A Random Walk in the Classroom

If you ask students who have taken my commodity price analysis class at the University of Illinois the one thing they remember most, it is almost always the coin flipping exercise. I think it is important to sometimes demonstrate concepts in a very tangible way so students can literally see them in action. So, after teaching the students a little about technical analysis and charting, I ask them to construct a price chart by flipping a coin in the first part of the exercise. You can easily do this yourself with a piece of graph paper. Start halfway up the page. Heads are one square up and tails are one square down. The pricing units per square are arbitrary. I have the student start at $10 and each square is 10 cents. The students flip a penny 30 times to simulate 30 days of market prices. In the second part of the assignment, I ask the students to draw chart patterns that we learned earlier in class. In other words, draw uptrend and downtrend lines, resistance and support levels, triangles, head and shoulders, etc. In the last part of the exercise, we discuss the predictive value of the chart patterns they drew on their simulated market prices.

As you might imagine, this exercise generates a good deal of cognitive dissonance in the students’ minds and faces. They understand that the probability of prices going up or down in their simulated markets is 50/50 because they flipped the coins themselves. But how can it be that the chart patterns look so realistic? We have arrived at the teachable moment. This is when I discuss the random walk model and how sequences of prices generated by the model have a startling resemblance to real-world market prices. My purpose with this exercise is to try to get students to think about what makes sense to them. Do they think market prices truly follow a random walk and technical analysis is worthless? Or do they think markets are not quite this perfect (in a statistical sense)? I want them to think critically and answer the question for themselves. The discussion is always one of my favorite parts of the class.

The inspiration for this class exercise is a paper published in the Journal of the American Statistical Association (JASA) by one of my professional heroes—Holbrook Working—in 1934. He generated what he called “random difference series” and noted the similarity to real-world stock and commodity price charts. He even showed it to a colleague who thought it was a chart of an actual commodity market. The concept he was writing about was so new that the random walk terminology was not yet in wide use. As a side note, Working was at least 30 years ahead of the finance profession in studying the random walk model but never got the credit he deserved. I talk about Working’s monumental contributions to economics and his frustrations at being largely ignored in Chapter Six, “The Engine of Economic Efficiency,” in my book Back to the Futures.

My students were gracious enough this year to let me share these pictures of the coin-flipping exercise. They always amaze me. I noticed a couple of students were not flipping the coins but were busily filling out their price charts. It turns out that Sirri has a coin flip app built into it. I tried it. Works slicks as a whistle. The students said they knew about it because sometimes they make decisions about whether to do something using it. I think it is pretty cool to see statistics in action like that! And kinda funny too.

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