Prof. Jeremy Siegel, The Wharton School of the University of Pennsylvania

"The magnitude of the equity premium taken from data estimated from 1889 or from 1926 is unlikely to persist in the future. The real return on fixed income assets is likely to be significantly higher than that estimated on earlier data. This is confirmed by the yields available on Treasury inflation-linked securities, which currently approach 4%. Furthermore, the return on equities is likely to fall from its former level due to the reduction in transactions costs and other factors which have driven equity prices higher relative to fundamentals. 

"All the above factors make it very surprising that Ivo Welch (1998) found that most economists still estimate the equity premium at 5% to 6%. This would require a 9% to 10% real return on stocks given the current real yield on treasury inflation-indexed securities. To prevent the P-E ratio from expanding further, real per share earnings would have to grow by nearly 8% to 9% per year given the current 1.2% dividend yield."

This study emphasizes reversion to the mean. It seems to imply the bull market could rage on only if history is made or we are entering a new paradigm. While not making predictions, the author is offering a warning based on available data.

Owen Lamont, the University of Chicago

"...dividends and earnings are important, but only for forecasting short-term movements in expected returns. The relative rate is uniformly unimportant. For long-horizon returns, price is all that matters. Recent low forecasts of returns are due to the fact that stock prices are high."

Forecasting models suggest investors look for dividends and earnings short-term, but for long-term buy at low stock prices. Does that mean today's market is appealing short-term but not long-term?

Lubos Pastor and Robert F. Shambaugh, University of Pennsylvania

"Evidence of structural breaks in the historical return distribution raises concerns about averaging a long series to estimate the current equity premium. Data before a break are relevant if one believes that large shifts in the premium are unlikely or that the premium is associated, to some degree, with volatility. The equity excess-return series over two centuries exhibits multiple structural breaks, the latest of which occurs early in the current decade. The average excess return since that break is nearly 10%, but incorporating prior beliefs as described above produces substantially lower estimates of the equity premium."

"Breaks" or lasting shifts in data in any historical analysis require some judgement in interpreting their relevance. That is why bullish experts who talk of a paradigm shift, upward naturally, cannot be discounted out of hand. This study presents conclusions that follow from various different assumptions. 

John Y. Campbell, Harvard University, and Robert Shiller, Yale University

"We think that the conventional valuation ratios - the dividend-price and price-smoothed-earnings ratios - have a special significance when compared with many other statistics that might be used to forecast stock prices. Today these ratios are extraordinarily bearish for the U.S. stock market.

...

"Linear regressions of price changes and total returns on the valuation ratios suggest substantial declines in real stock prices, and real stock returns close to zero; over the next ten years. This result must of course be interpreted with caution. The valuation ratios are so far from their historical averages that we have very little comparable historical data...

...

"There may be special circumstances now that will change the historical relations between the valuation ratios and subsequent stock market performance. But there have always been special circumstances, circumstances that are adduced every time the ratios have been at extremes and that have in the past allowed people to fail to heed the message of the ratios."

This is a strongly worded classic bear analysis of a superheated market. Curiously, this article was based on testimony given by the authors before the Board of Governors of the Federal Reserve System. 

Robert Shiller, Yale University

"Evidence has been presented here that bubble expectations and investor confidence as defined here do vary through time. There are significant semester-to-semester variations in the indicators derived here from investor responses."

A survey of institutional investors from 1989 to 1998 forms the basis of this study. 

Charles M. C. Lee and Bhaskaran Swaminathan, Cornell University

"...we provide strong evidence that U.S. equity market returns are predictable using a value-to-price (V/P) ratio that incorporates time-varying interest rates and projected earnings growth rates based on analyst consensus forecasts. We find that an aggregate V/P ratio has significant predictive power, not only for returns on the DJIA, but also for returns to the S&P 500, and a portfolio of small stocks. This result is robust to the inclusion of other forecasting variables in the prediction regression, such as B/P, E/P, D/P, as well as the short-term interest rate, the ex-ante default risk premium, and ex-ante term structure risk premium.

...

"...using data updated to Novermber 1998, we find that the U.S. equity market is as highly valued as it was before the late summer correction of 1998."

The value-to-price ratio used here is a discounted residual income valuation model that incorporates both time-varying interest rates and forward-looking earnings forecasts. It's obviously far more complex than traditional price-to-earnings and book-to-earnings ratios, which Lee and Swaminathan found to have "serious" problems as performance predictors.

Thomas Philips, Paradigm Asset Management

"These expressions clearly show that the expected return drops as valuation ratios rise...In addition, we determine the current expected return of the equity market, and provide a simple explanation for why investors have come to believe, incorrectly, that the expected return of the market is 15% or greater."

The authors' model uses valuation ratios to predict long-term returns, but they state that is has limited applications for tactical asset allocation. Once again it appears difficult to predict the short-term.

Jay R. Ritter and Richard S. Warr, Department of Finance - University of Florida, Gainesville

Notable quotes: 

"...Investors fail to add to income the real depreciation of nominal liabilities that occur because of inflation - resulting in the undervaluation of levered firms in the presence of inflation. In addition, they use nominal discount rates to value real cash flows - resulting in the entire stock market being undervalued when inflation is high." 

"...Not only is the level of debt and inflation a predictor of undervaluation, but the magnitudes of the results are economically significant. In the low inflation environment we are enjoying today, this mis-valuation has largely subsided. This correction is not necessarily due to the market now understanding how to value equities in the presence of inflation, but may be merely because of the subsidence of inflation."

Editor's note:

This study suggests that the recent bull run in the stock market can be viewed as a correction to the gross undervaluation of equities during earlier high inflation periods. It implies that stocks are now at more normal valuations. It provides guidelines for valuation but does not take a stance on which direction stock prices are headed. Two commonly made errors while valuing stocks are the capitalization error (using nominal rates to discount real cash flows) and the debt capital gain error (failure to recognize the gain that accrues to shareholders due to depreciation of the firm's liabilities). The authors warn investors against making these valuation errors that lead to undervaluation during inflationary periods. Are stock markets often undervalued during periods of high inflation?

Stock Prices, Expected Returns and Inflation

Steven A. Sharpe, Division of Research and Statistics, Federal Reserve Board

Notable quotes:

"I find that the negative relation between equity valuations and expected inflation is the result of two effects: a rise in expected inflation coincides with both (i) lower expected real earnings growth and (ii) higher required real returns. The earnings channel is not merely a reflection of inflation's recession signaling properties; rather, a substantial portion of the negative valuation effect appears to be the result of a negative relation between expected long-term inflation and projections of long-term real earnings growth. The effect of expected inflation on required (long-run) real stock returns is also substantial. A one percentage point increase in expected inflation is estimated to raise required real stock returns about one percentage point, which amounts to about a 20 percent decline in stock prices." 

"The traditional view that expected nominal rates of return on assets should move one-for-one with expected inflation is first attributed to Irving Fisher...During the mid to late 1970's, however, investors found little could be further from the truth; at least in the short and intermediate run, stock prices were apparently quite negatively affected by inflation, expected or not."

Editor's note: 

The author examines how investors and analysts expect low economic growth to follow high inflation. Investors demand greater returns on stocks as compensation for higher risks they face when investing in an inflationary environment. These effects result in lower stock prices when plugged into the discounted cash flow model, Wall Street's predominant valuation model. This study seems to depart from the traditional view of stocks being a potential hedge against unexpected inflation.

Endogenous Uncertainty and Market Volatility

Mordecai Kurz and Maurizio Motolese, Stanford University

Notable quotes: 

"Endogenous uncertainty is that component of social risk and volatility which is propagated within the economy by the beliefs and actions of agents. The theory of Rational Belief permits rational agents to hold diverse beliefs and consequently, a Rational Belief Equilibrium may exhibit patterns of Endogenous Uncertainty ... Given such diversity, some agents are optimistic and some pessimistic. In a simple model which allows for these two states of belief there is a unique parameterization under which the model makes all the predictions simultaneously. This parameter choice requires the optimists to be in the majority but the rationality of belief conditions requires the pessimists to have a higher intensity level. The intensity has a decisive effect which increases the demand for riskless assets, decreases the equilibrium riskless rate and increases the equity premium."

Editor's note: 

This study follows investor sentiment in equity markets. Its main idea seems to be that bearish sentiment can cause the market to crash much faster than it rises. 

Global Stock Markets and Economic Growth

Phillipe Jorion, Graduate School of Management - University of California, Irvine

Notable quotes:

"Estimates of the equity premium based on historical data are plagued by seemingly insurmountable problems. Researchers can turn to very long time series, on the order of a century, in order to achieve statistical precision. The problem, however is that much of this data may not be relevant to current conditions or, even worse, seriously biased due to the selection of the one series that has survived the sample."

"Another approach is to enrich our comprehension of historical data by turning to a large cross-section of countries. In particular, we can relate what should be a fundamental component of stock prices, economic growth, to our long-term measures of equity returns. This paper has shown that an important long-term determinant of equity returns is GDP growth per capita. Over much of this century, countries that have grown at a faster rate have also enjoyed greater stock market returns."

Editor's note: 

The author draws a relation between equity returns and GDP growth per capita, not GDP growth.

By force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior

John Y. Campbell, Harvard University, and National Bureau of Economic Research and John H. Cochrane, University of Chicago, Federal Reserve Bank of Chicago, and National Bureau of Economic Research

Notable quotes: 

"A number of empirical observations suggest tantalizing links between asset markets and microeconomics. Most important, equity risk premia seem to be higher at business cycle troughs than they are at peaks. Excess returns on common stocks over Treasury bills are forecastable, and many of the variables that predict excess returns are correlated with or predict business cycles. The literature on volatility tests mirrors this conclusion: price/dividend ratios move procyclically, but this movement cannot be explained by variation in expected dividends or interest rates, indicating large countercyclical variation in expected excess returns"

...When consumption falls, expected returns, return volatility, and the price of risk rise, and price/dividend ratios decline.

...All these interesting and seemingly unrelated phenomena are in fact reflections of the same phenomenon, which is at the core of the model: a time-varying, counter-cyclical risk premium."

Editor's note: 

The authors' model is based on the assumption that the return on T-bills is constant over time. It shows a negative relationship between consumption growth and expected stock returns. How long can the economy sustain current levels of high consumption growth and high expected returns? 

Where is the market going? Uncertain facts and novel theories

John H. Cochrane, Professor of Finance, University of Chicago

Notable quotes: 

"Statistical analysis suggests that the long-term average return on broad stock market indexes is 8 percent greater than the T-bill rate, with a standard error of about 3 percent. High prices are related to low subsequent excess returns. Based on these patterns, the excess return (equity premium) is near zero for the next five years or so, and then slowly rising to the historical average. The large standard deviation of excess returns, about 17 percent, means that actual returns will certainly deviate substantially from the expected return. Finally, one always gets more expected return by taking on more risk."

"In sum, the long-term average stock return may well be lower than the postwar 8 percent average over bonds, and currently high prices are a likely signal of unusually low expected returns. It is tempting to take a sell recommendation from this conclusion. There is one very important caution to such a recommendation. On average everyone has to hold the market portfolio. ...It is not enough to be bearish, one must be more bearish than everyone else."

Editor's note:

This study questions the ability of the market to sustain a high equity premium. Standard valuation models suggest that the equity premium is too high. The author reviews drastic changes that need to be made to the standard models in order to justify continued high premiums. It remains to be seen whether the new models and a high equity premium, or the traditional models and a low equity premium will triumph in the end. Will the recent boom in the stock market affect our view of future returns? Do high prices now mean lower prices in the future or have we reached a market floor?

Learning about Predictability: The Effect of Parameter Uncertainty on Dynamic Asset Allocation

Yihong Xia, University of California - Berkeley

Notable quotes: 

"This paper studies the effect of learning on portfolio choice when the investor has a long investment horizon and takes into account the empirical evidence of stock return predictability. We find that the optimal dynamic portfolio strategy is quite different from those strategies that ignore predictability or parameter uncertainty. The effect of learning is to introduce a significant hedge demand for the stock, and make the dynamic asset portfolio choice materially different from the myopic one."

Editor's note: 

This study follows investor demand for stocks over their lifetime. The paper suggests that as investors gain experience, the uncertainty associated with their stock returns declines. This decreased uncertainty increases their demand for stocks.

The Myth of Predictability: Does the Dividend Yield Forecast the Equity Premium?

Amit Goyal and Ivo Welch, Anderson Graduate School of Management at UCLA

Notable quotes: 

"Our paper reexamines the equity premium and stock market predictability from the perspective of a trader who has access only to historical data with which to estimate either a regression or the historical equity premium mean. It finds that a naive market-timing trader who just assumed that the equity premium was "like it has been" would not have underperformed a trader who employed dividend yield forecasting regressions. This is especially true for long run...The dividend yield could predict returns and the equity premium in sample better on longer horizons during the same sample period. Out-of-sample and in-sample inference leads to very different conclusions in the context of equity premium prediction."

"In the absence of any variable known to robustly predict the equity premium out of sample in a wide variety of specification, the profession should assume that no variable can predict the equity premium better than its own past average."

Editor's note: 

The authors seem to subscribe to the random walk theory of stock returns (stock prices cannot be forecast). Their study suggests that the equity premium cannot be forecast using the dividend yield or any other variable. Although their study shows that past dividend yields are reasonable predictors of past returns, it suggests that dividend yields cannot be used to predict future returns. So all you market timers might consider index investing as an alternative.