Figure 6: Decomposition of Historical Equity Returns 1926-2000

11%

10%

9%

8%

7%

6%

5%

4%

3%

2%

1%

0%

g(PO) is growth rate of dividend payout ratio, g(Div) is growth rate of dividend, g(BV) is the growth rate of book value, g(ROE) is the growth rate of return on book equity, g(FS) is the growth rate of equity factor share, and g(GDP/POP) is the growth rate of GDP per capita.

²² Stock Market Returns in the Long Run

11%

10%

9%

8%

7%

6%

5%

4%

3%

2%

1%

0%

Figure 7: Historical Earnings and Forecasted Equity Returns Based on Earnings Models: Model 3, 3F, & 3F(ERP)

²³ Stock Market Returns in the Long Run

Figure 8: Historical vs. Current Dividend Yield Forecasts Based on Earnings and Dividend Models:

Model 3, 3F(ERP), 4F, 4F', and 4F'(FG)

11%

10%

9%

INC(00) is the dividend yield in the year 2000. ADY is the additional dividend yield in the year 2000 assuming the dividend payout ratio equal the historical average of 59.20%. ADY is calculated to be 0.95%. AG is the additional growth.

*Violates Miller & Modigliani (1961), since low current dividend yields are matched with historical earnings growth when dividend yields were high.

** Model 4F’ attempts to corrects the error in model 4F: a) use growth rate of earnings instead of growth rate of dividends; b) adjust the dividend yield up 0.95% assuming the historical average dividend payout ratio; and c) add the additional growth implied by the high market P/E ratio.

*** Based on Model 4F’, we forecast the real earnings growth rate will be 4.96%.

²⁴ Stock Market Returns in the Long Run

Appendix

Table 1 Historical and Forecasted Equity Returns – All Models (Percent).

*2000 dividend yield

**Adjust the 2000 dividend yield up 0.95% assuming the historical average dividend payout ratio.

Stock Market Returns in the Long Run

REFERENCES

Ang, Andrew and Geert Bekaert. 2001. “Stock Return Predictability: Is It There?” Columbia University and NBER Working Paper.

Arnott, Robert and Ronald Ryan. 2001. “The Death of the Risk Premium: Consequences of the 1990’s,”

Journal of Portfolio Management, Spring 2001.

Campbell, John Y. and Robert J. Shiller. 2001. “Valuation Ratios and the Long Run Stock Market Outlook: An Update”, NBER Working Paper, No.8221.

Diermeier, Jeffrey J., Roger G. Ibbotson, and Laurance B. Siegel. 1984. “The Supply for Capital Market Returns,” Financial Analyst Journal, March/April, 1984.

Fama, Eugene F., and Kenneth R. French. 2001. “Disappearing dividends: Changing firm characteristics or lower propensity to pay,” Journal of Financial Economics 60, 3-43.

Fama, Eugene F. and Kenneth R. French. 2002. “The Equity Risk Premium,” Journal of Finance, April 2002.

Graham, John R. and Campbell R. Harvey. 2001. “Expectations of Equity Risk Premia, Volatility and Asymmetry from a Corporate Finance Perspective,” Working Paper, Fuqua School of Business, Duke University, August 3, 2001.

Green, Richard C. and Burton Hollifield. 2001. “The Personal-Tax Advantages of Equity,” Carnegie Mellon University Working Paper, January 2001.

Gordon, Myron. 1962. The Investment Financing and Valuation of the Corporation, Irwin: Homewood, Illinois.

Goyal, Amit and Ivo Welch. 2001. “Predicting the Equity Premium with Dividend Ratios” Yale School of Management and UCLA Working Paper.

Ibbotson Associates. 2001. Stocks, Bonds, Bills, and Inflation 2001 Yearbook, Ibbotson Associates, 2001.

Ibbotson, Roger G., Jeffrey J. Diermeier, and Laurance B. Siegel. 1984. “The Demand for Capital Market Returns: A New Equilibrium Theory,” Financial Analyst Journal, January/February, 1984, 22-33.

Ibbotson, Roger G., and Rex A. Sinquefield. 1976a. “Stocks, Bonds, Bills, and Inflation: Year-By Year Historical Returns (1926-1974),” The Journal of Business 49, No. 1 (January 1976), 11-47.

Ibbotson, Roger G., and Rex A. Sinquefield. 1976b. “Stocks, Bonds, Bills, and Inflation: Simulations of Future (1976-2000),” The Journal of Business 49, No. 3 (July 1976), 313-338.

Mehra, Rajnish, and Edward Prescott. 1985. “The Equity Premium: A Puzzle,” Journal of Monetary Economics, No. 2, 145-161.

Miller, Merton, and Franco Modigliani. 1961. “ Dividend policy, Growth and the Valuation of Shares,”

Journal of Business, October 1961.

Shiller, Robert J. 2000. “Irrational Exuberance,” Princeton University Press, Princeton, NJ.

Stock Market Returns in the Long Run

Siegel, Jeremy J. 1999. “The Shrinking Equity Risk Premium,” Journal of Portfolio Management, Fall 1999.

Vuolenteenaho, Tuomo. 2000. “Understanding the Aggregate Book-to- Market Ratio and Its Implications to Current Equity-Premium Expectations. Harvard University Working Paper.

Welch, Ivo. 2000. "Views of Financial Economists on the Equity Premium and Other Issues." The Journal of Business 73-4, October 2000, 501-537.

Wilson, Jack W. and Charles P. Jones. 2002. “An Analysis of the S&P 500 Index and Cowles’ Extensions: Price Indexes and Stock Returns, 1870-1999,” Journal of Business 75-3,July 2002.

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Stock Market Returns in the Long-run

¹ In our study, we define the equity risk premium as the difference between the long-run expected return on stocks and the long-term risk free (U.S. Treasury) yield. We do all of our analysis in geometric form, then convert at the end so the estimate is expressed in both arithmetic form and geometric form. Some other studies, including Ibbotson & Sinquefield (1976a,b), used the short-term U.S. Treasury Bills as the risk free rate.

² It is sometimes difficult to compare estimates from one study with another, due to changing points of reference. The equity risk premium estimate can be significantly different simply due to the use of arithmetic vs. geometric, or long-term risk free rate vs. short-term risk free rate (Treasury Bills), or the bond’s income return (yield) vs. the bond’s total return, or long-term strategic forecast vs. short-term market timing estimate. A more detailed discussion on arithmetic vs. geometric can be found in section III.

³ Welch’s (2000) survey reported a 7% equity risk premium measured as the arithmetic difference between equity and U.S. Treasury bill returns. To make an apple to apple comparison, we converted the 7% number into a geometric equity risk premium relative to the long term U.S. Government bond income return, which gives an estimate of almost 4%.

⁴ Each per share quantity is per share of the S&P 500 portfolio. Hereafter, we will merely refer to each factor without always mentioning per share, for example, earnings instead of earnings per share.

⁵ There are many theoretical models that suggest that the equity risk premium is dynamic over time. However, recent empirical studies (e.g. Goyal & Welch (2001)) and Ang & Bekaert (2001)) show there is no evidence of long-horizon return predictability by either earnings or dividend yields. Therefore, instead of trying to build a model for a dynamic equity risk premium, we assume that the long-term equity risk premium is constant. This provides a benchmark for analysis and discussion.

⁶ We updated the series with data from Standard & Poor’s to include the year 2000.

⁷ The 5.24% is the compounded average of the historical equity risk premium. The arithmetic average is 7.02%. Unless specified, we use geometric averages in the calculations for the entire study.

⁸ The average P/E ratio is calculated by reversing the average E/P ratio from 1926 to 2000.

⁹ Book Values are calculated based on the book-to-market ratios reported in Vuolenteenaho (2000). The aggregate book-to-market ratio is 2.0 in 1928 and 4.1 in 1999. We use the book value growth rate calculated during 1928 to 1999 as the proxy for the growth rate during 1926 to 2000. The average ROE growth rate is calculated from the derived book value and the earnings data.

¹⁰ We decided not to use model 1, 2, and 5 in forecasting, because the forecast of model 1 & 2 would be identical to the historical estimate reported in section II. The forecast of model 5 would require more complete book value and ROE data than we currently have available.

¹¹ The current tax code provides incentives for firms to distribute cash through share repurchases rather than through dividends. Green and Hollifield (2001) find that the tax savings through repurchases are on the order of 40-50% of the taxes that would have been paid by distributing dividends.

¹² Contrary to the efficient market models, Shiller (2000) and Campbell and Shiller (2001) argue that the price to earnings ratio appears to forecast the future stock price change.

¹³ We could use the GDP Per Capita model to estimate the long-term equity risk premium as well. The GDP Per Capita model implies the long run stock returns should be in line with the productivity of the overall economy. The equity risk premium estimated using the GDP Per Capita model would be slightly higher than the ERP estimate from the earnings model. This is because the GDP Per Capita grew slightly faster than corporate earnings. A similar approach can be found in Diermeier, Ibbotson, and Siegel (1984), which proposed using the growth rate of the overall economy as a proxy for the growth rate in aggregate wealth in the long run.

Stock Market Returns in the Long-run

Date: 2016-01-14; view: 585