A non-random walk down Wall Street

It is a popular notion that stock prices move randomly from day to day and month to month. A best-selling book expounds on the idea with all sorts of statistical analysis and charts. It’s a three-page idea packaged into a book that goes on for hundreds of pages.

If one is going to treat some phenomenon as random, a key assumption is that each of the little events we want to observe must occur independently of all of the other events.

For example, if you want to examine the odds of rolling a seven on a pair of dice, you can reliably assume that the result of your next roll has nothing to do with the last roll, or the ones before that. Each roll of the dice is utterly independent of all preceding rolls. Each roll is completely random.

On the other hand, the returns that an owner of stocks will realize on his portfolio depends entirely on past events. Even if the month-to-month price movements are random, the amount of money actually earned depends on a prior event, how much the investor paid for the stocks.

Too many pundits and analysts simply throw out broad-based average numbers, assume that the future is independent of the past, and advise investors accordingly.

Stock returns are utterly dependent on a continuing chain of events. In statistics, this is known as conditional probability. The probability of some thing occurring is dependent on what has already occurred.

For example, it is common for us to be told to expect to earn some amount on our stock portfolios, for the simple reason that they have averaged such returns in the past. Over the past 55 years, that number has been about 9.3 percent. We are told to expect 9.3 percent going forward, as if the returns in each future period have nothing to do with today’s conditions. This practice is absurd in the extreme.

Since we have to decide to buy stocks today - not in 1951 - we need to examine conditions today. The same pundits telling us to expect 9.3 percent tell us that today’s price-to-earnings ratio is moderate by historical standards, and that earnings are growing much faster than normal. Therefore, we are safe in assuming future high returns.

Let’s examine those assumptions in a framework of conditional probability. At the end of 2005, the price-to-earnings ratio of the S&P 500 stocks was 17.8. This is not far from a 100-year average of 15, making stocks appear to be somewhat fairly priced. But we should examine the returns to investors that bought stocks at a price of 17.8. Did they earn the expected 9.3 percent, or something else?

I sorted quarter-ending periods from 1900 to 2005 by the price-earnings ratio. I took the 5 percent of periods above and below today’s figure of 17.8.

I then asked the question, “What was the average five-year rate of return to investors starting from each of these periods?” This is a way of using conditional probability. What is the expected result, after some other fact has presented itself.

It turns out that investors only realized an average annual return of 2.7 percent in the 5 years following a price-earnings ratio of 17.8. I have presented this result to some media pundits, and the response is that, since earnings are growing so fast - 19.6 percent - investors will do better than the data shows. This is actually a good answer, since it gives us another conditional item to add to our analysis. We can now look at past periods that had both today’s price-earnings number and today’s high earnings growth rates.

I further sorted my data to examine the periods with high earnings growth. In the five years following past periods with both average price-earnings ratios of about 17.8, and earnings growth rates of 19.6 percent, investors have lost 3.6 percent per year! What the pundits see as relentlessly good news has proved to be a loser for investors in the past.

If we take an honest look at what investors have earned in 5-year periods following times like right now, we cannot be too encouraged. Not only was the mythical 9.3 percent not realized, but investors, on average, lost money.

Write to Rick Ashburn at rick@richardashburn.com or 7777 Fay Ave., Suite 230, La Jolla, 92037.