Monday, March 9, 2009

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.

1 comment:

S. B. said...

Careful with those stats. While it's accurate that 6.75% is the compounded average (i.e. the geometric mean) over that interval, the DJIA does not include dividends. With dividends, the average is several percentage points higher.

You can see a write-up of this issue with a different time period in question here:

But I totally agree about the survivorship bias.