Time and the Gordon Model

The Gordon Model makes its best predictions 5, 10 and 15 years into the future. It does not do as well at 20 and 30 years.

Background

The mathematics behind the Gordon Model suggest that it should be used only for making long-term predictions. Experience shows that it does an excellent job in the intermediate-term (ten years).

I use John Bogle’s modified version of the Gordon Model. He defines the Fundamental Return as the current dividend yield of the stock market (S&P500) plus the annualized earnings growth rate. He adds an adjustment, the Speculative Return, to account for variations in multiples (e.g., the price to earnings ratio).

My Procedure

I used only the January entries from Professor Robert Shiller’s S&P500 database. I used only real (inflation adjusted) prices, dividends and earnings.

I calculated each year’s dividend yield directly.

I determined earning E10 by dividing the (real) price P by P/E10. That is, E10=(P/[P/E10]).

I calculated earnings growth multipliers by taking the ratio of the value of E10 at a specified number of years into the future and dividing it by the initial level of E10. I converted this to an annualized rate of growth by solving the formula (1+annualized return)^(number of years N)=([the value of E10 when it is N years into the future]/[current year’s E10]).

I calculated the Speculative Return based upon the change in P/E10. I solved the formula (1+annualize speculative return)^(number of years N)=([the value of P/E10 when it is N years into the future]/[the current value of P/E10]).

I added the dividend yield, the growth in E10 and the adjustment for changes in P/E10 (the Speculative Return). I refer to this sum as the calculated return.

The calculated return assumes that I have estimated the earnings growth and multiple expansion (or compression) exactly right. Stated differently, the calculated return is the Gordon Model under ideal conditions (i.e., with correct inputs).

I compared the calculated returns with the actual historical returns.

The Results

I made a set of graphs. I found that I had to use all of the components in the Gordon Model. I found that 10 year comparisons were excellent. I found that the 20 and 30 year comparisons were progressively worse. I verified that this was not simply a timing mismatch. Introducing a time lead or lag would not have improved the 20 and/or 30 year results.

I calculated returns at years 5 and 15 and I compared them with actual returns. They were excellent, almost as good as the 10 year results.

I looked at the differences between the calculated returns and the actual historical returns. There were numerous instances of errors greater than 3% (annualized) in the 20 and 30 year tables. There were only two instances in the 10 year tables (1918 and 1932). The 15 year table had the same two instances (1918 and 1932). The 5 year table had three instances (1918, 1932 and 1942).

The average error with 10 year predictions was 0.96%. The average error with 20 year predictions was 1.23%. The average error with 30 year predictions was 1.66%.

The biggest error for the 10 year predictions was 4.01%. The biggest error for the 20 year predictions was 4.13%. The biggest error for the 30 year predictions was 4.93%.

Remarks

This fills in two pieces of information that have been missing: the best timeframe for predictions is a single decade and the forecasting error (ideal, with perfect inputs) averages just under 1% (with 10 year predictions). It can be as large as 4% (annualized).

Our research shows that the earliest 11 to 14 years are the most important for retirement portfolios. This explains why the Gordon Model has been so successful with Monte Carlo models. The best timeframe for the Gordon Model matches the most important period for determining Safe Withdrawal Rates.

Have fun.

John Walter Russell
July 15, 2006