Stock Return Predictor with Earnings Growth Rate Adjustment

The earnings term in P/E10 is centered 5 years prior to the current price. This has no effect if the earnings growth rate is steady. To the extent that the smoothed earnings growth varies, it can make sense to add an adjustment. It is straightforward to come up with a new set of regression equations. The art is in knowing what growth rate to assume, since five years belong to the future.

If you guess right, you get better numbers.

This is a refinement. It is similar to the special set of equations that I developed for a secular (long lasting) Bear Market. The secular Bear Market stock return predictor is included in my Simplified Retirement Trainers.

You can download a copy from my Yahoo Briefcase. It is the Stock Returns Adjusted file in the Lucky 7 Calculators Folder.

Yahoo Briefcase

The Adjustment

The earnings of E10 are centered five years earlier. The adjustment is [(1+the current real earnings) / (1+the real earnings from 5 years earlier)]. When the earnings growth rate is steady, assuming linear percentage real earnings growth, the adjustment in year N is [(1+rate)^N / (1+rate)^(N-5)] = (1+rate)^5.

To adjust for earnings growth, you divide P/E10 by the earnings growth multiplier. To adjust the percentage earnings yield 100E10/P, you multiply 100E10/P by the earnings growth multiplier.

Earnings Growth Rates

I generated charts of smoothed real earnings Ex, where x = 1, 3, 4, 5, 6, 7 and 10. I selected E7 for determining changes in the long term earnings growth rate.

I broke real earnings into time intervals. Then I converted the real earnings growth into an annualized rate: (real earnings in the final year/real earnings in the first year) = (1 + growth rate of real earnings)^(number of years in the time interval). NOTE: I also refer to the term (1 + growth rate of real earnings) as the growth multiplier.

First Period 1881 to 1940:

E7 grew from 7.014 in 1881 to 10.730 in 1940. This is 59 years. The growth multiplier is 10.730/7.014 to the 1/59 power = 1.00723. The growth rate was 0.72% per year.
Use a multiplier of 1.0072 per year.
The 5 year adjustment is 1.0072^5 = 1.0365.

The second period is from 1941 to 1970.

E7 grew from 11.842 in 1941 to 29.345 in 1970. This is 29 years. The growth multiplier was 29.345/11.842 to the 1/29 power = 1.03178. The growth rate was 3.18% per year.
Use a multiplier of 1.0318.
The 5 year adjustment is 1.0318^5 = 1.1694.

The third period is from 1971 to 1995.

E7 grew from 29.286 in 1971 to 31.021 in 1995. This is 24 years. The growth multiplier was 31.021/29.286 to the 1/24 power = 1.0024. The growth rate was 0.24% per year.
Use a multiplier of 1.0024.
The 5 year adjustment is 1.0024^5 = 1.0121.

The fourth period is from 1996 to 2006.

E7 grew from 31.580 in 1996 to 48.791 in 2006. This is 10 years. The growth multiplier was 48.791/31.580 to the 1/10 power = 1.0445. The growth rate was 4.45% per year.
Use a multiplier of 1.0445.
The 5 year adjustment is 1.0445^5 = 1.2432.

Multipliers

These are the multipliers:

1881-1940: 1.0365.
1941-1970: 1.1694.
1971-1995: 1.0121.
1996-2006: 1.2432.

I perform calculations based on the most recent levels of P/E10. I normalize everything to today’s rates by dividing by 1.2432.

1881-1940: 0.8337.
1941-1970: 0.9406.
1971-1995: 0.8141.
1996-2006: 1.0000.

New Regression Equations

I took a list of P/E10 versus year. I multiplied each value by its normalized multipliers. I used this to calculate the (earnings growth) adjusted percentage earnings yield, 100E10/P. I added adjacent columns with the real, annualized, total returns of the S&P500 index at Years 10, 20 and 30. I calculated regression equations.

For the calculator, I used 1923-1995 data for Year 10 equations. I used 1923-1985 data for Year 20 equations. I used 1923-1975 data for Year 30 equations.

Year 10:
y = 1.4039x-1.9084 plus and minus 7%.
R-squared = 0.3110.
Data from 1923-1995 sequences.

Year 20:
y = 1.3188x-1.9952 plus 4.0% and minus 3.5%.
R-squared = 0.6093.
Data from 1923-1985.

Year 30:
y = 0.3928x+4.2217 plus and minus 2%.
R-squared = 0.2117.
Data from 1923-1975.

Comparisons

Here are some comparisons with the Stock Return Predictor.

I assumed that P/E10 = 28.0.

Stock Return Predictor.

Year 10: 0.89.
Year 20: 2.43.
Year 10: 5.25.

Stock Predictor with Earnings Growth Adjustment.

Earnings Growth Rate Input: 0.00%.
Year 10: 2.12.
Year 20: 1.79.
Year 10: 5.35.

Stock Predictor with Earnings Growth Adjustment.

Earnings Growth Rate Input: 1.55%.
Year 10: 2.45.
Year 20: 2.10.
Year 10: 5.44.

Stock Predictor with Earnings Growth Adjustment.

Earnings Growth Rate Input: 4.45%.
Year 10: 3.11.
Year 20: 2.71.
Year 10: 5.62.

NOTE: The real earnings growth rate from 1901-2000 was 1.55% per year.

Assuming that real earnings continue to grow within these ranges, the adjustment at Year 10 is an increase of +1.23% to +2.22%. At Year 20, the adjustment is -0.64% to +0.28%. At Year 30, the adjustment is +0.10% to +0.37%.

Single year earnings have been highly volatile within the last few years. And we have not had a recession since 2003. The current growth rate of 4.45% may flatten out over the next five years because of depressed earnings.

Have fun.

John Walter Russell
January 1, 2007