Dividends and the Gordon Model

Dividend yields vary all over the place because prices vary. Prices depend upon current human perceptions. Dividend amounts are stable. Dividend amounts depend upon business activity.

A retiree can reasonably expect to see his initial dividend amount grow by 2.8% each year in addition to inflation.

Mathematical Derivation

The Gordon Model adds the dividend yield and dividend growth rate to calculate the Investment Return. John Bogle’s variant adds an adjustment for the change of multiples, which he refers to as the Speculative Return. The Total Return equals the sum of the Investment Return and the Speculative Return.

Although the mathematical derivation assumes the very long-term, the Gordon Model turns out to be most accurate between 5 and 15 years. The reason is that returns of reinvested dividends are often different from initial returns.

Time and the Gordon Model

From the Gordon Equation, the initial dividend yield plus the dividend growth rate plus the Speculative Return equals the Total Return. In the very long-term, the Speculative Return becomes smaller and smaller. In the very long-term, stocks have delivered a 6.5% real, annualized, total return. At typical valuations, the Speculative Return is zero. At bargain prices, the Speculative Return is positive. At high prices, the Speculative Return is negative.

When I enter P/E10=13.8, the Stock-Return Predictor calculates a Most Likely return of 6.50%.

This allows us to normalize yields.

If today’s P/E10 were 13.8, then the dividend yield plus the (real) dividend growth rate would equal 6.5%. Today’s dividend yield is much less, around 1.8% for the S&P500 index. But today’s prices are much higher than normal, P/E10=28 as opposed to 13.8. If prices were lower, then today’s dividend yield would be increased by the ratio of P/E10 levels: (today’s P/E10)/13.8.

The dividend growth rate does not depend upon the stock price. It is the change of the dividend amount divided by the initial dividend amount (when annualized to cover periods longer than a single year).

This leads us to the following equation:

6.5% = [(today’s P/E10)/13.8]*today’s dividend yield + dividend growth rate.

Dividend investors know today’s dividend yield. They need to estimate the dividend growth rate.

Solving: the (real) dividend growth rate = 6.5% - [(today’s P/E10)/13.8]*today’s dividend yield = 6.5% - [28/13.8]*1.8% = 6.5% - 3.7% = 2.8% per year, real, annualized.

The Stock-Return Predictor

There is an apparent conflict with the Stock-Return Predictor. It is easy to resolve.

When we put P/E10=28 into the Stock-Return Predictor, the estimated total return at Year 10 is 0.89%. The inner confidence limits (unlucky and lucky) are -2.1% and 3.9%. The outer extremes are -5.2% and 6.9%.

If P/E10 were to fall from 28 to 13.8 in ten years, the Speculative Return adjustment would be (1+rate)^10 = (13.8/28) or rate = -6.8% per year. The difference between the total return and the Speculative Return would be 0.89%-(-6.8%) = 7.7%. This is larger than the 6.5% long-term real, annualized total return by 1.2%.

If P/E10 were to fall from 28 to 6, which approximates a bottom, the Speculative Return would be -14.3%. This differs from the worst case total return of -5.2% by -5.2-(-14.3) = 9.1%.

If P/E10 were to remain unchanged at 28, the Speculative Return would be 0.0%. This differs from the best case total return of 6.9% by 6.9%-(-0.0) = 6.9%.

Using 6.5% for the Investment Return, the Stock-Return Predictor suggests that the actual return will exceed the Most Likely return by 1.2%. If prices were to fall all of the way to a bottom, returns would still be 2.6% (=9.1%-6.5%) more favorable than expected. If prices were to remain stable, returns would still be 0.4% (=6.9%-6.5%) more favorable than expected.

That is, the Stock-Return Predictor calculates a return that is 1.2% (from 2.6% to 0.4%) higher than the Gordon Model.

The explanation is straightforward: Reinvested dividends buy many more shares when prices are low.

Retirement Planning

A retiree can reasonably expect to see his initial dividend amount grow each year by 2.8% in addition to inflation. The failure mechanism (dividend cuts) is gentle. Provided that he invests in high quality companies at reasonable payout ratios, he can plan on a downside risk of only 10% (20% worst case) with full recovery within 5 years.

This number (2.8% per year, real) allows you to determine the right amount to boost your income via a liquidating TIPS ladder during the earliest years of retirement.

Have fun.

John Walter Russell
January 17, 2007