Refusing to See: Dividends

I read recently that dividend yields have no power to predict stock returns. That is ridiculous.

Here are my speculations as to how someone could reach such a conclusion. It is not easy.

Reality

Professor Robert Shiller has shown that the dividend yield has predictive power in terms of the stock market as a whole. He showed this in his paper to the Federal Reserve Board of Governors (along with Professor John Campbell). Dividend yield has predictive power ten years into the future. So does P/E10.

David Dreman showed convincingly that dividend yields have predictive power in terms of individual stocks. So have James O’Shaughnessy and Lowell Miller and other researchers. Visit the Books section for references. It works in both in the short-term and the medium-term.

The dividend discount model and variants (such as the Gordon Model and John Bogle’s formula for the Investment Return) place dividend yields in a key position for estimating stock returns.

Just to Make Sure

I collected some data just to make sure. Perhaps, I had missed something all along.

I used my Deluxe Calculator Version V1.1A08 to calculate 10-year, 20-year and 30-year total returns of the S&P500 for 1923-1972. [The calculator data ends in 2002. I stopped at 1972 because I was collecting 30-year returns.] I used P/E10 directly from Professor Shiller’s database. I calculated January dividend yields from his data.

I plotted the relationship between the real, annualized, total return versus the dividend yield and the percentage earnings yield 100E10/P. I used Excel.

These are the Excel formulas of total return y at year 10:
1. For x = dividend yield, y = 1.9301x – 2.7954 plus and minus 8% (eyeball estimate, year 10). R-squared = 0.298.
2. For x = the percentage earnings yield 100/[P/E10], y = 1.5192x – 4.5142 plus and minus 7% (eyeball estimate, year 10). R-squared = 0.4114.

These are the Excel formulas of total return y at year 20:
1. For x = dividend yield, y = 1.5558x – 1.0613 plus and minus 5% (eyeball estimate, year 20). R-squared = 0.4713.
2. For x = the percentage earnings yield 100/[P/E10], y = 1.082x – 1.4299 plus and minus 4% (eyeball estimate, year 20). R-squared = 0.508.

These are the Excel formulas of total return y at year 30:
1. For x = dividend yield, y = 0.6337x + 3.7366 plus and minus 3.0% (eyeball estimate, year 30). R-squared = 0.315.
2. For x = the percentage earnings yield 100/[P/E10], y = 0.4154x + 3.767 plus and minus 2.5% (eyeball estimate, year 30). R-squared = 0.3017.

Note: I discovered a couple of years ago that smoothed earnings are better than initial dividend yields for calculating Safe Withdrawal Rates. Dividends come out of earnings. There have been surprise dividend cuts in the past. Using smoothed earnings avoids such surprises.

Seeing the Obvious

The formulas all show statistical significance to the degree that the standard normal (Guassian, bell shaped) distribution applies. That is, the confidence level is obviously greater than 90% (two-sided, 95% one-sided).

The key understanding is that the formulas have more than 25 degrees of freedom. There are 50 data points. Two price fluctuations are more than sufficient to overcome the effects of data overlap. (A single price fluctuation is not sufficient.)

The square root of 25 is 5. The randomness in the lines is one-fifth of the variation among individual data points. The curves all rise by more than one-fifth of the range of variation of the data. Even when using eyeball estimates, they clearly rise more than two standard deviations.

This confirms Professor Robert Shiller’s and Professor John Campbell’s findings. Dividend yield and P/E10 have predictive capability in the medium-term.

Forsey-Sortino Model Findings

I have been using the Forsey-Sortino model in my latest Current Research. The model takes monthly returns and strings them together (at random, with replacement) to simulate 2500 single-year returns.

I have found that using monthly data directly strips away almost all of the relationship between the percentage earnings yield 100E10/P and the total return. In essence, monthly return data show how well the percentage earnings yield 100E10/P predicts what happens one month into the future.

I have grouped monthly data and assigned the value of P/E10 of the first month to the entire group. I have done this with single-year, two-year and four-year groupings.

I have found that such groupings extend the prediction interval to (roughly) the length of the group. That is, single-year groupings project stock market returns one year into the future. Two and four-year groupings project stock market returns two to four years into the future. They do NOT project stock market returns into future decades.

A Possible Explanation

Monthly returns provide lots of data points. They are convenient. They have a distribution similar to the normal (Gaussian, bell shaped) distribution except for the tails. They show a high degree of independence after two months. It is easy to reach statistical significance.

Using monthly data hides longer-term variations.

It is possible that researchers fell into a trap similar to what I found when using the Forsey-Sortino model.

Those other researchers were right. Dividend yields do have predictive power.

Have fun.

John Walter Russell
December 19, 2005