The indefatigably lucid John Norstad has posted a new essay at his
Finance Page site:
"Mean Reversion, Forecasting and Market Timing."
It includes a rather seductively familiar-looking graph of 1000 coin flips (heads, up one unit; tails, down one):
Note that the ending value 24 is well above the expected ending value of 0. In this simulation, by chance, 512 of the flips came up heads, and 488 of them came up tails, which is 24 more heads than tails. Also note that large up and down swings are quite common in the graph. We can even see a clear "bubble" early on in the simulation. There's a major "bull" market in heads where the graph rises quickly from below 0 to about 24, followed by a "crash" where the graph value quickly declines back down to about 9. Then the market appears to move "sideways" for a long time, followed by another major "bull" market right before the end of the simulation. [emphasis added]
There's much more on the illusions that lead us to try timing the market can appear persuasive, including 'common sense' assumptions about RTM, and widespread, endemic addiction to ex-post analysis.
In conclusion, he assigns the reader two problems:
Consider the following two statements:
A. We know that the average P/E ratio over the last 75 years is about 14. We can use historical market data to test strategies that buy stocks when the P/E ratio is below 14 and sell them when it is above 14. The strategies work very nicely and beat the market by a healthy margin in these tests. Therefore market timing works, and the same strategies will continue to work in the future.
B. Today, the P/E ratio is well above 14. Therefore, future stock market returns will be well below average.
Problem 1 (easy): What's wrong with these seductive arguments?
Problem 2 (hard - extra-credit

): Examine the 10,000 books, articles and papers that have been published promoting a bewildering variety of market forecasting and timing systems. Count up how many of them used in-sample means or otherwise used in-sample data to calibrate their models in the back-tests of their forecasting equations and timing strategies.