Statistical Lessons Learned

I advocate using statistics in investment research. I strongly advocate using confidence limits, even if crudely determined, when presenting estimates. Point estimates are almost useless. How much confidence would you have if you knew that today’s single year stock market prediction had inner confidence limits (around 60% to 70% confidence levels) of plus and minus 20%? You would ridicule the forecaster. Yet, that is typical of today’s reporting.

I have found that the standard, Gaussian, normal, bell shaped probability distribution does an excellent job of estimating what happens within the central 80% to 90% region. This is as-expected based on the Central Limit Theorem. As many already know, this approximation is not reliable at estimating infrequent events.

There is a critical qualifier. You must match time frames. You cannot use monthly data to estimate annual returns. You cannot use annual returns to estimate what will happen in a decade. You must use ten-year returns for predicting results ten years from now. This is why mutual fund projections are so unreliable. Only a few mutual funds have been around as long as 30 to 35 years.

I discovered the need to match time frames when investigating the Forsey-Sortino Model in Current Research E.

As always, it is important to relate statistical estimates to theory. The Gordon Model does this. [It is a variation of the Dividend Discount Model.] The investment return (roughly) equals the initial dividend yield plus the annual growth rate of the dividend amount. I use Professor Robert Shiller’s measure of valuations, P/E10. I have found that the earnings yield (100E10/P) of the market (S&P500) is an excellent surrogate for the initial dividend yield. The growth of earnings, and dividends as well, has been amazingly steady. Add to this the speculative return, which is the change of multiples over the time frame. We can use P/E10 or 100E10/P.

I have found that 100E10/P works well for estimating Safe Withdrawal Rates as well.

Have fun.

John Walter Russell
May 28, 2009