Predicting the Future of the Stock Market
How do you predict the future of the stock market?
Simple  by making two easier predictions about (1) the economy and (2) market valuations:
 How fast will corporate earnings grow?
 How much will P/E ratios change?
This calculator lets you run the numbers:
* Updated Jan 1, 2016
(Source: multpl.com. P/E is Shiller's PE10.)
Adding dividends to the change in the price level gives you total return:
Note that the huge wildcard here is the change in the P/E ratio, which can totally dominate the results.
If P/E ratios drop significantly, your returns may be crummy.
Inflation and Stock Returns
In 1979, Business Week ran a cover story titled
The Death of Equities  an article derided today as an example of mindless fear right before the greatest bull market ever.
But that judgment is unfair, because the article really explains how inflation had been bad for the stock market for two specific reasons:
 Inflation is bad for corporate earnings
(See the Business Week article, or this 1977 article by Warren Buffett, for details.)
 Inflation leads to lower P/E ratios
(That's because investors seek inflation hedges and wind up doing strange things, like buying gold at record highs instead of stocks at reasonable prices.)
In the 1970s the US government increased the money supply in order to finance the deficit (and let people blame the resulting inflation on the Arabs' raising oil prices).
Now that Big Deficits are back, we have to hope that our politicians won't try to feed us the same old witches' brew of inflation and scapegoats.
Update
This calculator first appeared in January 2011, inspired by a
Bogleheads' thread.
At that time it predicted such a low future return that a crash seemed likely.
It's now January 2016, and the market has kept going up like crazy, implying future returns that are even more meager.
So, there are two possibilities:
(a) you can use this tool for long term expectations, but not short term predictions, or
(b) the market is really definitely going to crash soon, no kidding.
You heard it here first!
How the Calculator Works
The logic used by the calculator is straightforward, but it takes a few steps to explain it.
First, it finds current earnings, using price and P/E ratio (both inputs):
E = (E/P) x P
E/P, the reciprocal of the P/E ratio, is known as the Earnings Yield.
It's often used all by itself to predict the future return rate.
(Drawback: it ignores changes to the P/E ratio.)
Next, it predicts future earnings:
E_{future} is deduced from current earnings and the predicted earnings growth rate, using the
compound interest formula.
Next, it predicts the future price:
P_{future} = E_{future} x (P/E)_{predicted}
(P/E)_{predicted} is an input.
It's what you predict that the P/E ratio will revert to in the future, which is generally assumed to equal the historical mean value of the P/E ratio.
Next, it finds the portion of the return that comes from price appreciation alone:
r_{price} is deduced from P and P_{future}, using the CAGR formula.
And finally, it adds the dividend yield to get the total predicted return:
r_{total} = r_{price} + (Dividend Yield)
This whole process is equivalent to the Gordon Growth Model,
except that it also accounts for predicted changes to the P/E ratio.
In other words, if P/E stays constant, then that last equation is equivalent to:
r_{total} = G + (Dividend Yield)
where G is the predicted value for the earnings growth rate.
