Predicting the Random Walk?

In my post on Friday, March 6th I discussed the possibility of the start of a rally for the SP500 Index. The upward turn at level 667 did develop into a relatively significant rally. I have circled the rally on the updated chart. It will be interesting to monitor to see where the market goes from here.

The success of this prediction may be viewed as possible evidence that the stock market is not just a random walk. That does not mean that there is no randomness in the stock market.

A Random Walk and Black Swans

Statistical experts say that stock price fluctuation over time is a random walk. If that is true , then why does the market increase in value over time?

I calculated the annual equivalent compound return for the Dow Jones Industrial Average from the low of 41 in 1932 (after the 1929 crash) to the most recent low of 6440 in 2009. It comes to about 6.75 percent compounded over 77 years. In other words, $1 would have appeared to have increased to $157 dollars.

The starting point and ending point of these types of calculations will make a relatively large difference. For example, if I use the 1992 peak of 381 and compare it to the 6,440 low in 2009 I get a an apparent annual compound return of only 3.75 percent. Yikes...put my money in saving bonds!

However, we should view this apparent increase as "an illusion" due to the effects of inflation over the last 80 years. We know that $1 in 1929 or 1932 bought a lot more "things" than $1 buys today in 2009.

If we subtract inflation from the stock market long term increase then prices may not have really gone up at all.

Another thing that occurs with a stock index is that stocks that drop in price below a certain minimum threshold value are periodically culled from the index and replaced with the lastest hot stocks. That's a little like dead people in a study group being placed with new live ones. This factor may also contribute to the apparent increase in the index over time. The real market increase may be lower than what the indexes suggest. The index was never designed to model the growth in the stock market.

With a random walk, we can say that if one waits long enough the true value of the DJIA can be expected to return to the starting point from time to time.

The current bear market may be just that...a "run" of values that happens by chance to be moving the markets back closer to the starting point.

And, Black Swans may just be the market randomly heading back to the starting point as should be expected with a random walk.

The problem I have with all of this is that I have called so many turns that even if the numbers, on their own, fit well into a statistical distribution, one having the appearance of a random walk, I have seen too much evidence to the contrary to believe it.

However, I can understand how others with less knowledge could come to that conclusion. That conclusion on their part would be perfectly logical. I guess, in a sense, good market predictions to those people would be just another Black Swan.

Market Timing

Still working my way through "The Four Pillars of Investing". I have read it once through and now I'm down to making some notes and trying to see if I've learned anything new.

Bernstein believes that no one can make a sustained profit from timing the market. He believes in the "random walk" theory of how the market works.

He refers to studies that found that stocks/mutual funds that have good returns for a number of years then mean revert and do poorly. So, using past performance to predict future performance is usually wrong. However, at one point in the book, he refers to a study that found that in the short term past performance is a good predictor of future performance.

This short-term prediction data is perhaps what draws the public to the market, like a moth to a flame, during the periodic bubbles. You don't have to be a math expert to see "the correlation".

Over the last few years the stock market has done great. For example, the last year has seen returns in the 20-30 % range for Canada and the US. If you take only that data set (its called data mining), pick short time periods at random, and use them to forecast the future returns, I expect the results would show a high correlation. Hindsight is 20/20.

So here we seem have conflicting realities. Short term data is a good predictor but longer term data is a bad predictor. I guess this means that the farther one gets from the beginning of a bull market the less confidence we can have that it will continue. The market moves from being a "good investment" towards being very speculative (a gamble).

One of the easy ways to measure this phenomenon is to look at P/E ratios for stocks. P/E is often shown on charts. For example, the Royal Bank is near a P/E of 15. Not extreme but not a great investment. Farther afield, looking at Research in Motion (RIM), it now has a P/E of 47. That is considered very speculative by any standard.

The reality is that the stock market changes over time. Sometimes it is a great place to invest but at other times it is like going to the Casino.

As the P/E ratios increase, the probability of a "Black Swan" appearing on the horizon increases.

It's not simple math. The equation changes over time. Maybe P/E or similar measurements needs to be brought into the prediction equation. Maybe it's not just "a random walk". Perhaps it is just a problem yet to be solved.