# Dividend Slices: Initial Investigation

I determined annual returns at Years 10, 20 and 30 for four major dividend slices using Professor Kenneth French’s database. I calculated regression equations in terms of the percentage earnings yield 100E10/P.

The relationship is strongest at Year 20. The Value weighted relationship is stronger than with Equal weighting.

R-squared values were lowest for the companies that paid no dividends. This is, in part, because they had greater scatter (i.e., a larger standard deviation).

# Database

I used Professor Kenneth French’s D+P database. I put it into my new Dividend Slices A calculator, which replaces the data in my Gummy 03A01 calculator with Value weighted slices A, B, C and D and with Equally weighted slices A, B, C and D.

Slice A companies paid no dividends. Slice B companies were in the lowest 30% of all dividend payers. Slice C companies were in the middle 40% of all dividend payers. Slice D companies were in the upper 30% of all dividend payers.

Professor French developed two sets of portfolios for each set of slices. One is Value (or Capitalization) weighted. The other is Equal weighted, where each company has an equal effect. He describes these portfolios in terms of their January through December total returns (annual).

[This describes only what I used. Professor French’s database includes monthly data, quintile data, decile data and much more detail.]

Kenneth R. French Data Library

I used P/E10 values from Professor Robert Shiller’s database.

Professor Shiller’s Irrational Exuberance Web Site

# Data Collection

I collected Year 10, Year 20 and Year 30 real, annualized, total returns for completed sequences with no deposits, withdrawals or expenses. The database covers 1928 through 2006.

I used Excel’s plotting capability to calculate regression equations and values of R-squared. I report eyeball estimates of the scatter (as opposed to LINEST values) because the distribution is nonsymmetrical and because they are adequate for my purposes.

I have placed my Excel spreadsheet into the “Dividend Slices” folder of my Yahoo Briefcase. It is the “Div Slices Total Returns” file.

Yahoo Briefcase

# Regression Equations

**Value Weighting**

**Year 10 Regression Equations, x=100E10/P, y=return**

Value A, y=0.5536x+0.7482 plus 9 and minus 10 and R-squared=0.0821.

Value B, y=0.6498x-0.0079 plus and minus 7 and R-squared=0.15.

Value C, y=0.868x-0.8167 plus 5 and minus 6 and R-squared=0.2551.

Value D, y=0.6946x+1.7426 plus 5 and minus 6 and R-squared=0.2109.

**Year 20 Regression Equations, x=100E10/P, y=return**

Value A, y=0.5657x+0.1598 plus and minus 5 and R-squared=0.1916.

Value B, y=0.8027x-1.5673 plus and minus 3 and R-squared=0.5408.

Value C, y=0.8197x-0.8756 plus and minus 4 and R-squared=0.4627.

Value D, y=0.6924x+1.4095 plus 4 and minus 3 and R-squared=0.4297.

**Year 30 Regression Equations, x=100E10/P, y=return**

Value A, y=0.2165x+2.6702 plus 5 and minus 4 and R-squared=0.0424.

Value B, y=0.2365x+2.6128 plus 3 and minus 2 and R-squared=0.1354.

Value C, y=0.2689x+3.1183 plus 3 and minus 2 and R-squared=0.1064.

Value D, y=0.2542x+4.6336 plus 3 and minus 2 and R-squared=0.2109.

**Equal Weighting**

**Year 10 Regression Equations, x=100E10/P, y=return**

Equal A, y=-0.1499x+9.5433 plus 10 and minus 12 and R-squared=0.0041.

Equal B, y=0.4861x+3.4442 plus 5 and minus 7 and R-squared=0.1005.

Equal C, y=0.5206x+4.4293 plus 6 and minus 7 and R-squared=0.1348.

Equal D, y=0.3651x+5.5919 plus 5 and minus 6 and R-squared=0.0864.

**Year 20 Regression Equations, x=100E10/P, y=return**

Equal A, y=0.0709x+7.3003 plus 10 and minus 7 and R-squared=0.002.

Equal B, y=0.519x+2.8019 plus 4 and minus 5 and R-squared=0.3406.

Equal C, y=0.5358x+3.9537 plus and minus 3 and R-squared=0.4133.

Equal D, y=0.4125x+4.944 plus 4 and minus 3 and R-squared=0.2888.

**Year 30 Regression Equations, x=100E10/P, y=return**

Equal A, y=0.2803x+5.7962 plus 6 and minus 5 and R-squared=0.035.

Equal B, y=0.1772x+5.401 plus and minus 3 and R-squared=0.065.

Equal C, y=0.1389x+6.9275 plus and minus 3 and R-squared=0.0479.

Equal D, y=0.1412x+6.9502 plus 3 and minus 2 and R-squared=0.0495.

# Statistical Considerations

R-squared tells us how much of the scatter (actually, variance) that the percentage earnings yield 100E10/P explains. It does not directly tell us about its significance.

The effective number of degrees of freedom is reduced because of overlapping data. [There is always one totally independent data point in any of the overlapping sequences. Each individual end point in an overlapping sequence has a range in the neighborhood of plus and minus 40%. The tenth root of 1.4 is 1.034. Plus and minus 3.4% is not sufficient to cover the range of variations. Twice that is more than enough.]

The number of sequences is 49 or more. The square root is 7 (or more). Taking the reciprocal and multiplying by 2, the scale factor is 29% (or less).

There is significance when 100E10/P causes returns to vary by 29% or more of the total scatter.

All except the weakest relationships are statistically significant. The exceptions are limited to the Equal weighted slices. Equally weighted slice A, which excludes dividend payers, is not significant at Years 10, 20 and 30.

Statistical significance does not guarantee usefulness.

# Data Analysis

Valuations (as measured by 100E10/P) influence all of the slices almost identically except for the Equally weighted Slice A, which consists of companies that pay no dividends.

Among dividend paying companies (slices B, C and D), the regression lines are nearly parallel. To an excellent approximation, companies with higher dividend payments have higher returns. That is, slice D is consistently better than slice C, which is consistently better than slice B.

Value weighted Slices A (no dividends) and B (lower 30% of dividend payers) have similar returns. Valuations have a minimal effect on Equally weighted Slice A.

Comparing R-squared levels, the effect of valuations is strongest at Year 20. It is stronger with Value weighting than with Equal weighting.

Comparing R-squared levels, the effect of valuations is stronger at Year 10 than at Year 30.

The scatter among dividend payers is similar to the scatter of the S&P500 as a whole (especially with Value weighting).

Among dividend payers, at Year 10 and Year 20, the effect of valuations is larger than the choice of a dividend slice. At year 30, the choice of the highest dividend slice is more important. The choice of the middle slice at Year 30 is equally important with Value weighting and more important with Equal weighting.

Have fun.

John Walter Russell

*March 24, 2007*