Research RoundtableThe Equity Premium

By: IVO WELCHYale School of ManagementYale University

Email Ivo.welch@yale.eduPostal: Yale University

Yale School of Management46 Hillhouse Ave.New Haven, CT 06520

Phone: (203) 436-0777Fax: (203) 436-0779

Organized by PETER TUFANOHarvard Business SchoolHarvard University

DiscussantsPETER BOSSAERTS, California Institute of TechnologyJOHN COCHRANE, University of Chicago, Graduate School of BusinessGENE FAMA, University of Chicago, Graduate School of BusinessWILL GOETZMANN, Yale University, School of ManagementROBERT S. HARRIS, Darden Graduate School of Business, University of VirginiaJOHN HEATON, Northwestern University, Kellogg Graduate School of ManagementROGER IBBOTSON, Yale University, School of ManagementMICHAEL J. MAUBOUSSIN, Chief U.S. Investment Strategist - Credit Suisse First Boston and

Adjunct Professor - Finance and Economics -Columbia Business SchoolANDRE F. PEROLD, Harvard University, Harvard Business SchoolJAY RITTER, University of Florida, Warrington College of BusinessROBERT 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

Date: June 30, 2000

I. A BRIEF INTRODUCTION TO THE EQUITY PREMIUMII. SELECTED BIBLIOGRAPHYIII. COMMENTS BY DISCUSSANTSIV. 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 andreturn on safe bonds. It is the prime input both in the CAPM (the model used by mostpractitioners in computing an appropriate hurdle rate), and in asset allocation decisions (thechoice of whether an investor should hold stocks or bonds).

Unfortunately, there is no universally accepted definition of the equity premium. In particular, onecan compute equity premia using different stock market indices, different bonds (either long-termor short-term), different methods of compounding or cumulating returns over time, and differenthistorical time periods. Such computational differences can lead to valid historical equitypremium quotations ranging from 4.3% per year up to about 9.4% per year, depending also onthe time period quoted (e.g., Welch [2000]). It is important for a user of equity premium estimatesto be clear about which definition is used and why it is the appropriate definition for the particularpurpose 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 theequity 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 isenormous 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 wellknown 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 havebeen so high and whether they will continue to be high. The first camp argues that these highequity premia were necessary to induce investors to participate in the stock market (e.g., Benartziand 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 returnsnecessary to entice investors have fallen in the last few years. This means, stocks can trade formuch higher prices today, which itself is both responsible for the recent stock marketappreciation, 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 notindicative 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 bubbleright now. Again, this implies much lower future returns in the future. In contrast to the secondcamp, 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 necessarilybecause they do not dare, but because it is difficult to bring unambiguous evidence to bear onthis matter---many seem to individually subscribe to it. [Footnote: This issue is closely connectedto the question of whether Internet stocks are right now overvalued. Once willing to concede thatinternet stocks are overvalued, it is not a far step to concede that it is possible that the stockmarket as a whole is overvalued, too.]

One can also bring additional evidence to bear on the second question without taking a stance onthe 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, becauseeveryone expects them to be lower in the near future. Finally, a new set of working papers areattempting 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 thatthe equity premium cannot be easily predicted over shorter horizons, such as one month; andthat even if the equity premium can be predicted over a longer horizon (e.g., over a 30-yearforecast), we do not have enough historical data to run regressions to validate 30-yearforecasting claims.

The variable most often mentioned as a possible predictor of equity premia is the prior-yeardividend-yield. This predictability was first explored in a rigorous manner by the seminal papersof Campbell and Shiller [1988], Fama and French [1988], and Blanchard [1993], which came tothe conclusion that dividend-yields do seem to have predictive ability. In a simple regressionpredicting equity premia one-year ahead with dividend-yields, the dividend yield shows greatstatistical significance. However, a long line of subsequent research has pointed to variousstatistical issues in this early work. Furthermore, most such models predict one-year-aheadforecasts of negative equity premia as of the year 2000---not a sensible prediction. Yet, even ifthere is disagreement of whether documented forecasting ability of dividend yields was real, thereis 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 offinance, but estimating it is also our most perplexing problem. If the profession fails to makeprogress in understanding the process driving the equity premium, progress on many of the mostimportant problems in finance---proper asset allocation and hurdle rates--are likely to be phyrricvictories 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), 75-118.

Campbell, John Y. and John H. Cochrane. "By Force Of Habit: A Consumption-BasedExplanation 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 FutureDividends 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 MacroeconomicsAnnual 1999, published by MIT press (edited by Bernanke and Rotemberg).

Mehra, Rajnish and Edward C. Prescott. "The Equity Premium: A Puzzle," Journal of MonetaryEconomics, 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 ProfessionalControversies." 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 doyou teach MBA students about the equity premium?” We thank them for their willingness toshare their ideas and experiences.

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PETER BOSSAERTSCalifornia Institute of Technology

The available attempts at explaining the historic U.S. equity premium have been based too muchon the very narrow, stationary, single-consumer, rational expectations equilibrium of Lucas. Toolittle is done to deviate from this implausibly strong notion of equilibrium. Rational expectationsequilibria do allow for mistaken expectations. They even allow for disagreement. And incompletemarkets. 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 togenuine dynamics (equilibrium price discovery). Finally, any scientifically relevant attempt atexplaining the historic U.S. equity premium simultaneously will have to explain historic evidenceover other countries (e.g., Japan in the 1990s) that is diametrically opposed (low real rates ofinterest, negative equity premium).

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JOHN COCHRANEUniversity 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 butpositive conditional. Did the average investor in 1947 really think that average stock returns wouldbe 9% over bonds, with a 16% volatility, and say "no thanks, I don't want to buy more stocksbecause that volatility scares me?" Probably not! Hence, much of the postwar sample must begood luck rather than the unconditional mean.

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GENE FAMAUniversity of Chicago, Graduate School of Business

The Gordon constant dividend growth model and realized returns produce similar estimates of thereal equity premium for 1872-1949, about 4.0 percent per year. For 1950-1999, the Gordonestimate, 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 estimateof 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 oneto two percent per year. (Comments based on work by Gene F. Fama and Kenneth R. French)

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WILL GOETZMANNYale University, School of Management

The equity premium is commonly defined as the percentage by which stock market returns areexpected to exceed a riskless bond investment. Theory argues for a positive equity premium. Arational, risk-averse investor with a riskless investment opportunity should demand greatercompensation for holding a riskier asset -- but how much greater? Empirical estimates of theequity 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 compositionand 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 overextended historical periods. Is the historically realized equity premium a good forecast for thefuture? The answer depends upon whether the economic factors contributing to the historicalpremium can be expected to continue as well.

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ROBERT S. HARRISUniversity 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 analyststo estimate the U. S. market premium. The results do not resolve the equity risk premium puzzlebut 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 marketpremium. This choice has some appealing characteristics but is subject to many arbitraryassumptions such as the relevant period for taking an average. Practice seems to mirror thisframing around historical returns. Recent survey results on best practices by corporations andfinancial advisors (see Bruner et al (1998)) reveals that almost all respondents used someaverage of past data in estimating a market risk premium and displayed considerable variation inthe choice of time period and method (arithmetic versus geometric) for averaging. Fewrespondents cited use of expectational data to supplement or replace historical returns inestimating the market premium. Many textbook treatments also rely on historical returns citing theIbbotson data for the U.S.

As Welch notes, however, shareholder required rates of return and risk premia are based ontheories about investors' expectations for the future. Fortunately, there is a relativelylongstanding tradition of estimating a market premium using publicly available expectational datafrom financial analysts. This approach uses some variant of a discounted cash flow model to inferthe market premium from the combination of analysts' forecasts of future performance andcurrent 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 financialanalysts is comparable in magnitude to long-term differences (1926 to 1998) in historical returnsbetween 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 debtinstruments.

Second, at least based on current evidence through 1998 the market premium does not appear tohave declined dramatically in the 1990s.

Third: the market risk premium changes over time. Moreover, these changes appear linked to thelevel of interest rates as well as ex ante proxies for risk drawn from financial markets. Higherinterest rates appear associated with lower market premia. The significant economic linksbetween the market premium and a wide array of risk variables suggests that the notion of aconstant risk premium over time is not an adequate explanation of pricing in equity versus debtmarkets.

Fourth, using analyst forecasts as a proxy for investor expectations has many desirable featuresbut more work is need to understand the extent to which optimism by analysts may affect theempirical estimates of market premia.

In the face of this evidence as well as Welch's comments, what is the message for practice andeducation? Humility seems a useful starting point. More research in the area is certainlywarranted. That having been said we should not "throw the baby out with the bathwater". At aconceptual level the market premium provides large benefits in sharpening thinking aboutresource allocation. One conclusion for practice that I draw is that common application of modelssuch as the CAPM will overstate changes in shareholder return requirements when governmentinterest rates change because risk premia seem to move inversely with interest rates. This isconsistent with much corporate practice that does not revise hurdle rates for modest variations ininterest rate conditions. A second conclusion is that we should sensitize students to the potentialfor risk premium variation. Having debunked the notion that the risk premium is, like Avogadro'snumber, a constant from on high, I adopt an administrative standard of a particular marketpremium (say 6%) for any class so that we do not constantly revisit the issue. A third implicationis that we should in teaching, practice and research look for objective yet forward looking datathat can be deployed to give insights on the market premium. Finally, our humility on the level ofthe market premium should make us take pains to invest in understanding the true underlyingrisks and opportunity inherent in an investment (say through sensitivity analysis, simulation oroptions frameworks).

(1) See for example Malkiel (1982), Brigham, Vinson, and Shome (1985), Harris (1986) Harrisand Marston (1992,1999). Ibbotson Associates (1998) use a variant of the DCF model withforward-looking growth rates as one means to estimate cost of equity; however, they do this as aseparate technique and not as part of the CAPM. For their CAPM estimates they use historicalaverages for the market risk premium. The DCF approach with analysts' forecasts has been usedfrequently in regulatory settings.

(2) These findings are drawn from Harris and Marston (1992,1999) who also summarize some ofthe earlier work.

REFERENCES

D. Brigham, D. Shome, and S. Vinson, "The Risk Premium Approach to Measuring A Utility'sCost 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 HistoricalEstimates," Financial Analysts Journal (January/February 1985), pp. 38-47.

R.S. Harris, "Using Analysts' Growth Forecasts to Estimate Shareholder Required Rates ofReturn," Financial Management (Spring 1988), pp. 58-67.

R.S. Harris and F.C. Marston, "The Market Risk Premium: Expectational Estimates UsingAnalysts' Forecasts," October 1999, Darden School Working Paper DSWP-99-08.

R.S. Harris and F.C. Marston, "Estimating Shareholder Risk Premia Using Analysts' GrowthForecasts," 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 FinancingU.S. Capital Formation, B.B. Friedman (ed.), National Bureau of Economic Research, Chicago,University of Chicago Press, 1982.

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JOHN HEATONNorthwestern University, Kellogg Graduate School of Management

Over the last century the average return to holding stocks was much higher than the averagereturn to holding bonds. If this difference reflected expected returns then the high returns onstocks should represent compensation for risk. When viewed in isolation the stock market doesappear to be quite volatile. The economy as a whole is much less risky, however. This isimportant because the typical household in the United States receives income from wages,salaries and other sources that more closely resembles aggregate GNP than stock marketreturns. The typical household should therefore be willing to invest a substantial amount in thestock market since the return is high and the risk can be diversified away using the household'sother sources of income. The resulting large demand for stocks would ultimately increase stockprices 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 diversificationpuzzle.

There are several potential explanations for this diversification puzzle. First is the fact that stockownership is relatively concentrated among wealthy individuals. These individuals tend to havebusiness income that is less like aggregate income and more like stock returns than the averagehousehold [see, for example, Heaton and Lucas (2000)]. For these people the diversificationpossibilities that can be obtained by holding stocks are small. Second, in the past, holding adiversified portfolio of financial assets was difficult due to high costs of trading, brokerage feesand the like.

As a result, the typical investor held a portfolio that was much more risky than the stock marketindex. This lack of diversification implies that the actual portfolios individuals held were muchriskier than a stock index. Both of these effects imply that historically investors required highreturns to hold equity.

Over time the level of diversification seems to have increased both because investors have beenable to hold better diversified portfolios by holding mutual funds and because wealthy individualsare able to better diversify their privately held equity. As a result, the required return to holdingstocks may have fallen in recent years which possibly explains the recent dramatic increase instock prices.

This argues that looking forward the average premium investors will receive by holding stocks islikely to be much lower than it was in the past.

References:

Heaton, John and Deborah Lucas (2000), ``Portfolio Choice and Asset Prices; The Importance ofEntrepreneurial Risk,'' Journal of Finance, 55, pp. 1163-1198.

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ROGER IBBOTSONYale University, School of Management

The first way that I would estimate ERP is to look at the historical payoff for risk. I would use theIbbotson 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 1926-1999period common stocks had a 11.3% compound annual return and a 13.3% annual arithmeticmean return. In contrast, long-term government bond income returns were 5.2%, giving a longhorizon 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 astationary distribution. A standard deviation of 20% gives a standard error of 2.7%. Usingshorter 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 theperiod 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 constantshare of the economy. Using historical estimates of real GNP growth, and inflows and outflows ofthe stock market, we can calculate the expected return on the stock market. The supply sideestimate of the stock market is substantially lower than the historical ERP, since the stock markethas 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 andrevising our supply side estimate.

There are several caveats to any estimation method. Is the U.S. the successful survivor, so thatpast returns or GNP growth are artificially high? Are we at an artificial peak in the stock market oreconomy (a bubble) which makes historical growth an upward biased prediction of the future? Isthe 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 futurestock market risk in fact higher than past risk, perhaps because of potential shocks? Are we in afaster 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 andthe supply side estimate of the ERP.

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MICHAEL J. MAUBOUSSINChief U.S. Investment Strategist, Credit Suisse First Boston andAdjunct Professor - Finance and Economics, Columbia Business School

There are three points I stress in discussing the equity risk premium (ERP). First, it is important toacknowledge that the capital asset pricing model-for all of its elegance-is unlikely to be the lastword 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 periodand data non-stationarity. Finally, use a long-term discounted cash flow model to estimateexpected return, and then subtract a long-term Treasury yield to estimate the ex-ante ERP. Along-term Treasury is used because it matches the duration of most stocks and properlyincorporates expected inflation. I believe that the ERP has been in a range of 2-5% in recentyears. We currently use about 4.0% at CSFB. This suggests an expected long-term nominalstock market return of about 10%.

One final note. A proper estimate of ERP has obvious significance in asset allocation. But for theactive equity manager-the avocation of many of my students-stock selection is a relativeendeavor. So stock selection distills to anticipating expectation shifts in key operating valuedrivers. As a result, ERP is not a defining issue.

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ANDRÉ PEROLDHarvard University, Harvard Business School

In my MBA investments course, I ask students to value the stock market on the basis of adiscounted cash flow analysis. The essential conclusion of this analysis is that if stocks are notovervalued, the forward looking risk premium is low (about 3%); or long-run future real cash flowgrowth 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, thedividend yield y, and the long-run future growth rate of expected dividends, g, are related throughk = y + g. Presently, in the U.S. market, y is less than 2% for cash dividends, and y is less than3% when net share repurchases are counted as dividends. The U.S. Treasury yield curve ismore or less flat at 6%. If the risk premium is 8%, future dividend growth must be 11% inperpetuity, or 9% real (assuming the 2% inflation rate imbedded in TIPS), versus the historicalreal growth rate of stock dividends of around 3%. If the risk premium is 3%, then future realdividend 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 managementand risk sharing by households, firms and governments. The result is investor portfolios that arebetter diversified and a global economy that is safer.-------------------------------

JAY RITTERUniversity of Florida, Warrington College of Business

In the 1980s, I followed the textbook mantra that the equity risk premium should be based onextrapolating the historical average into the future. By the late 1980s, I began to realize howwrong this was, as the Japanese market soared. This approach predicted that in the 1990s therewould be extremely high returns on Japanese stocks, just as today it implies that there will beunrealistically high returns on US stocks in the future.

In recent years, I have relied on the dividend growth model: E(r)= div yield + expected growthrate. Today, with the dividend yield being 1.1% and expected real growth of maybe 3% (stockoption exercise largely cancels out share repurchases in the aggregate), this gives an expectedreal 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 isto assume that the growth of real EPS will be far above historical trend. The high stock markethas lowered the expected real return on stocks, and the high real rate of interest has squeezedthe equity premium from below.

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ROBERT WHITELAWNew 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 toconvey this uncertainty in the classroom. The starting point of my discussion is the historical USpremium. I then talk about why this value might not be a good estimate of the true ex antepremium (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 currentexpectations of practitioners and individual investors. Finally, I briefly mention predictable time-variation, but I emphasize that variation over business cycle frequencies is probably not asimportant for long-term decision-making. I make a big effort not to pretend to have a definitiveanswer (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-moderatedelectronic bulletin board where readers can share their opinions about this topic. The address ofthis board is http://ssrn.com/forum/. The board will contain a copy of the materials above, andwe encourage you to post your own thoughts on the topic so the discussion can continue with theentire profession.