Eugene Fama and the Random Stock Walker

The video above was posted by Index Fund Advisors (IFA) congratulating Eugene Fama on winning the 2013 Nobel Price in Economics. IFA specializes in passive index fund investing, an investment strategy developed by Eugene Fama and Dimensional Fund Advisors (Fama sits on the board of Dimensional). The passive investing strategy is based on two simple, controversial hypotheses with many subtle implications: the Random Walk Hypothesis (RWH) and the Efficient Market Hypothesis (EMH). RWH and EMH are of great interest because they describe the null hypothesis in all Random Stock Walker models. Fama's Nobel prize provides an opportunity to develop the hypotheses.

A random walk in prices is described by the following equation:

where P is the price and E is an error term. A random walk model says the tomorrow's prices are a function of today's prices plus random error. Since the value for the error term cannot be predicted, the model also means that prices following a random walk cannot be forecast. 

Under what conditions might a price follow a random walk? Consider the basic market model:

where quantity demanded and quantity supplied depend on prices. If demand is higher than prices, supply increases to meet demand. The coefficients b and d determine how responsive quantities are to prices. The coefficients a and c are the level of demand and supply, respectively, when prices are zero. If a=c and b=d (they could all be zero, also) or are effectively very close (not statistically different), then the price in this market is a random walk.

The EMH argues that in an efficient market, where information is widely and rapidly available, supply and demand should adjust very quickly, that is, the response coefficients should be very similar. The market might drift predictably over time if a > c, and here is where passive investment comes in. If you invest in an index fund that drifts over time, you might expect to make some money--how much depends on how much drift and the direction of drift. If you try to actively trade stocks in this market, you are basically gambling (allowing the error term, E, to determine your earnings).

Fama also developed another important idea for the Random Stock Walker: the so-called joint-hypothesis problem. If your models are not working, you cannot tell whether it is an imperfection in the model or an imperfection in the market. You can only try to find a better model and even the best model you can find using brute force multi-model inference will be incomplete. 

The empirical evidence for the RWH and the EMH is extensive and contradictory. For the Random Stock Walker, most stocks either show growth, decline or stagnation. Using the AIC and multi-model inference, the RW null hypothesis can almost always be rejected. On the other hand, this doesn't mean you can uses models to make money in the stock market. There are periods when the markets are not predictable and, to paraphrase John Maynard Keynes, these periods can last longer than you can stay solvent.

One of the most unusual subtle implications of accepting the RWH and the EMH is that market bubbles cannot exist, a conclusion Eugene Fama has not been shy about publicizing. After the Dot-com Bubble, Subprime Mortgage Bubble, the Japanese Asset Price Bubble, etc. it's would seem hard to accept that markets always produce rational prices. But, that is a topic for another post when the work of another 2013 Nobel Prize winner, Robert J. Shiller, is discussed.

If awards are given to people we should emulate, then Eugene Fama certainly deserves a major award and the Noble Prize in Economics certainly is one. He has had the prototypical, successful academic career. He took a collection of ideas, the RWH and the EMH, and pushed them both theoretically and empirically as hard as they could be pushed. Whether he turns out to be right, wrong or somewhere in between, he did exactly what every academic is supposed to do. Science will have to sort out the rest.