Edited: Returns, Not Equity Premiums

The Stock-Return Predictor determines the real, annualized, total return of the S&P500 as a function of P/E10 (actually, 100E10/P).

This is superior to estimating nominal, annualized, total returns. This is vastly superior to estimating equity premiums.

Procedure

I used my latest Version 1.61 Deluxe Calculator V1.1A08b.

I defined each year’s equity premium as the stock market return minus the return from commercial paper.

R-squared Comparisons

For Nominal Equity Premiums 1921-1985, the values were:

R-squared = 0.0998, 0.3305, 0.1799, 0.2705 and 0.1968 for years 1, 5, 10, 15 and 20, respectively.

For Real Equity Premiums 1921-1985, the values were:

R-squared = 0.0839, 0.3323, 0.1837, 0.2793 and 0.2029 for years 1, 5, 10, 15 and 20, respectively.

For Nominal Returns 1921-1985, the values were:

R-squared = 0.1109, 0.4652, 0.2724, 0.2888 and 0.1286 for years 1, 5, 10, 15 and 20, respectively.

For Real Returns 1921-1985, the values were:

R-squared = 0.116, 0.4065, 0.4048, 0.5458 and 0.4466 for years 1, 5, 10, 15 and 20, respectively.

For nominal and real equity premiums, the R-squared values are very close.

The R-squared values for the real returns are very close to or substantially better than those for the nominal returns.

Keep in mind that R-squared tells us about the amount of the VARIANCE (or the square of the standard deviation) explained by the regression equations. Variances decrease substantially as the number of years increase. A higher R-squared does not always imply less scatter.

Conclusion

It is best to estimate real, annualized, total returns as a function of valuations (100E10/P). Estimating nominal returns does not do as well. Estimating equity premiums does poorly.

Have fun.

John Walter Russell
December 12, 2006