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A random walk to the Final Four

Grace Concelman | Wednesday, March 21, 2012

The stock market can seem so erratic. One day it’s up and analysts are screaming “buy, buy, buy!” The next day it’s down and the only “bye-rs” left are the washed up members of N*Sync.

There’s a theory in finance that stock prices follow a “random walk,” which means that changes in price have the same distributions for every stock and all changes are independent of one another. Basically, this means we cannot predict a stock’s future movement based on the fact that it was up or down in the past. If the random walk hypothesis was true, a portfolio of stocks chosen by monkeys throwing darts at stock names would perform just as well as a portfolio painstakingly crafted by the finest analysts on Wall Street.

Besides stocks, there are other things that seem to follow a random walk: the movement of molecules in gases, the spread of certain genes through populations, some Notre Dame students coming home from the Backer on a Saturday night or maybe even the NCAA basketball tournament.
The upsets in the tournament last weekend got me thinking: What if the games follow a random walk? If they do, then filling out a bracket by flipping a coin should produce the same results as carefully picking each winner.

So, I set up a highly unscientific experiment to compare how a bracket constructed by coin flips would fare against the aggregated national bracket in the first round. For the national bracket, which reflects the consensus from a wide variety of people submitting brackets, I advanced whichever team had a higher percentage of people choosing it to win.

For the random bracket, I flipped a coin and advanced the first team on heads and the second team on tails. I replicated the random bracket five times and averaged the results.
The random bracket correctly picked an average of 17.2 winners out of 32 winners in the first round whereas the national bracket picked 22 first round winners. So, according to my experiment, the tournament is not completely random.

But, the stock market isn’t completely random either. If it was, it would be impossible to make money consistently by only buying stocks. Critics of the random walk theory believe that stock prices do maintain trends over time. These critics believe the market is not totally efficient and that it is possible to outperform the market by buying and selling at the right time.

There are three different levels of market efficiency: strong, semi-strong, and weak. The example of the random bracket is a test for strong form market efficiency, which states that all information in a market (including insider information) is accounted for in a stock price. Semi-strong form states that all public information is accounted for, and weak form only states that past prices are included in the present stock price, so past performance cannot be used to predict future prices.
Since the totally random strong form bracket didn’t outperform the national bracket, I decided to test a weak form bracket. Weak form efficiency says that analysis of information publicly available about a company could be helpful in predicting the future movement of the company’s stock. I used a team’s seed in the tournament as public information that would predict a team’s performance in the first round of games, assuming that the seed reflected some sort of fundamental analysis. I automatically advanced the 1, 2, and 3 seeds from each region in the first round and used a coin flip to determine the rest of the games. The weak form brackets picked an average of 21 winners in the first round. Not bad, when compared to the national average of 22.

As it turns out, next year, instead of watching ESPN and trying to outsmart the rest of your bracket pool, you might be better off digging a quarter out of the couch cushions and asking good old George Washington to decide.

Grace Concelman is a senior majoring in finance and philosophy. She can be reached at [email protected]

The views expressed in this column are those of the author and not necessarily those of The Observer.