# 2 – M2L6 02 Mean Reversion V5

Let’s look at mean reversion in detail. We can plot a stock’s price movements against its moving average. We tend to see that when the price increases or decreases significantly from this moving average, the price then reverts back towards this moving average. To describe a mean reverting process with some math, we’ll use what’s called the Drift and Volatility model. To guide our understanding, we’ll imagine the stock movement as a boat that is floating passively in the ocean. The change in price of an asset over a period of time is a sum of a long-term average plus some randomness. This long-term average is called the drift term because it changes over time, but relatively slowly. Hence, the long-term average is like the ocean current that slowly and steadily carries the boat. The amount of drift depends upon the current price and the amount of time that has passed. The random part of the price change is called the Volatility Term. We can think of this volatility component as all the fish, dolphins or even whales that bump into the boat. All of these little bumps move the boat in a more random path around it stripped. The volatility term depends on the current price, a standard deviation and the amount of time that passes. The standard deviation is small when the markets are calm, so it’s like encountering a small group of fish. The standard deviation may become large during a market crash. This would be like encountering a group of wales. With math, the Drift and Volatility model looks like this. The dp_t on the left represents the change in price over the time t. The first term to the right of the equal sign a is the drift term. The drift term is made up of the current price, a constant average mu, and the change in time. The second term on the right is the volatility term. The volatility term is made up of the current price, a standard deviation sigma, a random noise factor epsilon and the square root of the change in time. If this equation feels intimidating, don’t worry. For now, just think about the boat drifting in the ocean, encountering fish, dolphins and maybe even some tropical islands.