, , ,

One of the most powerful ideas in statistics is the concept of regression toward the mean, first observed by Sir Francis Galton during the late 19th century. It is often called mean reversion in finance. Loosely speaking, there is a tendency for an asset that performed better than average in the previous time period to perform closer toward the average in the next time period.

In order to illustrate the concept, I need to omit some of more subtle assumptions and simplify the explanation. Suppose that investing in an average mutual fund yields an annual return of 10% every year, pretty decent. If a mutual fund gives you a return on investment of 20% during the last year, there is a good chance that it will give you a return less than 20% and closer to 10% in the following year.

But why?

Mean reversion is NOT a causal phenomenon. Nothing causes it to happen. A better question to ask is: what are the necessary conditions for mean reversion to occur? For our purpose, it boils down to the extent luck plays in the final outcome.

In his wonderful book, Michael Mauboussin uncoupled the roles played by skill and luck in business, sport and investing. For example, in baseball, luck plays a larger role in the final outcome of any game, whereas, skill is more dominant in basketball. I am not saying that playing either sports at elite level requires no skill, but when everyone has high level of skill, there is not much to distinguish each other apart, and therefore luck will play a larger role. This is known as the paradox of skill. The differences between the two sports come down the nature of play in each sport.

In investing, luck plays a larger role in success than skill, and that is the main reason why the market tends to mean revert.

What does mean reversion mean to you?

In finance, a period of low return is often followed by a period of high return. Suppose that you wish to invest in a trust fund. People tend to invest in funds that outperform against their peers over the last five years. These funds often charge you higher fees and operational costs, but deliver average returns. Further, you often buy them at their peak and thus paying higher prices. In the nutshell, the strategy that works in the past may not work in the future.

Past performance is not indicative of future results.

Mean reversion tells us about the importance of long term observation. The luck component tends to cancel out over a long period of time, whereas skill tends to be consistent over the same period. Here, long term may mean differently to different subjects. Thus, time is the best way to measure skill. This applies to most measurements in life, like exams.

So far, I have refrained from discussing about unit of time. I can only warn that one should be careful about the unit of time one uses (month, year or decade). As I said before, in a longer time unit, luck plays a lesser role. On the other hand, it dominates in a shorter time unit.