Investigating mean reversion in financial markets using Hurst Model

In the dynamic world of financial markets, the prices of assets can exhibit dramatic fluctuations, sometimes soaring to dizzying heights or plummeting to alarming lows. However, amidst the chaos, a fascinating phenomenon emerges: a tendency for prices to revert back to their long-term average or mean level. This concept known as mean reversion has intrigued traders, investors, and researchers for decades. Understanding mean reversion provides valuable insights into market dynamics, investor behavior, and the potential for profitable trading strategies. The aim of this study was to empirically investigate mean reversion in financial markets. This study employed a Hurst model for a sample of five financial markets from June 1, 2018 to June 1, 2023. The findings revealed that four out of the five sampled financial markets exhibit mean reversion, which challenges the efficient market hypothesis concept. Therefore, portfolio managers and active market participants can utilize long-term memory to optimize asset allocation decisions by considering the persistent effects of past returns and adjusting portfolio weights to take advantage of potential return predictability and manage risk. © 2023 by the authors. Licensee SSBFNET, Istanbul, Turkey


Introduction
Financial markets are complex and dynamic systems driven by the interactions of countless investors, traders and institutions.Prices of various financial assets such as stocks, bonds, commodities and currencies constantly fluctuate in response to changing economic conditions, investor sentiment and market forces.Amidst this volatility, a fascinating concept emerges-mean reversion.Mean reversion is a fundamental principle that describes the tendency of asset prices or financial indicators to return to their long-term average or mean level over time (Buzzacchi & Ghezzi, 2023).It suggests that extreme price movements, whether upward or downward are temporary and that prices will eventually revert back to their equilibrium levels (Schmidhuber, 2021).This phenomenon has captivated the attention of market participants, researchers and analysts as it provides insights into market dynamics, behavioural finance and the potential for profitable trading strategies.The concept of mean reversion is deeply rooted in the idea of market efficiency (Rizwan, Jolita, Dalia & Zahid, 2018).According to the efficient market hypothesis, asset prices fully reflect all available information making it difficult to consistently outperform the market (Fama, 1965).Mean reversion challenges this notion by suggesting that prices can deviate from their equilibrium levels, providing opportunities for investors to exploit temporary imbalances (Goudarzi, 2013).One of the key drivers of mean reversion is investor behaviour.Market participants are not always rational decision-makers and can exhibit herd mentality or emotional biases (Enow, 2022).When prices rise above their mean levels, investors may perceive them as overvalued and start selling, leading to a downward pressure on prices.Conversely, when prices fall below their mean levels, investors may see them as undervalued and start buying, pushing prices back up (Huang & Xu, 2021).This collective behaviour contributes to the oscillatory nature of asset prices.Supply and demand dynamics also play a crucial role in mean reversion (Schmeck & Schwerin, 2021).If the price of an asset increases above its mean level, it may incentivize increased supply or decreased demand as suppliers seek to capitalize on higher prices or buyers become more reluctant to purchase at elevated levels.This increase in supply or decrease in demand exerts downward pressure on prices, eventually driving them back towards their mean levels.Conversely, if the price falls below its mean level, decreased supply or increased demand may emerge leading to an upward price correction.

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Mean reversion strategies have gained popularity among traders and investors seeking to capitalize on these price movements.These strategies involve identifying assets that have experienced significant deviations from their mean levels and taking positions that anticipate a reversion to the equilibrium level.If a stock price has declined significantly below its historical average, a mean reversion trader may buy the stock expecting the price to bounce back towards its original value (Latini, Marco & Tiziano, 2019).Similarly, if a commodity price has surged above its average, a mean reversion trader may take a short position, anticipating a price decline.However, it is important to note that mean reversion is not a guaranteed phenomenon.There are instances when asset prices deviate from their mean for extended periods or even permanently.Factors such as structural shifts in the economy, technological advancements, regulatory changes or unforeseen events can disrupt mean reversion patterns and introduce new market dynamics.Understanding principles of mean reversion can help investors and traders identify potential opportunities and risks and develop trading strategies that exploit temporary price imbalances.
Therefore, the aim of this study was to empirically investigate mean reversion in financial markets using the most recent data.Specifically, this study investigates the following research question; Are there any empirical evidence to support the concept of mean reversion in financial markets?What are the implications of mean reversion to the concept of market efficiency and market participants?By validating or rebuffing the concept of mean reversion in stock markets, market participants can make informed investment decisions and develop strategies that capitalize on predictable patterns in stock price dynamics.Also, recognizing and understanding the properties of mean reversion can assist market participants to navigate the complexities of financial markets with greater insight and adaptability.Hence this study makes a noteworthy contribution.The section below highlights the literature review.

Literature Review
The theoretical foundations of mean reversion can be traced back to the concept of market efficiency and the efficient market hypothesis (EMH).The EMH posits that asset prices reflect all available information, rendering them unpredictable and following a random walk process (Enow. 2023).However, mean reversion challenges this notion by suggesting that prices can deviate from their mean levels and subsequently return to them (Dias, Guimarães & Rocha, 2015).
Early research on mean reversion focused on equity markets.Fama and French (1988) analyzed stock returns and found evidence of mean reversion, indicating that stocks that performed poorly in the past tended to have higher returns in the future, while those that performed well exhibited lower future returns.This finding contradicted the notion of efficient markets and provided support for mean reversion as a source of potential profitability in stock trading.Chaves & Viswanathan (2016) examined commodity futures markets and found evidence of mean reversion in commodity prices, suggesting that price movements in these markets tend to be temporary and eventually correct themselves.Similarly, studies have documented mean reversion in bond yields, exchange rates, and other financial indicators, highlighting the pervasive nature of this phenomenon across different asset classes.Empirical evidence supporting mean reversion has also been bolstered by advancements in econometric techniques.Engle and Granger (1987) introduced the concept of cointegration, which allows for the detection of long-term relationships between non-stationary variables.Cointegration analysis has been widely employed to identify mean-reverting relationships in financial time series data, confirming the presence of mean reversion in various markets.Moreover, researchers have investigated the factors that drive mean reversion and contribute to its persistence.Behavioral finance theories suggest that investor sentiment and irrational behavior play a significant role in mean reversion.
De Bondt and Thaler (1985) proposed the concept of investor overreaction, which suggests that investors tend to overreact to news or events, causing prices to deviate from their fundamental values.Eventually, rational investors step in and correct the mispricing, leading to mean reversion (Enow, 2023).
The practical implications of mean reversion have attracted the attention of traders and investors who seek to capitalize on this phenomenon.Mean reversion strategies involve buying assets that have experienced significant price declines and selling assets that have experienced significant price increases, with the expectation that prices will revert back towards their mean.However, it is important to note that implementing mean reversion strategies is not without challenges, as timing the entry and exit points can be difficult, and the duration of price deviations from the mean can vary significantly.Furthermore, the persistence of mean reversion has been subject to debate.Some researchers argue that the presence of mean reversion can be time-varying and influenced by structural changes in the market or shifts in investor behaviour (Akdogan, 2018).Also, the duration of price deviations from the mean can vary significantly, making it difficult to precisely time trades.
The debate surrounding mean reversion is ongoing and the field of financial economics continues to explore the complexities of market behaviour and the role of mean reversion in shaping prices.Hence this study adds to the debate and frontier of the mean reversion in financial markets.The section below highlights the blueprint of the study.

Methodology
A Hurst exponent model was used to quantify the mean reversion properties of stock market returns in five selected markets namely; The Nasdaq index, the French stock market index (CAC 40 index), Frankfurt stock exchange (DAX index), Japanese stock index (JPX-Nikkei 225) and Johannesburg stock exchange (JSE index) for a five-year period from June 1, 2018 to June 1, 2023.The Hurst exponent is often used to analyse autocorrelation and the predictability of stock price movements which is very useful to ascertain whether a time series exhibits a trend, mean-reversion, or random walk behaviour over different time horizons (Bui & Ślepaczuk, 2022).This model is an intuitive method of estimating the extend in which a fitted a linear regression line correlates with a logarithm of the rescaled range as a function of the time series (Vogl, 2022).In its simplest form, the mathematical expression for the Hurst model is highlighted below; The statistical analysis Hurst exponent, denoted by ∀  is presented below.
∀  < 0.5: A Hurst exponent with p-value less than 0.5 indicates a persistent or trending behavior in the time series suggesting a positive autocorrelation.Hence the existence of mean reversion and the potential for predictable patterns.
∀  ≥ 0.5: A Hurst exponent with p-value greater than or equal to 0.5 suggests an anti-persistent or mean-reverting behaviour implying a negative autocorrelation, therefore the absence of mean reversion.The findings and discussion are presented in the section below.

Results and Analysis
The Hurst model findings and analysis are presented below.Consistent with the studies of Chaves & Viswanathan (2016); Gianfreda, Maranzano, Parisio & Pelagatti (2023), the findings revealed evidence of mean reversion in the Nasdaq, CAC 40, DAX and Nikkei 225.However, there is no evidence to suggest mean reversion exist in the JSE.This was evident in the p-values of the Hurst exponent that are less than the 5% threshold in the Nasdaq, CAC 40, DAX and Nikkei 225.This finding suggest that past returns in the Nasdaq, CAC 40, DAX and Nikkei 225 can be reliably use to forecast future returns by adjusting to their mean levels overtime.The implications of mean reversion in these financial markets are significant for market participants.Investors and market participants can incorporate long-term memory into their investment strategies by considering historical price patterns and trends.Strategies such as momentum or contrarian approaches can be employed to capitalize on the mean reversion properties of stock market returns.Portfolio managers can also utilize mean reversion to optimize asset allocation decisions, adjusting portfolio weights based on historical trends to enhance performance and manage risk effectively.

Conclusion
Theoretical models advocating for the existence of mean reversion in financial markets points to investment behaviour and fundamental variables as potential drivers.Recognizing and incorporating mean reversion into investment strategies and risk management practices can provide market participants with insights to exploit predictable patterns and optimize portfolio performance for market participants.From the findings in section 4, mean reversion was observed in the Nasdaq, CAC 40, DAX and Nikkei 225 and questions the concept of market efficiency by opening avenues for market participants to exploit predictable patterns and potentially generate abnormal returns.More specifically, portfolio managers can utilize the following steps to optimize asset allocation decisions in the Nasdaq, CAC 40, DAX and Nikkei 225; i.
Determine the mean and deviation by calculate the mean or average value of the asset's price over a specific time period.ii.
Determine thresholds or boundaries that indicate when the asset is considered overbought (priced too high) or oversold (priced too low).These thresholds can be based on the standard deviation from the mean or other technical indicators.iii.
Continuously monitor the price of the asset and observe how it deviates from the mean.When the price moves beyond the overbought or oversold thresholds, it signals a potential mean reversion opportunity.iv.
Once a price deviation beyond the thresholds is identified, take appropriate trading actions.If the price is overbought, consider selling or shorting the asset with the expectation that it will revert back towards the mean.Conversely, if the price is oversold, consider buying or longing the asset, anticipating a reversion to the mean.v.
To manage risk, set stop-loss orders to limit potential losses if the price continues to move against your position.Additionally, determine take-profit levels to secure profits when the price reverts back towards the mean.These levels can be based on historical price movements, technical indicators or other risk management criteria.vi.
Continuously monitor the market and track the performance of your mean reversion trades.Make adjustments to your strategy as needed based on changing market conditions or the effectiveness of your approach.It's important to adapt to new information and be flexible in your trading decisions.
Despite the profound findings of this study, it is important to note that the interpretation of the Hurst exponent should be considered in conjunction with other analyses and not used as a standalone indicator.The Hurst exponent provides a measure of mean reversion but does not capture short-term dynamics or the full complexity of stock market behaviour.
Despite the extensive research on mean reversion in financial markets, there are still areas that require further exploration.The impact of mean reversion on market stability, the role of different market participants in driving persistence, and the interaction between long-term memory and market microstructure are areas of further research.

Table 1 :
Hurst Model Output