The Region

The Recent Ascent in Stock Prices: How Exuberant Are You?

Are investors "irrationally exuberant" about the rising stock market? New research offers fresh insight into one of the economy's most vexing questions.

John B. Carlson | Economic Adviser, Federal Reserve Bank of Cleveland

Published December 1, 1999  | December 1999 issue

"... how do we know when irrational exuberance has unduly escalated asset values, which then become subject to unexpected and prolonged contractions? ...We have not been able, as yet, to provide a satisfying answer to this question, but there are reasons in the current environment to keep the question on the table."
Fed Chairman Alan Greenspan

It has been about three years since Chairman Greenspan posed the foregoing question and thereby launched the phrase "irrational exuberance" into the economic idiom. Since then, of course, some stock-price indexes have doubled, and the question still remains unanswered. Over the same period, favorable U.S. economic performance continued to surprise even some of the more optimistic prognosticators. Because stock prices are presumably forward looking, earlier exuberance appears, at least up to this point, to have been validated by experience.

Some analysts insist that the party will continue. Among the most ardent are James K. Glassman and Kevin A. Hassett, who argue that the market is rationally exuberant. Their assessment hinges on two key assumptions: first, that future earnings growth will continue at a pace comparable to the post-World War II experience, and second, that investors are demanding a smaller premium for stock returns relative to other financial instruments. Glassman and Hassett assert this premium has permanently declined because investors have become "calmer and smarter." Moreover, they argue that the premium should be zero. This suggests that as investors become even calmer and smarter, stock prices could increase—not just moderately but by threefold or more!

Whether one agrees with Glassman and Hassett or not, their perspective illustrates how sensitive stock prices are to key investor judgments. To appreciate this sensitivity, it is useful to review briefly the fundamentals of stock price determination. This is done in the following section. Each of the assumptions made by Glassman and Hassett will then be discussed in turn. We shall see that given their assumptions, their conclusions are not unreasonable. This is, of course, no endorsement for their assumptions. I will offer an array of valuations for the S&P 500 index given alternative sets of assumptions. Readers are left to make their own judgments.

The Fundamentals

Investors purchase stocks because they expect to receive some future income stream-either in the form of dividends and/or the proceeds from the eventual sale of the shares of stock. The standard model of stock valuation posits that a stock's price equals the discounted present value of this income stream. Because the amount of income ultimately depends on the firm's potential to generate earnings, a key fundamental determinant of the stock's value will be expected earnings growth. The more a firm is expected to earn, the more investors will pay for its stock.

Future income from stocks must be discounted to compensate investors for assuming inherent risks and associated costs. The discount rate is the rate of return the investor demands as compensation. The higher the discount rate, the lower the price the investor is willing to pay for the stock. The discount rate is commonly called the expected return because it is the return the investor earns if the income stream is realized as expected.

Expected Returns

In competitive financial markets, expected returns on stocks are linked to returns on alternative assets, including Treasury bonds and bills. Because stock returns are generally perceived as being riskier than those on "safer" instruments such as Treasury bonds and bills, investors typically exact a higher return. This extra return is called the "equity premium."

When thinking about stock returns, it is important to keep in mind the distinction between historical returns and expected returns. Historically, returns in stocks have been quite stable over long horizons. Using U.S. data from 1802-1998, Jeremy Siegel computes returns for equity and alternative assets (see Table 1). While real (inflation-adjusted) equity returns have been consistently around 7 percent for long horizons, returns on U.S. Treasury securities have varied substantially.

Table 1
Compound Annual Real Returns (percent)
U.S. Data 1802-1998

























Source: Siegel (1999)

To those who view the stock market as relatively volatile, the stability of these measured historical returns is perhaps surprising. They clearly illustrate that a buy-and-hold strategy in stocks has paid off handsomely relative to "safer" alternatives. Since 1926, the equity premium has averaged around 6 percent.

Optimists like Glassman and Hassett argue that for long-horizon investors, stocks are no more risky than the recently issued 10-year Treasury inflation-protected security (TIPS), which currently yields around 4 percent. Thus, they view this yield as the appropriate (that is, rational) required return for a sufficiently diversified portfolio of stocks, such as an index fund. That is, they argue that there should be no equity premium. This view implies that the stock market has been historically undervalued. Thus, the recent bull market is seen as evidence that investors are becoming calmer and smarter.

One need not solely rely on the argument that investors are becoming calmer and smarter to explain why expected returns may have fallen. Siegel offers an alternative explanation. While he believes that 7 percent does approximate the real long-term return on equity indices, it does not represent the realized return to the equity holder after expenses—such as transactions and management fees. Once one accounts for such costs, Siegel argues, realized returns were more like 5 percent for the typical investor.

Siegel notes that recent innovations in financial instruments, such as the advent of index funds, have sharply reduced the costs of investing in diversified portfolios. Some index funds, for example, charge less than 1/4 percent of asset value per year. Fees associated with standard mutual funds, on the other hand, often amount to more than 2 percent per year. Because lower investment costs allow investors to realize a greater portion of the income flows from holding stocks, one would expect measured stock returns (which are not net of costs) to fall. Siegel believes that current expected return on stocks is more in line with the historical "realized" return of 5 percent.

Earnings Growth

Even if the expected return were 5 percent, current market values of U.S. stock indices would imply that equity holders expect earnings growth to exceed historical averages. Since 1871, earnings per share have increased at an average annual rate of 1.7 percent for S&P companies. Since the World War II era, earnings per share have grown at an average rate of over 3 percent. Figure 1 illustrates just how favorable earnings growth has been in recent years for S&P 500 companies. After declining over much of the 1970s and 1980s, earnings accelerated sharply in the 1990s.

Figure 1
Figure-S&P 500 Earnings and Dividends

Source: Standard and Poor's Corp.

As Figure 1 illustrates, neither earnings nor dividends grow at constant rates. Rather, we observe that variations in the growth rates of both are quite persistent. Thus, it is plausible to argue that recent above-trend rates in earnings growth will persist for some time before settling down to a rate more commensurable with historical averages.

Siegel makes a strong case for persistently (though not permanently) higher earnings growth. He notes that the United States has emerged as the leader in the fastest growing segments of the world economy, particularly in information technology and pharmaceuticals. He also notes that U.S. brand names such as Coca Cola, Procter and Gamble, Disney and others have quite successfully penetrated the global market. Together, these factors could justify temporarily but persistently higher earnings growth for U.S. firms. It is clearly possible, though by no means certain, for earnings levels to double from current levels before resuming longer-term trend rates.

Putting It All Together

There are many reasonable explanations for why stock market indices should have accelerated in the 1990s. However, depending on one's own assumptions, current index levels could be viewed as undervalued or overvalued. Table 2 provides alternative valuations of the S&P index that correspond to different assumptions about earnings growth and expected returns. Each valuation has been calculated using the present-value formulation for the levels given for each of the fundamentals. These computations build in an assumption that earnings decelerate smoothly from the recent five-year average rates to corresponding trend-rate assumptions.

Table 2
Alternative Valuations for S&P 500 Index

(Value on September 15, 1999:1317)
Expected Return (percent)

























Source: Author's calculations.

The table is intended to provide a simple consistency check between recent levels of stock prices and a level warranted by one's assumptions about earnings growth and expected returns. If, for example, one agrees with Glassman and Hassett that the appropriate expected return is 4 percent (recent yield on the 10-year TIPS), and if one assumes trend earnings growth of 3 percent, then the warranted value of the S&P index is 2085. This is well above recent levels of around 1300. On the other hand, if one believes that stocks are somewhat more risky than the TIPS and hence demands an expected return of 5 percent (1 percent equity premium), then the market is clearly overvalued under the assumption of 3 percent earnings growth. How exuberant are you?

Readers may also use the table to interpolate what approximate return they might expect from an S&P 500 index fund given their assumption about earnings growth. For example, if one believes that trend earnings growth is 3 percent, then this valuation exercise indicates that the current level of the S&P 500 is consistent with an expected return of between 4 1/2 percent and 5 percent. An expected return of 5 percent would imply a modest equity premium of 1 percent as measured against the TIPS yield. It should be evident from this exercise that it is difficult to justify expected returns above 5 percent unless one is extremely optimistic about trend earnings growth. Thus, the historical return of 7 percent on stocks is not a good projection for future returns.

Concluding Thoughts

We have seen how sensitive stock-index valuations are to key assumptions about earnings growth and expected return. Standard economic theory provides little guidance for pinning down precise values. One's assumptions must ultimately be based on judgment. This is why some readers undoubtedly will be exuberant while others will be leery. One inescapable conclusion, however, is that at today's prices, future long-term returns of 7 percent seem extremely unlikely.

Further, recent stock-price levels undeniably reflect a high degree of investor confidence. History reveals that sharp drops in stock prices occur spontaneously with no apparent change in fundamentals. The experiences of October 1987 and October 1997 offer two recent examples. Such events are viewed as unpredictable collapses in investor confidence. They are evident only in retrospect. For buy-and-hold investors, such swings may be of little consequence. For investors with short horizons, on the other hand, it would appear unwise to count all recent paper gains as permanent until they are realized. Just as one cannot know if investors are irrationally exuberant, one cannot know if a sudden drop in investor confidence is around the corner.

This article is reprinted from the Federal Reserve Bank of Cleveland's Economic Commentary.