The Market Risk Premium
Content
Research Roundtable The Equity Premium
By: IVO WELCH Yale School of Management Yale University [email protected] Yale University Yale School of Management 46 Hillhouse Ave. New Haven, CT 06520 (203) 436-0777 (203) 436-0779 PETER TUFANO Harvard Business School Harvard University
Email Postal:
Phone: Fax: Organized by
Discussants PETER BOSSAERTS, California Institute of Technology JOHN COCHRANE, University of Chicago, Graduate School of Business GENE FAMA, University of Chicago, Graduate School of Business WILL GOETZMANN, Yale University, School of Management ROBERT S. HARRIS, Darden Graduate School of Business, University of Virginia JOHN HEATON, Northwestern University, Kellogg Graduate School of Management ROGER IBBOTSON, Yale University, School of Management MICHAEL J. MAUBOUSSIN, Chief U.S. Investment Strategist - Credit Suisse First Boston and Adjunct Professor - Finance and Economics -Columbia Business School ANDRE F. PEROLD, Harvard University, Harvard Business School JAY RITTER, University of Florida, Warrington College of Business ROBERT WHITELAW, New York University, Stern School of Business Discussion board available at: http://ssrn.com/forum/ Document: Available from SSRN Electronic Paper Collection: http://papers.ssrn.com/paper.taf?abstract_id=234713 June 30, 2000
Date:
I. II. III. IV.
A BRIEF INTRODUCTION TO THE EQUITY PREMIUM SELECTED BIBLIOGRAPHY COMMENTS BY DISCUSSANTS BULLETIN BOARD FOR DISCUSSION OF THE EQUITY PREMIUM
I.
A BRIEF INTRODUCTION TO THE EQUITY PREMIUM
Loosely speaking, the equity premium is the difference between the return on risky stocks and return on safe bonds. It is the prime input both in the CAPM (the model used by most practitioners in computing an appropriate hurdle rate), and in asset allocation decisions (the choice of whether an investor should hold stocks or bonds). Unfortunately, there is no universally accepted definition of the equity premium. In particular, one can compute equity premia using different stock market indices, different bonds (either long-term or short-term), different methods of compounding or cumulating returns over time, and different historical time periods. Such computational differences can lead to valid historical equity premium quotations ranging from 4.3% per year up to about 9.4% per year, depending also on the time period quoted (e.g., Welch [2000]). It is important for a user of equity premium estimates to be clear about which definition is used and why it is the appropriate definition for the particular purpose it is used for. There are three inter-related questions of primary interest to researchers: [1] Why has the historical equity premium been so high? [2] What is a good forward-looking prediction for the equity premium for the long run? [3] Can one use other variables, such as dividend yields, to come up with a good forecast of the equity premium, at least over a 1-5 year period? As first pointed out by Mehra and Prescott [1985], a return differential of, say, 8% per year is enormous especially over a long enough horizon. Ibbotson and Associates, the "gold-standard" provider of historical equity premium data, show that an investment of $1 in 1925 would be worth $5,116 by 1998, whereas an investment in treasury bills would only be worth $15. (And it is well known that treasury bill returns generally suffer higher taxes than capital gains!) The profession falls into three loosely defined camps with respect to why equity premia have been so high and whether they will continue to be high. The first camp argues that these high equity premia were necessary to induce investors to participate in the stock market (e.g., Benartzi and Thaler [1995], Campbell and Cochrane [1999]). This argument implies an equity premium (possibly) as high in the future as in the past. The second camp argues that the expected returns necessary to entice investors have fallen in the last few years. This means, stocks can trade for much higher prices today, which itself is both responsible for the recent stock market appreciation, and for the expectation of much lower returns in the future (e.g., Heaton and Lucas [1999]). Closely related are arguments that historical equity premia are mismeasured, and not indicative of ex-ante equity premium expectations (e.g., Goetzmann and Jorion [1999], Siegel [1999]). The third camp argues that the stock market has gone crazy and we are all in a bubble right now. Again, this implies much lower future returns in the future. In contrast to the second camp, this camp would be less surprised by a crash or crash-like rapid drop in the stock-market. Although few academics have published this view (except Shiller [2000])---not necessarily because they do not dare, but because it is difficult to bring unambiguous evidence to bear on this matter---many seem to individually subscribe to it. [Footnote: This issue is closely connected to the question of whether Internet stocks are right now overvalued. Once willing to concede that internet stocks are overvalued, it is not a far step to concede that it is possible that the stock market as a whole is overvalued, too.] One can also bring additional evidence to bear on the second question without taking a stance on the first question: There are a number of publicly accessible forecasts from investors, academics, corporations. (Welch [2000]). Typically, investors seem to expect higher equity premia, academics seem to expect equal (or just slightly lower) equity premia, and corporations and
consulting firms seem to expect lower equity premia than those realized in the past. In sum, these forecasts run counter to the view that equity premia have recently been so high, because everyone expects them to be lower in the near future. Finally, a new set of working papers are attempting to attribute "plausible" equity premia based on long-term forecasts of real growth (e.g., Diamond [2000], Welch [1998]). The third question is equally tricky as the first two questions. There is universal consensus that the equity premium cannot be easily predicted over shorter horizons, such as one month; and that even if the equity premium can be predicted over a longer horizon (e.g., over a 30-year forecast), we do not have enough historical data to run regressions to validate 30-year forecasting claims. The variable most often mentioned as a possible predictor of equity premia is the prior-year dividend-yield. This predictability was first explored in a rigorous manner by the seminal papers of Campbell and Shiller [1988], Fama and French [1988], and Blanchard [1993], which came to the conclusion that dividend-yields do seem to have predictive ability. In a simple regression predicting equity premia one-year ahead with dividend-yields, the dividend yield shows great statistical significance. However, a long line of subsequent research has pointed to various statistical issues in this early work. Furthermore, most such models predict one-year-ahead forecasts of negative equity premia as of the year 2000---not a sensible prediction. Yet, even if there is disagreement of whether documented forecasting ability of dividend yields was real, there is little disagreement that this predictive ability has disappeared in the 1990s (Goyal-Welch [2000]). Where does this leave us? The equity premium is not only the single most important number of finance, but estimating it is also our most perplexing problem. If the profession fails to make progress in understanding the process driving the equity premium, progress on many of the most important problems in finance---proper asset allocation and hurdle rates--are likely to be phyrric victories only.
II.
SELECTED BIBLIOGRAPHY
Benartzi, Shlomo and Richard H. Thaler. "Myopic L Aversion And The Equity Premium Puzzle," Quarterly Journal of Economics, 1995, v110(1), 73-92. Blanchard, Olivier J. "Movements In The Equity Premium," Brookings Papers, 1993, v24(2), 75118. Campbell, John Y. and John H. Cochrane. "By Force Of Habit: A Consumption-Based Explanation Of Aggregate Stock Market Behavior," Journal of Political Economy, 1999, v107(2,Apr), 205-251. Campbell, John Y. and Robert J. Shiller. "The Dividend-Price Ratio And Expectations Of Future Dividends And Discount Factors," Review of Financial Studies, 1988, v1(3), 195-228. Fama, Eugene F. and Kenneth R. French. "Dividend Yields And Expected Stock Returns," Journal of Financial Economics, 1988, v22(1), 3-26. Jorion, Philippe and William N. Goetzmann. "Global Stock Markets In The Twentieth Century," Journal of Finance, 1999, v54(3,Jun), 953-980. Goyal, Amit, and Ivo Welch. "Predicting the Equity Premium." UCLA/Yale Working Paper. http://welch.som.yale.edu/
Heaton John and Deborah Lucas. "Stock Prices and Fundamentals." NBER Macroeconomics Annual 1999, published by MIT press (edited by Bernanke and Rotemberg). Mehra, Rajnish and Edward C. Prescott. "The Equity Premium: A Puzzle," Journal of Monetary Economics, 1985, v15(2), 145-162. Siegel, Jeremy J. "The Shrinking Equity Premiums," Journal of Portfolio Management, 1999, v26(1,Fall), 10- 17. Welch, Ivo. "Views of Financial Economists On The Equity Premium And On Professional Controversies." Journal of Business, 2000, forthcoming. III. REACTIONS BY DISCUSSANTS Each of the discussants was given the article above and asked to address the question, “What do you teach MBA students about the equity premium?” We thank them for their willingness to share their ideas and experiences. -----------------------------PETER BOSSAERTS California Institute of Technology The available attempts at explaining the historic U.S. equity premium have been based too much on the very narrow, stationary, single-consumer, rational expectations equilibrium of Lucas. Too little is done to deviate from this implausibly strong notion of equilibrium. Rational expectations equilibria do allow for mistaken expectations. They even allow for disagreement. And incomplete markets. Moreover, there is an objectionable assumption behind all of modern empirical analysis, namely that recorded market prices are always equilibrium prices. Too little attention is paid to genuine dynamics (equilibrium price discovery). Finally, any scientifically relevant attempt at explaining the historic U.S. equity premium simultaneously will have to explain historic evidence over other countries (e.g., Japan in the 1990s) that is diametrically opposed (low real rates of interest, negative equity premium). ------------------------------JOHN COCHRANE University of Chicago, Graduate School of Business I don't really have much to add. My own view is about 3-4% unconditional and much lower but positive conditional. Did the average investor in 1947 really think that average stock returns would be 9% over bonds, with a 16% volatility, and say "no thanks, I don't want to buy more stocks because that volatility scares me?" Probably not! Hence, much of the postwar sample must be good luck rather than the unconditional mean. -------------------------------GENE FAMA University of Chicago, Graduate School of Business The Gordon constant dividend growth model and realized returns produce similar estimates of the real equity premium for 1872-1949, about 4.0 percent per year. For 1950-1999, the Gordon estimate, 3.40 percent per year, is only about forty percent of the estimate from realized returns, 8.28 percent. The difference between the realized return for 1950-1999 and the Gordon estimate of the expected return is largely due to unexpected capital gains, the result of a decline in
discount rates. Forward-looking Gordon estimates of the expected equity premium are about one to two percent per year. (Comments based on work by Gene F. Fama and Kenneth R. French) ----------------------WILL GOETZMANN Yale University, School of Management The equity premium is commonly defined as the percentage by which stock market returns are expected to exceed a riskless bond investment. Theory argues for a positive equity premium. A rational, risk-averse investor with a riskless investment opportunity should demand greater compensation for holding a riskier asset -- but how much greater? Empirical estimates of the equity premium are typically based upon historical realizations of stock and riskless bond returns. As such a "pure" estimate of the historical equity premium may be impossible. The composition and leverage of the equity markets continually changes and a purely riskless asset does not exist. Never-the-less, the average U.S. equity premium generally exceeded 6% per annum over extended historical periods. Is the historically realized equity premium a good forecast for the future? The answer depends upon whether the economic factors contributing to the historical premium can be expected to continue as well. -----------------------------ROBERT S. HARRIS University of Virginia, Darden Graduate School of Business The Market Risk Premium: Expectational Estimates Ivo Welch's comments nicely capture much recent academic thinking on the market risk premium. I'd like to add observations from work that directly uses expectational data from financial analysts to estimate the U. S. market premium. The results do not resolve the equity risk premium puzzle but provide interesting additions to what counsel might be provided to practitioners and students. Investigators have most often used averages of historical realizations to estimate a market premium. This choice has some appealing characteristics but is subject to many arbitrary assumptions such as the relevant period for taking an average. Practice seems to mirror this framing around historical returns. Recent survey results on best practices by corporations and financial advisors (see Bruner et al (1998)) reveals that almost all respondents used some average of past data in estimating a market risk premium and displayed considerable variation in the choice of time period and method (arithmetic versus geometric) for averaging. Few respondents cited use of expectational data to supplement or replace historical returns in estimating the market premium. Many textbook treatments also rely on historical returns citing the Ibbotson data for the U.S. As Welch notes, however, shareholder required rates of return and risk premia are based on theories about investors' expectations for the future. Fortunately, there is a relatively longstanding tradition of estimating a market premium using publicly available expectational data from financial analysts. This approach uses some variant of a discounted cash flow model to infer the market premium from the combination of analysts' forecasts of future performance and current stock prices (1). In my view, four key findings are instructive (2). First, for the last two decades, the market premium implied by expectational data from financial analysts is comparable in magnitude to long-term differences (1926 to 1998) in historical returns between stocks and bonds. As a result, the evidence does not resolve the equity premium puzzle
and suggests that investors still expect to receive large spreads to invest in equity versus debt instruments. Second, at least based on current evidence through 1998 the market premium does not appear to have declined dramatically in the 1990s. Third: the market risk premium changes over time. Moreover, these changes appear linked to the level of interest rates as well as ex ante proxies for risk drawn from financial markets. Higher interest rates appear associated with lower market premia. The significant economic links between the market premium and a wide array of risk variables suggests that the notion of a constant risk premium over time is not an adequate explanation of pricing in equity versus debt markets. Fourth, using analyst forecasts as a proxy for investor expectations has many desirable features but more work is need to understand the extent to which optimism by analysts may affect the empirical estimates of market premia. In the face of this evidence as well as Welch's comments, what is the message for practice and education? Humility seems a useful starting point. More research in the area is certainly warranted. That having been said we should not "throw the baby out with the bathwater". At a conceptual level the market premium provides large benefits in sharpening thinking about resource allocation. One conclusion for practice that I draw is that common application of models such as the CAPM will overstate changes in shareholder return requirements when government interest rates change because risk premia seem to move inversely with interest rates. This is consistent with much corporate practice that does not revise hurdle rates for modest variations in interest rate conditions. A second conclusion is that we should sensitize students to the potential for risk premium variation. Having debunked the notion that the risk premium is, like Avogadro's number, a constant from on high, I adopt an administrative standard of a particular market premium (say 6%) for any class so that we do not constantly revisit the issue. A third implication is that we should in teaching, practice and research look for objective yet forward looking data that can be deployed to give insights on the market premium. Finally, our humility on the level of the market premium should make us take pains to invest in understanding the true underlying risks and opportunity inherent in an investment (say through sensitivity analysis, simulation or options frameworks). (1) See for example Malkiel (1982), Brigham, Vinson, and Shome (1985), Harris (1986) Harris and Marston (1992,1999). Ibbotson Associates (1998) use a variant of the DCF model with forward-looking growth rates as one means to estimate cost of equity; however, they do this as a separate technique and not as part of the CAPM. For their CAPM estimates they use historical averages for the market risk premium. The DCF approach with analysts' forecasts has been used frequently in regulatory settings. (2) These findings are drawn from Harris and Marston (1992,1999) who also summarize some of the earlier work. REFERENCES D. Brigham, D. Shome, and S. Vinson, "The Risk Premium Approach to Measuring A Utility's Cost of Equity," Financial Management (Spring 1985), pp. 33-45. R.F. Bruner, K. Eades, R. Harris and R. Higgins, Best Practices in Estimating the Cost of Capital: Survey and Synthesis," Financial Practice and Education (Spring/Summer 1998), pp. 13-28. W.T. Carleton and J. Lakonishok, "Risk and Return on Equity: The Use and Misuse of Historical Estimates," Financial Analysts Journal (January/February 1985), pp. 38-47.
R.S. Harris, "Using Analysts' Growth Forecasts to Estimate Shareholder Required Rates of Return," Financial Management (Spring 1988), pp. 58-67. R.S. Harris and F.C. Marston, "The Market Risk Premium: Expectational Estimates Using Analysts' Forecasts," October 1999, Darden School Working Paper DSWP-99-08. R.S. Harris and F.C. Marston, "Estimating Shareholder Risk Premia Using Analysts' Growth Forecasts," Financial Management (Summer 1992), pp. 63-70. Ibbotson Associates, Inc., 1998 Cost of Capital Quarterly, 1998 Yearbook Ibbotson Associates, Inc., 1997 Stocks, Bonds, Bills, and Inflation, 1997 Yearbook. B. Malkiel, "Risk and Return: A New Look," in The Changing Role of Debt and Equity in Financing U.S. Capital Formation, B.B. Friedman (ed.), National Bureau of Economic Research, Chicago, University of Chicago Press, 1982. -------------------------------JOHN HEATON Northwestern University, Kellogg Graduate School of Management Over the last century the average return to holding stocks was much higher than the average return to holding bonds. If this difference reflected expected returns then the high returns on stocks should represent compensation for risk. When viewed in isolation the stock market does appear to be quite volatile. The economy as a whole is much less risky, however. This is important because the typical household in the United States receives income from wages, salaries and other sources that more closely resembles aggregate GNP than stock market returns. The typical household should therefore be willing to invest a substantial amount in the stock market since the return is high and the risk can be diversified away using the household's other sources of income. The resulting large demand for stocks would ultimately increase stock prices and reduce expected returns. The fact that this did not occur historically results in the "equity premium puzzle." Viewed in this way the equity premium puzzle is really a diversification puzzle. There are several potential explanations for this diversification puzzle. First is the fact that stock ownership is relatively concentrated among wealthy individuals. These individuals tend to have business income that is less like aggregate income and more like stock returns than the average household [see, for example, Heaton and Lucas (2000)]. For these people the diversification possibilities that can be obtained by holding stocks are small. Second, in the past, holding a diversified portfolio of financial assets was difficult due to high costs of trading, brokerage fees and the like. As a result, the typical investor held a portfolio that was much more risky than the stock market index. This lack of diversification implies that the actual portfolios individuals held were much riskier than a stock index. Both of these effects imply that historically investors required high returns to hold equity. Over time the level of diversification seems to have increased both because investors have been able to hold better diversified portfolios by holding mutual funds and because wealthy individuals are able to better diversify their privately held equity. As a result, the required return to holding stocks may have fallen in recent years which possibly explains the recent dramatic increase in stock prices. This argues that looking forward the average premium investors will receive by holding stocks is likely to be much lower than it was in the past.
References: Heaton, John and Deborah Lucas (2000), ``Portfolio Choice and Asset Prices; The Importance of Entrepreneurial Risk,'' Journal of Finance, 55, pp. 1163-1198. ----------------------------ROGER IBBOTSON Yale University, School of Management The first way that I would estimate ERP is to look at the historical payoff for risk. I would use the Ibbotson and Sinquefield results reported in the Stocks, Bonds, Bills and Inflation 2000 Yearbook, published by Ibbotson Associates (www.ibbotson.com) which shows that over the 1926-1999 period common stocks had a 11.3% compound annual return and a 13.3% annual arithmetic mean return. In contrast, long-term government bond income returns were 5.2%, giving a long horizon historical arithmetic mean ERP of 8.1%. The historical payoff for risk is a good guide to the future risk premium, but it is not perfect. First, there is considerable estimation error even assuming the 74 years returns were drawn from a stationary distribution. A standard deviation of 20% gives a standard error of 2.7%. Using shorter estimation periods increases the estimation error. Goetzmann, Ibbotson and Liang (2000) have constructed a raw data series based upon individual security prices and dividends over the period 1815-1925. This longer series may help us estimate the ERP with lower estimation error. Another way to estimate the ERP is to recognize that the stock market is a part of the economy. In Diermeier, Ibbotson, and Siegel (1984), we assume that the stock market remains a constant share of the economy. Using historical estimates of real GNP growth, and inflows and outflows of the stock market, we can calculate the expected return on the stock market. The supply side estimate of the stock market is substantially lower than the historical ERP, since the stock market has been increasing its share of the economy. We would not expect this to continue indefinitely, so that we would consider both methods in making an ERP estimate. I am currently updating and revising our supply side estimate. There are several caveats to any estimation method. Is the U.S. the successful survivor, so that past returns or GNP growth are artificially high? Are we at an artificial peak in the stock market or economy (a bubble) which makes historical growth an upward biased prediction of the future? Is the ERP too high based upon reasonable risk aversion parameters? Has the risk decreased, lowering the ERP? On the other hand, some caveats might cause us to increase our estimate of ERP. Is future stock market risk in fact higher than past risk, perhaps because of potential shocks? Are we in a faster moving "new economy" so that time moves faster, increasing the ERP? Overall, I think the best estimate of the ERP is to use some combination of the historical ERP and the supply side estimate of the ERP. -----------------------------MICHAEL J. MAUBOUSSIN Chief U.S. Investment Strategist, Credit Suisse First Boston and Adjunct Professor - Finance and Economics, Columbia Business School There are three points I stress in discussing the equity risk premium (ERP). First, it is important to acknowledge that the capital asset pricing model-for all of its elegance-is unlikely to be the last word on our understanding of risk and reward. Second, the ERP should be estimated ex-ante.
Ex-post definitions come with a lot of calculational baggage, most notably choice of time period and data non-stationarity. Finally, use a long-term discounted cash flow model to estimate expected return, and then subtract a long-term Treasury yield to estimate the ex-ante ERP. A long-term Treasury is used because it matches the duration of most stocks and properly incorporates expected inflation. I believe that the ERP has been in a range of 2-5% in recent years. We currently use about 4.0% at CSFB. This suggests an expected long-term nominal stock market return of about 10%. One final note. A proper estimate of ERP has obvious significance in asset allocation. But for the active equity manager-the avocation of many of my students-stock selection is a relative endeavor. So stock selection distills to anticipating expectation shifts in key operating value drivers. As a result, ERP is not a defining issue. ------------------------------ANDRÉ PEROLD Harvard University, Harvard Business School In my MBA investments course, I ask students to value the stock market on the basis of a discounted cash flow analysis. The essential conclusion of this analysis is that if stocks are not overvalued, the forward looking risk premium is low (about 3%); or long-run future real cash flow growth must be extremely high. The result seems robust to the choice of cash flow model. For example, in the growth perpetuity model applied to stock dividends; the discount rate, k, the dividend yield y, and the long-run future growth rate of expected dividends, g, are related through k = y + g. Presently, in the U.S. market, y is less than 2% for cash dividends, and y is less than 3% when net share repurchases are counted as dividends. The U.S. Treasury yield curve is more or less flat at 6%. If the risk premium is 8%, future dividend growth must be 11% in perpetuity, or 9% real (assuming the 2% inflation rate imbedded in TIPS), versus the historical real growth rate of stock dividends of around 3%. If the risk premium is 3%, then future real dividend growth must be 4% in perpetuity. We discuss possible explanations for the low ex ante risk premium. Mine is risk management. There are today the institutions, instruments and technologies to permit efficient risk management and risk sharing by households, firms and governments. The result is investor portfolios that are better diversified and a global economy that is safer. ------------------------------JAY RITTER University of Florida, Warrington College of Business In the 1980s, I followed the textbook mantra that the equity risk premium should be based on extrapolating the historical average into the future. By the late 1980s, I began to realize how wrong this was, as the Japanese market soared. This approach predicted that in the 1990s there would be extremely high returns on Japanese stocks, just as today it implies that there will be unrealistically high returns on US stocks in the future. In recent years, I have relied on the dividend growth model: E(r)= div yield + expected growth rate. Today, with the dividend yield being 1.1% and expected real growth of maybe 3% (stock option exercise largely cancels out share repurchases in the aggregate), this gives an expected real return on US equities of about 4%. With inflation-indexed T-bonds giving a real yield of 4% today, this results in an equity premium of zero. The only way to get a positive equity premium is to assume that the growth of real EPS will be far above historical trend. The high stock market has lowered the expected real return on stocks, and the high real rate of interest has squeezed the equity premium from below.
------------------------------ROBERT WHITELAW New York University, Stern School of Business What do you teach your students about the market risk premium? There is substantial disagreement about the magnitude of the market risk premium, and I try to convey this uncertainty in the classroom. The starting point of my discussion is the historical US premium. I then talk about why this value might not be a good estimate of the true ex ante premium (e.g., survivorship bias, estimation error) or of the current forward looking premium (e.g., changes in risk aversion). I also bring up international evidence and information about the current expectations of practitioners and individual investors. Finally, I briefly mention predictable timevariation, but I emphasize that variation over business cycle frequencies is probably not as important for long-term decision-making. I make a big effort not to pretend to have a definitive answer (in general, MBA students can handle ambiguity), but I will give my opinion if asked.
IV.
BULLETIN BOARD FOR DISCUSSION OF THE EQUITY PREMIUM
In order to foster discussion about this (and other) issues, we have set up an self-moderated electronic bulletin board where readers can share their opinions about this topic. The address of this board is http://ssrn.com/forum/. The board will contain a copy of the materials above, and we encourage you to post your own thoughts on the topic so the discussion can continue with the entire profession.
By: IVO WELCH Yale School of Management Yale University [email protected] Yale University Yale School of Management 46 Hillhouse Ave. New Haven, CT 06520 (203) 436-0777 (203) 436-0779 PETER TUFANO Harvard Business School Harvard University
Email Postal:
Phone: Fax: Organized by
Discussants PETER BOSSAERTS, California Institute of Technology JOHN COCHRANE, University of Chicago, Graduate School of Business GENE FAMA, University of Chicago, Graduate School of Business WILL GOETZMANN, Yale University, School of Management ROBERT S. HARRIS, Darden Graduate School of Business, University of Virginia JOHN HEATON, Northwestern University, Kellogg Graduate School of Management ROGER IBBOTSON, Yale University, School of Management MICHAEL J. MAUBOUSSIN, Chief U.S. Investment Strategist - Credit Suisse First Boston and Adjunct Professor - Finance and Economics -Columbia Business School ANDRE F. PEROLD, Harvard University, Harvard Business School JAY RITTER, University of Florida, Warrington College of Business ROBERT WHITELAW, New York University, Stern School of Business Discussion board available at: http://ssrn.com/forum/ Document: Available from SSRN Electronic Paper Collection: http://papers.ssrn.com/paper.taf?abstract_id=234713 June 30, 2000
Date:
I. II. III. IV.
A BRIEF INTRODUCTION TO THE EQUITY PREMIUM SELECTED BIBLIOGRAPHY COMMENTS BY DISCUSSANTS BULLETIN BOARD FOR DISCUSSION OF THE EQUITY PREMIUM
I.
A BRIEF INTRODUCTION TO THE EQUITY PREMIUM
Loosely speaking, the equity premium is the difference between the return on risky stocks and return on safe bonds. It is the prime input both in the CAPM (the model used by most practitioners in computing an appropriate hurdle rate), and in asset allocation decisions (the choice of whether an investor should hold stocks or bonds). Unfortunately, there is no universally accepted definition of the equity premium. In particular, one can compute equity premia using different stock market indices, different bonds (either long-term or short-term), different methods of compounding or cumulating returns over time, and different historical time periods. Such computational differences can lead to valid historical equity premium quotations ranging from 4.3% per year up to about 9.4% per year, depending also on the time period quoted (e.g., Welch [2000]). It is important for a user of equity premium estimates to be clear about which definition is used and why it is the appropriate definition for the particular purpose it is used for. There are three inter-related questions of primary interest to researchers: [1] Why has the historical equity premium been so high? [2] What is a good forward-looking prediction for the equity premium for the long run? [3] Can one use other variables, such as dividend yields, to come up with a good forecast of the equity premium, at least over a 1-5 year period? As first pointed out by Mehra and Prescott [1985], a return differential of, say, 8% per year is enormous especially over a long enough horizon. Ibbotson and Associates, the "gold-standard" provider of historical equity premium data, show that an investment of $1 in 1925 would be worth $5,116 by 1998, whereas an investment in treasury bills would only be worth $15. (And it is well known that treasury bill returns generally suffer higher taxes than capital gains!) The profession falls into three loosely defined camps with respect to why equity premia have been so high and whether they will continue to be high. The first camp argues that these high equity premia were necessary to induce investors to participate in the stock market (e.g., Benartzi and Thaler [1995], Campbell and Cochrane [1999]). This argument implies an equity premium (possibly) as high in the future as in the past. The second camp argues that the expected returns necessary to entice investors have fallen in the last few years. This means, stocks can trade for much higher prices today, which itself is both responsible for the recent stock market appreciation, and for the expectation of much lower returns in the future (e.g., Heaton and Lucas [1999]). Closely related are arguments that historical equity premia are mismeasured, and not indicative of ex-ante equity premium expectations (e.g., Goetzmann and Jorion [1999], Siegel [1999]). The third camp argues that the stock market has gone crazy and we are all in a bubble right now. Again, this implies much lower future returns in the future. In contrast to the second camp, this camp would be less surprised by a crash or crash-like rapid drop in the stock-market. Although few academics have published this view (except Shiller [2000])---not necessarily because they do not dare, but because it is difficult to bring unambiguous evidence to bear on this matter---many seem to individually subscribe to it. [Footnote: This issue is closely connected to the question of whether Internet stocks are right now overvalued. Once willing to concede that internet stocks are overvalued, it is not a far step to concede that it is possible that the stock market as a whole is overvalued, too.] One can also bring additional evidence to bear on the second question without taking a stance on the first question: There are a number of publicly accessible forecasts from investors, academics, corporations. (Welch [2000]). Typically, investors seem to expect higher equity premia, academics seem to expect equal (or just slightly lower) equity premia, and corporations and
consulting firms seem to expect lower equity premia than those realized in the past. In sum, these forecasts run counter to the view that equity premia have recently been so high, because everyone expects them to be lower in the near future. Finally, a new set of working papers are attempting to attribute "plausible" equity premia based on long-term forecasts of real growth (e.g., Diamond [2000], Welch [1998]). The third question is equally tricky as the first two questions. There is universal consensus that the equity premium cannot be easily predicted over shorter horizons, such as one month; and that even if the equity premium can be predicted over a longer horizon (e.g., over a 30-year forecast), we do not have enough historical data to run regressions to validate 30-year forecasting claims. The variable most often mentioned as a possible predictor of equity premia is the prior-year dividend-yield. This predictability was first explored in a rigorous manner by the seminal papers of Campbell and Shiller [1988], Fama and French [1988], and Blanchard [1993], which came to the conclusion that dividend-yields do seem to have predictive ability. In a simple regression predicting equity premia one-year ahead with dividend-yields, the dividend yield shows great statistical significance. However, a long line of subsequent research has pointed to various statistical issues in this early work. Furthermore, most such models predict one-year-ahead forecasts of negative equity premia as of the year 2000---not a sensible prediction. Yet, even if there is disagreement of whether documented forecasting ability of dividend yields was real, there is little disagreement that this predictive ability has disappeared in the 1990s (Goyal-Welch [2000]). Where does this leave us? The equity premium is not only the single most important number of finance, but estimating it is also our most perplexing problem. If the profession fails to make progress in understanding the process driving the equity premium, progress on many of the most important problems in finance---proper asset allocation and hurdle rates--are likely to be phyrric victories only.
II.
SELECTED BIBLIOGRAPHY
Benartzi, Shlomo and Richard H. Thaler. "Myopic L Aversion And The Equity Premium Puzzle," Quarterly Journal of Economics, 1995, v110(1), 73-92. Blanchard, Olivier J. "Movements In The Equity Premium," Brookings Papers, 1993, v24(2), 75118. Campbell, John Y. and John H. Cochrane. "By Force Of Habit: A Consumption-Based Explanation Of Aggregate Stock Market Behavior," Journal of Political Economy, 1999, v107(2,Apr), 205-251. Campbell, John Y. and Robert J. Shiller. "The Dividend-Price Ratio And Expectations Of Future Dividends And Discount Factors," Review of Financial Studies, 1988, v1(3), 195-228. Fama, Eugene F. and Kenneth R. French. "Dividend Yields And Expected Stock Returns," Journal of Financial Economics, 1988, v22(1), 3-26. Jorion, Philippe and William N. Goetzmann. "Global Stock Markets In The Twentieth Century," Journal of Finance, 1999, v54(3,Jun), 953-980. Goyal, Amit, and Ivo Welch. "Predicting the Equity Premium." UCLA/Yale Working Paper. http://welch.som.yale.edu/
Heaton John and Deborah Lucas. "Stock Prices and Fundamentals." NBER Macroeconomics Annual 1999, published by MIT press (edited by Bernanke and Rotemberg). Mehra, Rajnish and Edward C. Prescott. "The Equity Premium: A Puzzle," Journal of Monetary Economics, 1985, v15(2), 145-162. Siegel, Jeremy J. "The Shrinking Equity Premiums," Journal of Portfolio Management, 1999, v26(1,Fall), 10- 17. Welch, Ivo. "Views of Financial Economists On The Equity Premium And On Professional Controversies." Journal of Business, 2000, forthcoming. III. REACTIONS BY DISCUSSANTS Each of the discussants was given the article above and asked to address the question, “What do you teach MBA students about the equity premium?” We thank them for their willingness to share their ideas and experiences. -----------------------------PETER BOSSAERTS California Institute of Technology The available attempts at explaining the historic U.S. equity premium have been based too much on the very narrow, stationary, single-consumer, rational expectations equilibrium of Lucas. Too little is done to deviate from this implausibly strong notion of equilibrium. Rational expectations equilibria do allow for mistaken expectations. They even allow for disagreement. And incomplete markets. Moreover, there is an objectionable assumption behind all of modern empirical analysis, namely that recorded market prices are always equilibrium prices. Too little attention is paid to genuine dynamics (equilibrium price discovery). Finally, any scientifically relevant attempt at explaining the historic U.S. equity premium simultaneously will have to explain historic evidence over other countries (e.g., Japan in the 1990s) that is diametrically opposed (low real rates of interest, negative equity premium). ------------------------------JOHN COCHRANE University of Chicago, Graduate School of Business I don't really have much to add. My own view is about 3-4% unconditional and much lower but positive conditional. Did the average investor in 1947 really think that average stock returns would be 9% over bonds, with a 16% volatility, and say "no thanks, I don't want to buy more stocks because that volatility scares me?" Probably not! Hence, much of the postwar sample must be good luck rather than the unconditional mean. -------------------------------GENE FAMA University of Chicago, Graduate School of Business The Gordon constant dividend growth model and realized returns produce similar estimates of the real equity premium for 1872-1949, about 4.0 percent per year. For 1950-1999, the Gordon estimate, 3.40 percent per year, is only about forty percent of the estimate from realized returns, 8.28 percent. The difference between the realized return for 1950-1999 and the Gordon estimate of the expected return is largely due to unexpected capital gains, the result of a decline in
discount rates. Forward-looking Gordon estimates of the expected equity premium are about one to two percent per year. (Comments based on work by Gene F. Fama and Kenneth R. French) ----------------------WILL GOETZMANN Yale University, School of Management The equity premium is commonly defined as the percentage by which stock market returns are expected to exceed a riskless bond investment. Theory argues for a positive equity premium. A rational, risk-averse investor with a riskless investment opportunity should demand greater compensation for holding a riskier asset -- but how much greater? Empirical estimates of the equity premium are typically based upon historical realizations of stock and riskless bond returns. As such a "pure" estimate of the historical equity premium may be impossible. The composition and leverage of the equity markets continually changes and a purely riskless asset does not exist. Never-the-less, the average U.S. equity premium generally exceeded 6% per annum over extended historical periods. Is the historically realized equity premium a good forecast for the future? The answer depends upon whether the economic factors contributing to the historical premium can be expected to continue as well. -----------------------------ROBERT S. HARRIS University of Virginia, Darden Graduate School of Business The Market Risk Premium: Expectational Estimates Ivo Welch's comments nicely capture much recent academic thinking on the market risk premium. I'd like to add observations from work that directly uses expectational data from financial analysts to estimate the U. S. market premium. The results do not resolve the equity risk premium puzzle but provide interesting additions to what counsel might be provided to practitioners and students. Investigators have most often used averages of historical realizations to estimate a market premium. This choice has some appealing characteristics but is subject to many arbitrary assumptions such as the relevant period for taking an average. Practice seems to mirror this framing around historical returns. Recent survey results on best practices by corporations and financial advisors (see Bruner et al (1998)) reveals that almost all respondents used some average of past data in estimating a market risk premium and displayed considerable variation in the choice of time period and method (arithmetic versus geometric) for averaging. Few respondents cited use of expectational data to supplement or replace historical returns in estimating the market premium. Many textbook treatments also rely on historical returns citing the Ibbotson data for the U.S. As Welch notes, however, shareholder required rates of return and risk premia are based on theories about investors' expectations for the future. Fortunately, there is a relatively longstanding tradition of estimating a market premium using publicly available expectational data from financial analysts. This approach uses some variant of a discounted cash flow model to infer the market premium from the combination of analysts' forecasts of future performance and current stock prices (1). In my view, four key findings are instructive (2). First, for the last two decades, the market premium implied by expectational data from financial analysts is comparable in magnitude to long-term differences (1926 to 1998) in historical returns between stocks and bonds. As a result, the evidence does not resolve the equity premium puzzle
and suggests that investors still expect to receive large spreads to invest in equity versus debt instruments. Second, at least based on current evidence through 1998 the market premium does not appear to have declined dramatically in the 1990s. Third: the market risk premium changes over time. Moreover, these changes appear linked to the level of interest rates as well as ex ante proxies for risk drawn from financial markets. Higher interest rates appear associated with lower market premia. The significant economic links between the market premium and a wide array of risk variables suggests that the notion of a constant risk premium over time is not an adequate explanation of pricing in equity versus debt markets. Fourth, using analyst forecasts as a proxy for investor expectations has many desirable features but more work is need to understand the extent to which optimism by analysts may affect the empirical estimates of market premia. In the face of this evidence as well as Welch's comments, what is the message for practice and education? Humility seems a useful starting point. More research in the area is certainly warranted. That having been said we should not "throw the baby out with the bathwater". At a conceptual level the market premium provides large benefits in sharpening thinking about resource allocation. One conclusion for practice that I draw is that common application of models such as the CAPM will overstate changes in shareholder return requirements when government interest rates change because risk premia seem to move inversely with interest rates. This is consistent with much corporate practice that does not revise hurdle rates for modest variations in interest rate conditions. A second conclusion is that we should sensitize students to the potential for risk premium variation. Having debunked the notion that the risk premium is, like Avogadro's number, a constant from on high, I adopt an administrative standard of a particular market premium (say 6%) for any class so that we do not constantly revisit the issue. A third implication is that we should in teaching, practice and research look for objective yet forward looking data that can be deployed to give insights on the market premium. Finally, our humility on the level of the market premium should make us take pains to invest in understanding the true underlying risks and opportunity inherent in an investment (say through sensitivity analysis, simulation or options frameworks). (1) See for example Malkiel (1982), Brigham, Vinson, and Shome (1985), Harris (1986) Harris and Marston (1992,1999). Ibbotson Associates (1998) use a variant of the DCF model with forward-looking growth rates as one means to estimate cost of equity; however, they do this as a separate technique and not as part of the CAPM. For their CAPM estimates they use historical averages for the market risk premium. The DCF approach with analysts' forecasts has been used frequently in regulatory settings. (2) These findings are drawn from Harris and Marston (1992,1999) who also summarize some of the earlier work. REFERENCES D. Brigham, D. Shome, and S. Vinson, "The Risk Premium Approach to Measuring A Utility's Cost of Equity," Financial Management (Spring 1985), pp. 33-45. R.F. Bruner, K. Eades, R. Harris and R. Higgins, Best Practices in Estimating the Cost of Capital: Survey and Synthesis," Financial Practice and Education (Spring/Summer 1998), pp. 13-28. W.T. Carleton and J. Lakonishok, "Risk and Return on Equity: The Use and Misuse of Historical Estimates," Financial Analysts Journal (January/February 1985), pp. 38-47.
R.S. Harris, "Using Analysts' Growth Forecasts to Estimate Shareholder Required Rates of Return," Financial Management (Spring 1988), pp. 58-67. R.S. Harris and F.C. Marston, "The Market Risk Premium: Expectational Estimates Using Analysts' Forecasts," October 1999, Darden School Working Paper DSWP-99-08. R.S. Harris and F.C. Marston, "Estimating Shareholder Risk Premia Using Analysts' Growth Forecasts," Financial Management (Summer 1992), pp. 63-70. Ibbotson Associates, Inc., 1998 Cost of Capital Quarterly, 1998 Yearbook Ibbotson Associates, Inc., 1997 Stocks, Bonds, Bills, and Inflation, 1997 Yearbook. B. Malkiel, "Risk and Return: A New Look," in The Changing Role of Debt and Equity in Financing U.S. Capital Formation, B.B. Friedman (ed.), National Bureau of Economic Research, Chicago, University of Chicago Press, 1982. -------------------------------JOHN HEATON Northwestern University, Kellogg Graduate School of Management Over the last century the average return to holding stocks was much higher than the average return to holding bonds. If this difference reflected expected returns then the high returns on stocks should represent compensation for risk. When viewed in isolation the stock market does appear to be quite volatile. The economy as a whole is much less risky, however. This is important because the typical household in the United States receives income from wages, salaries and other sources that more closely resembles aggregate GNP than stock market returns. The typical household should therefore be willing to invest a substantial amount in the stock market since the return is high and the risk can be diversified away using the household's other sources of income. The resulting large demand for stocks would ultimately increase stock prices and reduce expected returns. The fact that this did not occur historically results in the "equity premium puzzle." Viewed in this way the equity premium puzzle is really a diversification puzzle. There are several potential explanations for this diversification puzzle. First is the fact that stock ownership is relatively concentrated among wealthy individuals. These individuals tend to have business income that is less like aggregate income and more like stock returns than the average household [see, for example, Heaton and Lucas (2000)]. For these people the diversification possibilities that can be obtained by holding stocks are small. Second, in the past, holding a diversified portfolio of financial assets was difficult due to high costs of trading, brokerage fees and the like. As a result, the typical investor held a portfolio that was much more risky than the stock market index. This lack of diversification implies that the actual portfolios individuals held were much riskier than a stock index. Both of these effects imply that historically investors required high returns to hold equity. Over time the level of diversification seems to have increased both because investors have been able to hold better diversified portfolios by holding mutual funds and because wealthy individuals are able to better diversify their privately held equity. As a result, the required return to holding stocks may have fallen in recent years which possibly explains the recent dramatic increase in stock prices. This argues that looking forward the average premium investors will receive by holding stocks is likely to be much lower than it was in the past.
References: Heaton, John and Deborah Lucas (2000), ``Portfolio Choice and Asset Prices; The Importance of Entrepreneurial Risk,'' Journal of Finance, 55, pp. 1163-1198. ----------------------------ROGER IBBOTSON Yale University, School of Management The first way that I would estimate ERP is to look at the historical payoff for risk. I would use the Ibbotson and Sinquefield results reported in the Stocks, Bonds, Bills and Inflation 2000 Yearbook, published by Ibbotson Associates (www.ibbotson.com) which shows that over the 1926-1999 period common stocks had a 11.3% compound annual return and a 13.3% annual arithmetic mean return. In contrast, long-term government bond income returns were 5.2%, giving a long horizon historical arithmetic mean ERP of 8.1%. The historical payoff for risk is a good guide to the future risk premium, but it is not perfect. First, there is considerable estimation error even assuming the 74 years returns were drawn from a stationary distribution. A standard deviation of 20% gives a standard error of 2.7%. Using shorter estimation periods increases the estimation error. Goetzmann, Ibbotson and Liang (2000) have constructed a raw data series based upon individual security prices and dividends over the period 1815-1925. This longer series may help us estimate the ERP with lower estimation error. Another way to estimate the ERP is to recognize that the stock market is a part of the economy. In Diermeier, Ibbotson, and Siegel (1984), we assume that the stock market remains a constant share of the economy. Using historical estimates of real GNP growth, and inflows and outflows of the stock market, we can calculate the expected return on the stock market. The supply side estimate of the stock market is substantially lower than the historical ERP, since the stock market has been increasing its share of the economy. We would not expect this to continue indefinitely, so that we would consider both methods in making an ERP estimate. I am currently updating and revising our supply side estimate. There are several caveats to any estimation method. Is the U.S. the successful survivor, so that past returns or GNP growth are artificially high? Are we at an artificial peak in the stock market or economy (a bubble) which makes historical growth an upward biased prediction of the future? Is the ERP too high based upon reasonable risk aversion parameters? Has the risk decreased, lowering the ERP? On the other hand, some caveats might cause us to increase our estimate of ERP. Is future stock market risk in fact higher than past risk, perhaps because of potential shocks? Are we in a faster moving "new economy" so that time moves faster, increasing the ERP? Overall, I think the best estimate of the ERP is to use some combination of the historical ERP and the supply side estimate of the ERP. -----------------------------MICHAEL J. MAUBOUSSIN Chief U.S. Investment Strategist, Credit Suisse First Boston and Adjunct Professor - Finance and Economics, Columbia Business School There are three points I stress in discussing the equity risk premium (ERP). First, it is important to acknowledge that the capital asset pricing model-for all of its elegance-is unlikely to be the last word on our understanding of risk and reward. Second, the ERP should be estimated ex-ante.
Ex-post definitions come with a lot of calculational baggage, most notably choice of time period and data non-stationarity. Finally, use a long-term discounted cash flow model to estimate expected return, and then subtract a long-term Treasury yield to estimate the ex-ante ERP. A long-term Treasury is used because it matches the duration of most stocks and properly incorporates expected inflation. I believe that the ERP has been in a range of 2-5% in recent years. We currently use about 4.0% at CSFB. This suggests an expected long-term nominal stock market return of about 10%. One final note. A proper estimate of ERP has obvious significance in asset allocation. But for the active equity manager-the avocation of many of my students-stock selection is a relative endeavor. So stock selection distills to anticipating expectation shifts in key operating value drivers. As a result, ERP is not a defining issue. ------------------------------ANDRÉ PEROLD Harvard University, Harvard Business School In my MBA investments course, I ask students to value the stock market on the basis of a discounted cash flow analysis. The essential conclusion of this analysis is that if stocks are not overvalued, the forward looking risk premium is low (about 3%); or long-run future real cash flow growth must be extremely high. The result seems robust to the choice of cash flow model. For example, in the growth perpetuity model applied to stock dividends; the discount rate, k, the dividend yield y, and the long-run future growth rate of expected dividends, g, are related through k = y + g. Presently, in the U.S. market, y is less than 2% for cash dividends, and y is less than 3% when net share repurchases are counted as dividends. The U.S. Treasury yield curve is more or less flat at 6%. If the risk premium is 8%, future dividend growth must be 11% in perpetuity, or 9% real (assuming the 2% inflation rate imbedded in TIPS), versus the historical real growth rate of stock dividends of around 3%. If the risk premium is 3%, then future real dividend growth must be 4% in perpetuity. We discuss possible explanations for the low ex ante risk premium. Mine is risk management. There are today the institutions, instruments and technologies to permit efficient risk management and risk sharing by households, firms and governments. The result is investor portfolios that are better diversified and a global economy that is safer. ------------------------------JAY RITTER University of Florida, Warrington College of Business In the 1980s, I followed the textbook mantra that the equity risk premium should be based on extrapolating the historical average into the future. By the late 1980s, I began to realize how wrong this was, as the Japanese market soared. This approach predicted that in the 1990s there would be extremely high returns on Japanese stocks, just as today it implies that there will be unrealistically high returns on US stocks in the future. In recent years, I have relied on the dividend growth model: E(r)= div yield + expected growth rate. Today, with the dividend yield being 1.1% and expected real growth of maybe 3% (stock option exercise largely cancels out share repurchases in the aggregate), this gives an expected real return on US equities of about 4%. With inflation-indexed T-bonds giving a real yield of 4% today, this results in an equity premium of zero. The only way to get a positive equity premium is to assume that the growth of real EPS will be far above historical trend. The high stock market has lowered the expected real return on stocks, and the high real rate of interest has squeezed the equity premium from below.
------------------------------ROBERT WHITELAW New York University, Stern School of Business What do you teach your students about the market risk premium? There is substantial disagreement about the magnitude of the market risk premium, and I try to convey this uncertainty in the classroom. The starting point of my discussion is the historical US premium. I then talk about why this value might not be a good estimate of the true ex ante premium (e.g., survivorship bias, estimation error) or of the current forward looking premium (e.g., changes in risk aversion). I also bring up international evidence and information about the current expectations of practitioners and individual investors. Finally, I briefly mention predictable timevariation, but I emphasize that variation over business cycle frequencies is probably not as important for long-term decision-making. I make a big effort not to pretend to have a definitive answer (in general, MBA students can handle ambiguity), but I will give my opinion if asked.
IV.
BULLETIN BOARD FOR DISCUSSION OF THE EQUITY PREMIUM
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