Motivation for the Research
After the sharp run-up in stock prices during the bull market of the late 1990s and their subsequent collapse in 2001-2002, the prices of equities as measured by the S,P 500 are once again uncommonly high relative to companies' current and prospective earnings. This raises the question,

Are stock prices too high relative to the underlying value of the companies they represent?

If this is the case, it implies that valuations may be destined to collapse, potentially derailing the recovery.

Research Approach
The authors summarize the performance of the stocks that comprised the S,P 500 index during the recent bull and bear markets, comparing their valuations with previous experience since the 1940s. They then employ an analytical model, substituting actual or estimated values for key variables to derive theoretical estimates for the risk premium on equity. Combining these estimates with the real rate of return on government bonds, they derive the real discount rate required of equity. Finally, the authors use the model of equity prices to explore the contributions of the factors that are likely to influence the price of equity in the future.

Key Findings

• Current valuations do not necessarily mark a bubble: Rapidly growing earnings and high returns on capital, consistent with a return to full employment, could justify prevailing prices.
  
• The results imply that shareholders' risk premium for equity rose during the 1990s; should this premium fall, as is likely with the recovery of business conditions, it could offset much of the negative effect of rising real interest rates on stock prices.
  
• If earnings grow at least half as fast as analysts expect, current prices might accommodate a one- or two-percentage-point increase in the real rate of interest. (Analysts' expectations of earnings growth are currently far higher than the projected growth of potential GDP.)
  
• Variations in the valuation of the largest companies can account for a very large share of the change in the value of the entire S,P 500 in both bull and bear markets, and the prices of stocks relative to earnings for the largest companies are also more volatile than those of smaller companies.

Implications
Because valuations of the largest companies are so important in determining the value of the S,P 500 index, the prospects for these companies' earnings growth are a key determinant of whether current valuation of the index is reasonable. Another key variable is the required equity premium, in turn influenced by earnings growth and the return on capital, especially for the largest companies in the index.