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 calculated the real and nominal, annualized, total returns of the S&P500 index by setting the stock allocation to 100% and expenses equal to zero. I calculated the real and nominal, annualized, total returns of commercial paper by setting the stock allocation to 0%, the fixed income series as commercial paper and expenses equal to zero.

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

As an aside: the equity premium based on nominal returns should be close to the real return from stocks alone.

Equations

Nominal Equity Premiums 1921-1985

y=equity premium and x=100E10/P

Year 1 predictions:
y = 2.0441x-8.6876
R-squared = 0.0998.

Year 5 predictions:
y = 1.6153x-6.9489
R-squared = 0.3305.

Year 10 predictions:
y = 0.7839x-0.8058
R-squared = 0.1799.

Year 15 predictions:
y = 0.8542x-0.9276
R-squared = 0.2705.

Year 20 predictions:
y = 0.6012x-1.1179
R-squared = 0.1968.

Real Equity Premiums 1921-1985

y=equity premium and x=100E10/P

Year 1 predictions:
y = 1.8242x-7.4001
R-squared = 0.0839.

Year 5 predictions:
y = 1.6021x-7.0034
R-squared = 0.3323.

Year 10 predictions:
y = 0.7661x-0.8036
R-squared = 0.1837.

Year 15 predictions:
y = 0.8404x-0.9764
R-squared = 0.2793.

Year 20 predictions:
y = 0.5914x-1.0223
R-squared = 0.2029.

Nominal Returns 1921-1985

y=return and x=100E10/P

Year 1 predictions:
y = 2.0691x-4.7531
R-squared = 0.1109.

Year 5 predictions:
y = 1.7971x-3.8698
R-squared = 0.4652.

Year 10 predictions:
y = 0.8384x+3.3636
R-squared = 0.2724.

Year 15 predictions:
y = 0.7433x+4.6456
R-squared = 0.2888.

Year 20 predictions:
y = 0.386x+7.6188
R-squared = 0.1286.

Real Returns 1921-1985

y=return and x=100E10/P

Year 1 predictions:
y = 2.1466x-8.2481
R-squared = 0.116.

Year 5 predictions:
y = 1.7156x-6.3836
R-squared = 0.4065.

Year 10 predictions:
y = 1.0795x-1.8946
R-squared = 0.4048.

Year 15 predictions:
y = 1.0917x-1.7405
R-squared = 0.5458.

Year 20 predictions:
y = 0.7491x+0.9323
R-squared = 0.4466.

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.

Real returns have the best curve fits. Nominal returns came in second. Both do better than real and nominal equity premiums.

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