Gordon Model Summary

This is a summary about return predictions based upon the Gordon Model.

1) The Gordon Model calculates a discount rate R when dividends grow steadily.
2) This discount rate R is calculated as R = dividend yield + dividend growth rate.
3) This discount rate tells us about the present value of the income stream absent any reinvestment of dividends. It is similar to bond coupons.
4) This discount rate equals (the predicted long-term) stock market return if and only if suitable reinvestments can be found. That is, R = the long-term stock market return (with dividends reinvested) if and only if dividends can be reinvested at the same discount rate.
5) The annualized, real, long-term stock market return with dividends reinvested has been amazingly consistent, falling within the range of 6.5% to 7.0%.
6) As long as the discount rate R calculated from the Gordon Model falls between 6.5% and 7.0%, stocks are fairly priced and R = the stock market return.
7) When R is less than 6.5%, stocks are overpriced and suitable reinvestments will not be found. Prices will fall relative to dividends until the discount rate R from Gordon Model (eventually) lies between 6.5% and 7.0%. That is, prices will not grow fast enough for dividend yields to stay the same. Instead, dividend yields will increase until R, which is the sum of the dividend yield and the dividend growth rate, lies between 6.5% and 7.0%.
8 ) When R is greater than 7.0%, stocks are underpriced and suitable reinvestments will not be found. Prices will increase relative to dividends until the discount rate R from the Gordon Model (eventually) lies between 6.5% and 7.0%. That is, prices will grow so fast that dividend yields will not remain the same. Instead, dividend yields will decrease until R, which is the sum of the dividend yield and the dividend growth rate, lies between 6.5% and 7.0%.
9) In all cases the investments available for purchases made from dividends will change until the Gordon Model discount rate falls within the range of long-term stock market returns, between 6.5% and 7.0%.
10) Dividends themselves are well behaved. The sum of a dividend amount and its growth rate is stable enough for us to draw useful conclusions based on the Gordon Model.
11) We can take advantage of the stable, known, long-term, real, annualized return of the stock market and apply it to the dividends themselves. This leads us to scale prices so that the discount rate from the Gordon Model falls between 6.5% and 7.0%.
12) We calculate a Fair Price when we scale the discount rate: [Fair Price/Current Price] = [the discount rate R calculated from the Gordon Model] / [6.5% to 7.0%].
13) Notice that the dividend yield (and, therefore, the Price to Dividend ratio) is not constrained. Instead, the constraint applies to the sum of the dividend yield and its growth rate. This means that the Fair Price adjustment is affected by the growth rate.
14) For the mathematically inclined, using R for the discount rate and g for the dividend growth rate, the Gordon Model can be written as (R-g) = the dividend yield. Notice that the growth rate term g is not the growth multiplier G = (1+g). When we scale to calculate the Fair Price, a more accurate equation would be [Fair Price/Current Price] = [the dividend yield at Current Prices / dividend yield at a Fair Price] = [R-g] / [6.5% to 7.0% - g] = [the dividend yield] / [6.5% to 7.0% - the dividend growth rate].

Here are a couple of observations.

1) The Gordon Model is helpful for SWR investigations because it focuses on what retirees need: income streams.
2) Applying the Gordon Model directly to come up with a stock market total return input to Monte Carlo models is wrong when calculating Safe Withdrawal Rates. [This includes William Bernstein’s applications in The Four Pillars of Investing.].
3) The effect of errors (related to stock market returns) in calculating Safe Withdrawal Rates diminishes greatly soon after the first decade.
4) The error caused by using the Gordon Model is mitigated because it is the income stream during the first few years of retirement that influences the Safe Withdrawal Rate most heavily.

Have fun.

John Walter Russell
I wrote this on July 26, 2004.