The world of trading can (mostly) be broken down into two broad styles. Either momentum (aka trend following) or mean-reversion. Either you find a trend and hold on to it (momentum), or you find a market inefficiency that you think will be corrected (mean-reversion).

There's an even clearer, irrefutable way to differentiate the two, using your alpha signal. The alpha signal is either positively correlated to returns, or inversely related to returns. For example, if your signal is positive, and it predicts a positive return, then it's a momentum signal. If a signal is positive, and it predicts negative returns, then it is a mean-reversion signal. It's as simple as that.

**A Fundamental Perspective**:

This concept isn't just relevant to trading or quantitative investing. Even fundamental investors - whether they like to admit it or not - can be thought of using this framework. Most investors look for improving company fundamentals, such as sales or earnings, or increased positive news flow. These are all signs a trend-following strategy, the most common type for investors.

Look at the two main fundamental investment styles, growth and value investing, these can be reduced to trend-following and mean-reversion.

Let's take value investing, these investors look for very beaten down stocks with a low valuation to buy. A low valuation is a negative signal (as opposed to a high valuation which is a positive signal), but it predicts a reversal in the value of the company. Ergo, this can be referred to as a mean reversion style.

Growth for example, is a trend following strategy. Growth is typically associated with high value stocks that we expect to continue to outperform. I.e. a positive signal predicting a positive return, or momentum.

**A Quantitative Perspective**:

The fundamental perspective is quite intuitive. However, when looking at these two strategies through a mathematical lens, there are some interesting characteristics that arise. Once you understand these characteristics, you can start to tilt the balance in your favor.

**Let's break down momentum first.** Momentum is typically characterized by having a low win rate, that is most of your momentum trades actually lose money, however the trades that do make you money, make a lot of money. The hope is that riding these winners will make up for all the loses of the previous trades.

Stated in a statistical sense, the strategy has a positive skew. That is the bulk of the distribution is in shallow losses, but you have a very long right tail of positive winners. It is these large positive winners far out on the right side of the distribution that allows your to overcome these more common shallow loses. Or at least that is how to do this strategy correctly.

Because of this characteristic, trend-following strategies typically have a high degree of volatility. This is when you are waiting for the market or stock to start to trend, there can be a lot of false starts when the market is moving side-ways. It is when the cycle-starts that you can ride your winners - either long or short.

Remember, the main challenge is to keep losses small. So a shift in mind-set to risk management is key.

**Now let's discuss mean-reversion.** Mean-reversion can be thought of as the complete antithesis to trend-following. Instead of the high loss rate of trend-following, mean-reversion has a high win rate. Mean-reversion compounds numerous small profits as the strategy captures inefficiencies that quickly revert. This high win rate ensures low-volatility and consistent performance.

However, instead of the tail being your friend, this time the tail is your enemy. Stated plainly, instead of a few large winners making up for many small loses, with mean-reversion, a few large losses can wipe out all the small gains you have been accumulating.

In statistical sense, the strategy has negative skew. That is, the bulk of the distribution is in small profits, but you have a very long left tail of negative winners. It is the negative winners far out the left side of the distribution that can sink the ship.

Mean reversion strategies do best in flat markets, where prices oscillate in a side-ways band. They also perform decently well in bear markets, as bear markets are typically more jittery on the way down then bull markets are on the way up. One area where mean-reversion strategies do not do well is in changing regimes, when markets break out and form consistent price trends. Interestingly enough, this is the exact moment when trend-following strategies tend to start to do best.

Risk management is equally as key with mean-reversion. Limiting those large left tail losses will be key to ensuring a long-term robust strategy.

**In summary**, regardless of the type of asset class you trade, whether you're a fundamental investor or quant, short or long term, you can be broken down into one of two investment strategies - either trend-following or mean-reversion. Either you expect prices to continue on the same path, or to correct themselves and revert.

These strategies are the complete opposite of each other. It is only in knowing the characteristics of each of these strategies, their return distributions, and their risks, can we optimize for their return. With trend-following, you're going to have a lot of losing trades before you strike out big. With mean-reversion, you are going to have many small profitable trades before potentially large left tail losses.