Predicting Stock Market Returns

We need to predict stock market returns for retirement planning. Monte Carlo models require such predictions as inputs. So does my SWR Translator.

For the very long-term of 50 or 60 years, we can use a single, historically based estimate. The annualized real return (that is, after adjusting for inflation) of the stock market is 6.5% to 7.0%.

[An annualized return is the single number r that satisfies the following equation: (the final balance at the end of N years / the initial balance) = (1+r)^N. The value of r depends upon the start year and N. Historically, when the time period N is 50 to 60 years or longer, the value of r has consistently fallen between 0.065 and 0.070 regardless of the start year.]

In the short-term, the stock market is almost random. However, bull markets and bear markets have different statistics. It is best to treat them separately.

Ed Easterling of Crestmont Research has come up with the most useful definitions of bull and bear markets that I have seen. A secular (long-lasting) bull market is one with an increasing price-to-earnings ratio P/E. A secular (long-lasting) bear market is one with a decreasing price-to-earnings ratio. Here are some links to his site.
Crestmont Research
Crestmont Research Stock Section
Crestmont Research Secular Cycles
Crestmont Research Secular Swings

Today’s price-to-earnings ratio of the stock market is close to its pre-bubble highs. We expect it to decrease. There are other ways to view the market. They all reach the same conclusion: we are in a secular bear market.

[It is possible, but unlikely, that the price-to-earnings ratio will increase. It is possible, but unlikely, that we are in another secular bull market. If so, we are in a super-bubble.]

From Ed Easterling’s charts: because we are in a bear market, the probability that the market will fall by 16% or worse is 32%. The probability that the market return will stay within plus and minus 16% is 50%. The probability that the market will increase by 16% or more is 18%.

[All of these are nominal year-to-year returns. They are not adjusted for inflation. There are 50 data points: that is, 50 years in bear markets.]

For the intermediate-term, we start with the Dividend Discount Model and adjust it for changes in the price-to-earnings ratio. This is also known as the Williams Model and (when simplified further) as the Gordon Growth Model (or Gordon Equation).

The Dividend Discount Model examines the discounted value of all of a company’s dividends. Provided that the dividend amount grows at a steady rate over a very long time period and that the price-to-dividend ratio (which is 1/dividend yield) remains constant, the total return = the initial dividend yield + the dividend growth rate (approximately, after simplification).

This is the discounted total return. Discounting relates a future value to a present value using the formula (Future Value / Present Value) = (1+r)^N. The same number r is used for each year. All values of N are used, at least, until N is very large. [We convert each year’s income into its present value. Then we add all of the present value amounts together.] The single number r is similar to an interest rate.

For the mathematically inclined, I refer you to an excellent article at Gummy’s site. [Gummy is the name used by Professor Peter Ponzo (retired) on several discussion boards.]
Gummy's (Peter Ponzo's) web site
Gummy's Dividend Discount Model Tutorial

Many people use the earnings growth rate as a surrogate for the dividend growth rate. This is OK so long as you remember that we are looking at an idealized equation, not the actual behavior of the market.

[Ideally, the portion of earnings not paid as dividends increases the growth of future earnings. Assuming that the percentage of earnings that are distributed as dividends remains constant, this causes the dividend growth rate to increase.]

John Bogle of Vanguard defines the Investment Return of the stock market as its dividend yield + earnings growth rate (using the S&P500 composite). He refers to the effect of price-to-earnings ratio changes as the Speculative Return.

The Total Return = the Investment Return + the Speculative Return.

I prefer to use Professor Robert Shiller’s P/E10 when calculating the speculative component. P/E10 uses the average of a decade of (trailing) earnings as opposed to the earnings from a single year. Earnings can fluctuate considerably from one year to the next. Averaging over a decade smoothes the earnings component considerably.

Now we come to a paradox. The Dividend Discount Model estimates returns for the long-term. It is almost always wrong. It seldom provides an answer equal to the long-term return of the market. Yet, the Dividend Discount Model is useful.

[Adjustments for the speculative component do not resolve this paradox. In the very long-term, variations in the price-to-earnings ratio have only a slight effect on the (annualized) percentage return.]

The Dividend Discount Model requires that we reinvest all of our dividends into investments with the same rate of return that we started with. This assumption breaks down. The stock market corrects itself. It returns to historical norms.

That is, the sum of the dividend yield and the dividend growth rate (or the earnings growth rate) must remain the same for the Dividend Discount Model to work. But prices are related to earnings (loosely) and dividend yields are constrained. Eventually, there is a change in the price-to-earnings ratio (and the dividend yield). There are no more investments that meet the requirements of the Dividend Discount Model. The available investments are either better or worse than before, but not the same.

The approximation of steady dividend (or earnings) growth is reasonably accurate in the intermediate-term (of 10 years or so).

When we calculate Safe Withdrawal Rates, the first decade of returns has the greatest influence. By year 10 or 11 or 12, we almost always find that a portfolio has grown large enough to survive without danger or else it is in danger already. [Less than one-third of the Historical Surviving Withdrawal Rates fall into a region of uncertainty.] Whether we use the Historical Sequence method or a Monte Carlo model (or my SWR Translator) makes little difference. Dividend Discount Model predictions need not be accurate beyond the intermediate-term.

Have fun.

John Walter Russell
July 20, 2005