# Stock Market Performance

Welcome to the next issue of “Intractable Problems”, a column which I hope will challenge and stimulate your thinking skills. In this issue I want to show you that there are enough similarities between the stock market performance and a completely random process for all of us to seriously consider using guesses for choosing stock! This suggestion may very well be contentious, for I am quite sure that there are some of us who truly believe that long-term financial success has something to do with stock market performance. [1]

Let’s begin and choose our stocks by throwing darts. A random event, I say. We will compare our market performance to the performance of stocks picked by a collection of market experts. The January 11, 1994, Wall Street Journal reported that a dart solution averaged a 42% gain from July 7, 1993, to December 31, 1993, compared with an 8% gain for the Dow Jones and 2% gain for the experts.

What can possibly account for this? Can it be that success in the market is similar to flipping a coin? Perhaps success has more to do with beginner’s luck at picking the winning stocks the first time, rather than expert opinion.

Let’s assume that when flipping a fair coin, I always bet on heads, and you always bet tails. We flip a coin once a day for 1000 days. We count the number of times I win and the number of times you win. I am ahead at any point in time if more heads have come up, whereas you are ahead if there have been more tails. If there have been one thousand flips, it is considerably more likely that either you or I have been ahead more than 90% of the time, rather than 45% to 55% of the time as you might expect. Now, you may not believe this so go ahead and check it out, it’s true!

This result occurs because each flip is independent from all previous trials, and whether I win or not has absolutely nothing to do with whether I am currently ahead in the score. The deviation from the mean is not like a rubber band.  There is no stronger force pulling the statistic back to the middle simply because we deviate further and further from it. This is true in spite of the fact that the proportion of heads does approach 1/2 as the number of flips increases.

What this means is that some stock pickers will become known as winners and others as losers yet there may be no real difference between them. It all depends on whether the person gets stuck on the right side of heads or tails.

So, here’s a career opportunity for you.  Throw a dart, guess a stock.  If you happen to win, let everyone know your choice and choose again.  If you lose, keep low and don’t say anything.  Continue ad nauseum.  If you happen to be lucky and have a series of consecutive wins, everyone will start to believe in you.  Now you are important.  By the way, does anyone remember Joe Granville?

Perhaps stock market success has an awful lot to do with chance and probability.   Being in the right place at the right time.  Getting lucky.  But, since we can’t predict our fortune, the only sure way to succeed is through hard work. Perhaps if we keep on trying and trying and trying, then one day our ship may come in!

Next issue, look for a series of truths, packaged in a form suitable for understanding computer projects and other interesting facets of life.

##### Footnotes

1. Paulos, J. A Mathematician Reads the Newspaper, HarperCollins Publishing, 1995, pp. 74-78