Bitcoin prices are an attractive topic for people who study behavioral finance. Behavioral means anything but rational expectations, Nash equilibrium, and the Efficient Market Hypothesis. It is easy to argue that the fundamental value of Bitcoin is zero — it doesn’t yield income and there is no limit on the supply of cryptocurrency because new cryptocurrencies can be introduced. I certainly consider the positive price of Bitcoin to be a failure of the efficient market hypothesis.

The case is also attractive because the price certainly seems to roughly correspond to what one would expect based on one of the oldest behavioral models. For decades psychologists and experimental economists have noted that people tend to usually assume that time series are mean reverting — guessing that what recently went up will soon go down. People are then surprised if a variable goes up and up and interpret this as something other than random fluctuation, as a new trend. Basically, the story is that people treat a random walk as if it were a stationary process around a broken trend. This isn’t totally surprising as time series econometricians find it exceedingly difficult to distinguish random walks from stationary processes around broken trends.

There are many models in which agents switch back and forth from forecasts in which they predict mean reversion to chasing trends — forecasts in which they expect a variable to continue to change in the direction it has recently changed. In the models, agents switch based on the past performance of the two forecasting rules. Hands are waved so that all don’t switch at the same time and people never become firmly and permanently convinced that one rule is best.

I wrote a little MatLab program in which such agents trade an asset (with no particular fundamental value) & simulated the asset price a few times. Of a few dozen trials one looked like this (remember you have to click more to see figures)