# What is the Mean Reversion Strategy?

Mean reversion is the idea that poor performance will rise to average, and stellar performance will fall back to the average over time. In short, good and bad days are outliers, and most days will be average.

It's a simple concept, and makes a lot of sense for dealing with real life. If you have a good day, you can bet that tomorrow will likely be less good as it returns to normal. And crucially if you have a bad day, you know that the next day will be better!

However, mean reversion is also applied to quantitative analysis and trading.

My first two automated stock trading algorithms were based on momentum strategies and the mean reversion phenomenon. I learned a number of things from doing that, mostly that algo-trading (and day trading) aren't worth it for small time investors like myself.

## What is Mean Reversion?

Picture a bell curve (a normal distribution). The height of the curve corresponds to some probability. The centre (our average) is most likely, and the outlying extremities are less likely:

What if we get an event that's an outlier on either end of the curve?

Well, the odds are such that whichever side has more area under the curve is the most likely to happen next.

So if you have an event that's on the right of the curve, you expect the next event to be lower. Likewise if you have an event on the left of the curve, you expect it to be higher next.

So what happens if a stock metric suddenly is up something ridiculous, like 27% up over one day? Or if it falls 15% in one day?

It's the same question. Most days for specific metrics a stock has changes near 0%, so any extreme differences are out of the ordinary! We expect the stock to "revert to the mean" soon.

Note however that this only makes sense for metrics that are relatively stable, that stick near their average over the long term. That's an assumption that is important to understand later on.

## How do you Trade Using Mean Reversion?

The most naive approach to mean reversion strategies is to trade based on stock price. Let's say you select 500 stocks to act on as your "trading universe."

Every day you select the top 5-percentile of stocks to short, assuming that their price is going to fall soon. You also select the bottom 95-percentile stocks to hold long, assuming that they will go up as they revert to the mean.

What you end up with is the 25 highest performing and 25 highest loss stocks being traded. Ideally you expect them to reverse direction shortly after buying them, allowing you to make profit once they cross your entry price.

This approach has serious flaws, especially if you are trading stocks that have momentum. There's usually an underlying reason why a stock is rising or falling, whether it's growth or somehow failing. Mean reversion doesn't account for root causes, it just assumes a pure statistical model.

If the stock keeps rising or falling, then your strategy is losing money.

What's more, most stocks do not have a stable stock price average. Generally you can assume that stock prices increase with time by random walking upwards. A constantly growing stock price does *not* have a stable average, obviously. It keeps getting dragged upward.

Let's look at a more reasonable mean reversion approach, using the Price to Earnings ratio as the underlying signal instead of share price.

For one thing, you'll find that P/E ratios are fairly consistent between companies in an industry. They tend to be more stable than measures like share price, and don't grow or fall endlessly.

Then the mean reversion strategy becomes simple: find the average P/E ratio for a given stock, and short or hold whenever there is a large deviation from its average.

## Is a Mean Reversion Strategy Worthwhile?

If you're reading this blog, then I'd say **no, it's not in your best interest to use a mean reversion strategy.**

For one thing, I'm scornful of quantitative analysis trading in general: it's playing a game where wins are incidental, and you're competing against the best and brightest teams of multi-million dollar PhDs who will gladly vacuum up any money you bring to the algo-trading table.

There are countless obstacles to overcome to implement a good mean reversion algorithm, and at best your returns for all that effort are fractional gains.

Mean reversion also has another major flawed assumption that goes back to that normal distribution/bell curve. In the real world, probabilities aren't often normally distributed, you can end up with something bimodal or multi-modal.

What that means is that instead of having one main section of high probability, there's two or more maximas of high probability. You get two or more humps in the curve, which throws off the entire assumption of mean reversion.

Instead of active trading strategies, I'm yet another proponent for buy-and-hold with index funds. If you wish to get wealthy and stay that way, it's better to take the steady path rather than burning up money chasing better returns.

With that in mind, if you enjoy learning about different trading strategies I invite to your attention this article: