Mean Reversion and Kelly Criterion: A Trader's Introduction

As a trader with a few years of experience, you understand that markets don't move in straight lines. They ebb and flow, oscillating around a central value. This tendency is the heart of mean reversion trading. This article introduces the foundational concept of mean reversion and pairs it with a effective mathematical tool for position sizing: the Kelly Criterion. Our goal is to move beyond intuitive trading and toward a more quantitative approach to risk and reward.

What is Mean Reversion?

Mean reversion is the theory that asset prices and historical returns eventually revert to their long-run mean or average level. This mean could be a simple moving average, a volume-weighted average price (VWAP), or a more complex regression line. When a stock's price moves significantly away from this mean, it can be considered overextended, creating a potential trading opportunity for a reversion back to that average.

For example, if a stock has an average price of $100 over the last 50 days and it suddenly drops to $85 on no specific news, a mean reversion trader might bet that the price will rise back toward $100. The key is identifying how far is "too far" and when the snap-back is likely to occur.

Why Position Sizing is Important

You can have the best entry signal in the world, but without proper position sizing, a single losing streak can wipe out your account. Many intermediate traders focus solely on entry and exit signals, neglecting the important question of "how much should I risk on this trade?" Answering this question correctly is often the dividing line between inconsistent results and long-term profitability.

This is where the Kelly Criterion comes in. It provides a mathematical framework for determining the optimal size for a series of bets to maximize long-term capital growth.

Introducing the Kelly Criterion

The Kelly Criterion was developed by John L. Kelly Jr., a scientist at Bell Labs, in the 1950s. It's a formula used to determine the optimal theoretical size for a bet. In trading, it helps you decide what percentage of your capital to allocate to a particular trade, based on the probability of success and the potential risk/reward.

The formula is:

Kelly % = W – [(1 – W) / R]

Where:

• W = Your historical win rate for a specific setup.
• R = Your historical risk/reward ratio (average gain on winning trades / average loss on losing trades).

Let's look at a simple example in a table:

Plugging these into the formula:

Kelly % = 0.60 - [(1 - 0.60) / 2.0] Kelly % = 0.60 - [0.40 / 2.0] Kelly % = 0.60 - 0.20 Kelly % = 0.40 or 40%

This result suggests that to maximize your account's growth over the long run, you should risk 40% of your capital on this specific trade setup. As we will discuss in later articles, risking the "full Kelly" is extremely aggressive and not recommended. However, this calculation provides a effective mathematical baseline for your position sizing decisions.

A Simple Trade Setup Example

Here is a basic mean reversion trade setup that we will build upon in this series:

• Asset: SPDR S&P 500 ETF (SPY)
• Mean: 20-period Simple Moving Average (SMA)
• Entry Signal: Buy when the price closes 5% below the 20-period SMA.
• Stop Loss: A close 7% below the 20-period SMA.
• Profit Target: A return to the 20-period SMA.

Before trading this, you would need to backtest it to determine the historical W and R to then feed into the Kelly formula. This series of articles will guide you through each step of this process, from calculating your inputs to applying fractional Kelly strategies and using oscillators to refine your entries. By the end, you will have a robust framework for sizing your mean reversion trades with mathematical precision.