# Mean Reversion

### Reviewed by Subject Matter Experts

Updated on July 19, 2023

## What Is Mean Reversion?

Mean reversion is a key financial concept that hypothesizes that asset prices and returns eventually return towards their long-term mean or average.

In other words, it's the idea that extreme fluctuations in price—whether high or low—are likely to revert to their historical average over time.

In the field of financial analysis, mean reversion plays a significant role in determining investment strategies, risk management, and portfolio diversification.

It helps financial analysts predict price movements and develop investment strategies based on historical price patterns.

While mean reversion can be a useful concept in investing and trading, it's worth noting that it's not foolproof.

Markets can and do remain irrational for long periods, and prices can deviate from their mean for many reasons, such as changes in the underlying business, macroeconomic shifts, or changes in investor sentiment.

## Understanding the Theory of Mean Reversion

### Statistical Foundations

#### Probability

The probability of an event occurring, particularly in financial markets, often dictates the actions of investors and traders. In the context of mean reversion, probability is used to determine the likelihood of a price returning to its mean.

#### Standard Deviation and Variance

Standard deviation and variance are two critical statistical tools used in the theory of mean reversion.

These measures help in quantifying the degree of dispersion or volatility in a data set—such as the price of a financial asset—and play a key role in calculating the potential for reversion to the mean.

### Fundamental Assumptions

#### Equilibrium

At the heart of the theory of mean reversion is the concept of equilibrium. It's the idea that markets, despite their frequent ups and downs, have a state of balance or "normalcy" to which they eventually return.

This equilibrium state is typically represented by the long-term average price of a financial asset.

#### Efficient Market Hypothesis

The efficient market hypothesis (EMH) is a fundamental pillar of modern financial theory. It asserts that financial markets are "informationally efficient," meaning that asset prices always reflect all available information.

However, the theory of mean reversion often stands in contrast to EMH, suggesting that markets can overreact or underreact to new information, creating temporary price distortions that eventually correct themselves.

## Mean Reversion in Financial Markets

### Stock Prices

#### Random Walk Theory vs Mean Reversion

The Random Walk Theory posits that the prices of securities move randomly and that past movement cannot predict future movement.

However, the mean reversion theory provides a contrasting viewpoint, stating that prices deviating significantly from their historical averages eventually revert back. This difference forms the core of the debate between the theories.

#### Case of Mean Reversion in Stock Markets

One notable example of mean reversion can be observed in the aftermath of the dot-com bubble of the late 1990s. During this period, technology stocks saw inflated prices far from their long-term averages.

However, in the early 2000s, these prices drastically fell and returned closer to their historical means.

### Foreign Exchange Rates

#### Currency Pair Analysis

In the foreign exchange market, mean reversion can be used to analyze currency pairs. This analysis is based on the idea that exchange rates are likely to revert to their historical averages over time. Traders can use mean reversion strategies to take advantage of temporary price deviations.

#### Historical Trends

For instance, the EUR/USD pair has seen periods of substantial overvaluation and undervaluation over the past decade. However, these rates have often reverted to their long-term average, supporting the idea of mean reversion.

### Commodity Prices

#### Factors Influencing Commodity Reversion

Several factors can influence mean reversion in commodity prices, such as changes in supply and demand, geopolitical events, and market sentiment.

For example, an unexpected increase in crude oil production might temporarily lower prices, but as the market adjusts to this new supply, prices may revert to their long-term average.

#### Impact of Global Events

The 2008 financial crisis serves as a prime example of mean reversion in commodity prices. Post-crisis, the prices of many commodities fell sharply but gradually recovered over the following years to levels more in line with their historical averages.

## Models and Strategies Using Mean Reversion

#### Selection of Securities

In a pair trading strategy, two co-integrated securities are identified. When the spread between them widens, the underperforming security is bought, and the outperforming security is sold short, assuming that the spread will eventually revert to its mean.

#### Risk-And-Reward Assessment

This strategy's success depends on accurately assessing the risk and potential reward of the selected securities. It is crucial to consider factors such as the securities' volatility, correlation, and response to market events.

### Arbitrage Strategy

#### Risk Arbitrage

Risk arbitrage, also known as merger arbitrage, is a strategy that exploits the price discrepancies between the current market price of a stock and the price of the same stock post-merger.

The mean reversion concept comes into play as the price discrepancy is expected to close, i.e., revert to the mean, once the merger is completed.

#### Statistical Arbitrage

Statistical arbitrage involves a portfolio of long and short positions in stocks in the expectation that the prices will revert to their historical or statistical norms. The selection of these stocks is generally carried out using complex algorithms and quantitative models.

### Quantitative Models

#### Ornstein-Uhlenbeck Process

The Ornstein-Uhlenbeck process is a stochastic process used in quantitative finance to model mean reversion. It is used to describe the evolution of financial variables, such as interest rates or commodities prices, that tend to revert to a long-term mean value.

#### GARCH Model

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is used to estimate the volatility of returns.

It assumes that the amount of randomness, or variance, in the returns changes over time but reverts back to a long-term average. Hence, it is suitable for modeling mean reversion.

## Mean Reversion in Portfolio Management

### Asset Allocation Strategy

#### Diversification and Rebalancing

Applying mean reversion in asset allocation can influence diversification and rebalancing strategies. An investor might choose to rebalance a portfolio when asset prices stray too far from their long-term averages, under the assumption that they will eventually revert.

#### Timing and Market Conditions

Timing and market conditions also play crucial roles. For instance, an investor might identify assets that are trading below their historical averages during a market downturn, with the expectation that these assets will revert to their means when the market recovers.

### Risk Management

#### Understanding Volatility

Mean reversion can be a helpful tool in understanding and managing volatility in a portfolio. If asset prices are expected to revert to the mean, periods of high volatility (i.e., large price deviations from the mean) may be viewed as temporary and not necessarily indicative of a longer-term trend.

#### Hedging Strategies

Investors can also use mean reversion to inform hedging strategies. For example, if a certain asset's price has deviated significantly from its mean, an investor might take a counter position in a correlated asset to hedge against the possibility of the first asset's price reverting to the mean.

## Limitations of Mean Reversion

### Market Anomalies and Black Swan Events

Mean reversion relies on the assumption that prices will revert to a long-term mean, but certain unpredictable events, known as Black Swan events, can drastically alter a market's equilibrium.

These events can cause significant deviations from the mean that may not correct for a considerable time.

### Criticisms of the Efficient Market Hypothesis

While the EMH is a cornerstone of modern finance, it has been criticized for oversimplifying complex market dynamics. If markets were perfectly efficient and always accurately priced, there would be little room for mean reversion as prices would never deviate significantly from the mean.

### Market Manipulation and Insider Trading

Market manipulation and insider trading can distort price movements and influence mean reversion. These practices can create artificial price deviations that may not revert to the mean as naturally or predictably as expected.

## Final Thoughts

Mean reversion is a fundamental concept in finance that suggests asset prices and returns tend to move towards their long-term mean or average over time.

By understanding the foundations and assumptions of mean reversion, such as probability, standard deviation, variance, equilibrium, and the EMH, financial analysts can make informed predictions about price movements and develop strategies based on historical patterns.

Mean reversion is observable in various financial markets, including stock markets, foreign exchange markets, and commodity markets.

Traders can utilize mean reversion strategies to capitalize on temporary price deviations in currency pairs, identify co-integrated securities for pair trading, or exploit price discrepancies in risk arbitrage.

Quantitative models like the Ornstein-Uhlenbeck process and the GARCH model are employed to model and estimate mean reversion in financial variables.

However, it is important to acknowledge the limitations of mean reversion, such as the impact of market anomalies, Black Swan events, and market manipulation.

Considering the above provides investors with a framework to navigate volatile markets and potentially capitalize on price movements that revert to the mean.