: when bond prices fall, interest rates rise. The term structure considers how the interest rates on bonds of different maturities are related. The principal theory of the term structure of interest rates is known as the expectations theory. The basic idea of this theory is very intuitive: agents should expect to gain the same return by investing in a long-term bond or by investing in a succession of short-term bonds. For simplicity, we restrict attention here to zero-coupon bonds. Thus, imagine an investor who can invest (at time t) in a two-year bond with annual interest rate (1) r, or who can instead invest in a one-year bond at the interest rate r t, and then take the (1) proceeds and reinvest them in another one-year bond paying an interest rate r t+1 : The expectations theory of the term structure then states that (1 + r t ) 2 = (1 + r t )(1 + r t+1). As an approximation, we can write (2) (1) (2) r r t (1) (1) + r t t+1. 2 (1) 6 We can again consider the more general case, in which this equation holds up to the period before the bond comes to maturity. The price when the bond comes to maturity is simply the face value: After repeated substitution we obtain r r p t+m = F r PDV = ( ) C + ( ) 2 C + ( ) 3 C ( ) M (C + F), so the price of a bond does indeed equal the present discounted value of the coupon payments and the face value. Note that zero-coupon bonds are particularly simple to price: ZC F p =. t (1 + r) M r

18 402 CHAPTER 16 Government Debt and Budget Deficits In other words, the annual return on the two-year bond is approximately the average of this year s and next year s return on one-year bonds. This basic approach is easily extended to bonds of longer maturity. (1) Investors making decisions this year do not know next year s interest rate (r t+1) with certainty, however. Thus, the term structure actually describes a relationship between the interest rate on a long bond and current and expected future interest rates on short bonds. The interest rate on long bonds relative to short bonds thus reflects agents expectations about future interest rates. To see this clearly, subtract r (1) t from both sides of the previous equation to get (2) (1) t+1 rt r r. t t 2 According to this equation, the long rate will exceed the short rate if interest rates are expected to rise, and the short rate will exceed the long rate if interest rates are expected to fall. The expectations theory of the term structure explains theoretically why different interest rates tend to move together, since it shows that the interest rate on a long bond is simply an average of the interest rates on short bonds. The expectations theory does not explain another fact about the term structure, however: long bonds generally have a higher return than short bonds. According to the expectations theory, the interest rate on long bonds is lower whenever investors anticipate a fall in interest rates, but it seems improbable that investors are always expecting interest rates to rise. The term structure as set out so far neglects the fact that individuals may have a preference for shorter bonds because they dislike the risk associated with changes in the price (that is, capital gains or losses) of long-term bonds. There may therefore be a liquidity premium that must be paid in order to persuade individuals to hold long bonds. In this case, the long rate will exceed the short rate even if no change in interest rates is anticipated. Since this is what we observe in the data, it seems likely that liquidity premiums are important. r (1) (1)

19 ADVANCED TOPIC 16-6 Bubbles, Excess Volatility, and Fads There are a number of dramatic historical incidents known as speculative bubbles, where the price of an asset rises and falls dramatically. One of the most famous is Tulipmania: In the Netherlands in the seventeenth century, certain rare varieties of tulip bulbs sold at extraordinarily high prices. For example, a Semper Augustus bulb sold for 2,000 guilders in 1625, an amount of gold worth about $16,000 at $400 per ounce. 1 At the end of 1636 and the beginning of 1637, tulip bulb prices rose very rapidly and then collapsed suddenly; two years later, bulbs were selling for less than 0.1 guilder. Another famous example is the South Sea Bubble, during which the price of shares in the South Sea Company rose more than eightfold between January and July 1720 and then fell back to about their original level in the next three months. 2 In these cases, it seems that the price of an asset changes not because of a change in the fundamentals, but because investors are demanding the asset in the anticipation of future price rises, brought about in turn by more investors demanding the asset in the expectation of still further price rises, and so on. 3 These incidents make many economists skeptical of the purported efficiency of financial markets. Further evidence of inefficiency in financial markets is the observation that asset prices are much too variable to be explained in terms of changes in fundamentals. 4 The economist Robert Shiller is a strong proponent of this view. Informal evidence of such excess volatility comes from the observation of major variation in asset prices, such as the stock market crash of October 1987 or the recent movements in real estate prices in some parts of the United States. Shiller and others have also provided more formal tests. Shiller s argument rests on a property of rational expectations and some simple statistics. He noted that if the path of future dividends were known with certainty, then the perfect-foresight price of a stock would be given by the present value of the stream of dividends. 5 The actual price that investors are willing to pay represents their prediction of this perfect-foresight price. If investors have rational expectations, then the actual price will be the best possible forecast of the perfect-foresight price. The perfect-foresight price then equals the actual price plus an unpredictable error term: pf p t = p t + u t. The term u t is the forecast error. If agents have rational expectations, this will be random and unpredictable. Shiller s insight was that the actual price should be smoother than the perfect-foresight price, since some of the variation in the perfect-foresight price should be the result of forecast errors. But this is manifestly not true in the data: actual stock prices are very volatile, and the perfect-foresight price is relatively smooth. 6 Dividends turn out not to vary very much, so it is hard to explain why stock prices exhibit large fluctuations. 1 P. Garber, Famous First Bubbles, Journal of Economic Perspectives 4, no. 2 (Spring 1990): 37. The description of historical bubbles here is based on Garber s account. Garber actually argues that this and other classic examples of bubbles should not be viewed as signaling failure of efficiency or rationality of investors. 2 Ibid., see Figure 3. 3 Interestingly, the existence of bubbles need not imply irrationality. Economists have derived conditions under which the price of an asset can contain a bubble component, even when agents are rationally anticipating the future price movements of the asset. A good, though difficult, discussion is in O. Blanchard and S. Fischer, Lectures in Macroeconomics (Cambridge, Mass.: MIT Press, 1989), Chapter 5. 4 There is extensive literature on this subject, which largely originated from the following two papers: R. Shiller, Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends? American Economic Review 71 (1981): ; S. LeRoy and R. Porter, The Present Value Relation: Tests Based on Implied Variance Bounds, Econometrica 49 (1981): See Supplement 16-4, Stock Prices and Efficient Markets. 6 More formally, under rational expectations the forecast error should be uncorrelated with the actual price, since otherwise the forecast is not optimal. The theory can then be tested by looking at the variance of the actual and perfect-foresight prices. Shiller s original argument was criticized by a number of authors on the basis of some technical statistical arguments (very roughly, under some dividend policies, the stock price may follow a random walk; if so, the test is not valid). Subsequent tests that correct such statistical problems still retain the basic message, however. 403

20 404 CHAPTER 16 Asset Prices and Interest Rates Researchers have also tried to see if the actual behavior of asset prices can be explained (after the fact) by the behavior of fundamentals. Richard Roll looked at the price of orange juice futures and argued that changes in these prices should be primarily caused by news of the Florida weather. 7 In contrast to what market efficiency would suggest, he found that these prices varied much more than could be accounted for by weather news. Yet another way to look for inefficiency in asset markets is to see whether there are unexploited profit opportunities ways to get something for nothing. Economists have looked to see if there are trading rules: simple rules that could be mechanically applied and that would earn above average profits. Karl Case and Robert Shiller suggested that a simple trading strategy could have exploited profit opportunities in the real estate market. 8 Bruce Lehmann showed that a contrarian strategy of taking short positions in winners (selling stocks whose prices have recently increased) and long positions in losers (buying stocks whose prices have recently fallen) would have made a profit over the period Such findings are intriguing but do not prove inefficiency. First, it has to be demonstrated that excess profits are large enough to overcome the transactions costs of implementing the rule. Second, identifying a profitable trading rule on the basis of past data is not a guarantee that it will work in the future. Third, as Donald McCloskey points out, such researchers must answer the American Question: if you re so smart, why ain t you rich? 10 Of course, some providers of investment advice do get rich by advising the market. The fact that some advisers do succeed in outperforming the market is also apparently inconsistent with simple notions of market efficiency. There are many such providers operating, however, and so we should expect that some should turn out to do well just by chance. The important question is, do we think that an investment service is likely to be able to beat the market in the future if we observe that it has succeeded in so doing in the past? On the basis of his research on different asset markets, Shiller argues that market efficiency cannot provide an adequate explanation of the behavior of asset prices. Shiller s preferred theory is that fads and fashions play an important role in the determination of such prices. Progress in explaining the behavior of asset prices may require economists to move beyond naive models of rational behavior and pay much more attention to work in social psychology and sociology. Surveys seem to provide support for this view. For example, Shiller and co-researchers found that a majority of investors themselves explain the fall in the stock market in October 1987 in terms of investor psychology rather than movements in fundamentals. Surveys also reveal that speculative considerations were a major motivation for house purchases in areas experiencing real estate booms. 11 Not all economists share Shiller s view. Some believe that markets are basically efficient; apparent weaknesses in efficient-market models may just signal that we do not yet understand the fundamentals well enough. 12 Others agree that markets are inefficient but suggest that cognitive psychological, rather than social psychological (that is, individually rather than socially based), explanations are more promising R. Roll, Orange Juice and Weather, American Economic Review 74 (December 1984): K. Case and R. Shiller, The Efficiency of the Market for Single Family Homes, American Economic Review 79 (1989): B. Lehmann, Fads, Martingales, and Market Efficiency, Quarterly Journal of Economics 105 (February 1990): D. McCloskey, The Rhetoric of Economics (Madison: University of Wisconsin Press, 1985), See R. Shiller, Speculative Prices and Popular Models, Journal of Economic Perspectives 4, no. 2 (Spring 1990): 55 66; R. Shiller and K. Case, The Behavior of Home Buyers in Boom and Post-Boom Markets, New England Economic Review (1988): 29 46; and also R. Shiller, Market Volatility (Cambridge, Mass.: MIT Press, 1989), Ch See, for example, J. Cochrane, Volatility Tests and Efficient Markets: A Review Essay, Journal of Monetary Economics 27 (June 1991): One important question, analyzed by Sanford Grossman, concerns how different individuals private information is aggregated into the prices of stocks. Grossman observes that for any individual investor the price of a stock provides an (imperfect) summary of the information of other agents. Now suppose some investors (noise traders) trade for reasons unconnected with changes in information. If the demand of these traders falls, then other traders observe a fall in the price. These traders know that this may reflect new negative information of other informed traders, and so change their demands. Grossman argues that such behavior may help to explain financial panics such as the October 1987 crash. See S. Grossman, The Informational Role of Prices (Cambridge, Mass.: MIT Press, 1989). 13 See, for example, S. LeRoy, Efficient Capital Markets and Martingales, Journal of Economic Literature 27, no. 4 (December 1989): 1616.