Mean Reversion Research Articles

Analyzing water-related equity indices in times of COVID-19

The impact of COVID-19 on water-related equity indices is analyzed in this paper for different regions around the world by using fractionally integrated methods and an artificial neural network model. Using fractional integration, a lack of mean reversion is observed in all cases except in the USA, which means that, for these regions, a change in the trend will be permanent after COVID-19 unless additional measures are implemented. At the same time, a structural break is observed in all cases between the 4th and March 10, 2020, likely due to the drastic lockdown imposed in many if not most countries. Long memory was tested for the post-break period and mean reversion was found not only in North America but also in Europe. Moreover, the results were strongly aligned with those obtained using the neural network model. This suggests that the water-related equity indices and associated levels of investments in water and related utilities have moved back to their pre-Covid-19 levels.

Modelling profitability of private equity: A fractional integration approach

This paper analyses the stochastic behaviour of private equity returns (a measure of profitability) applying fractional integration to an extensive dataset including quarterly data spanning the last four decades for various geographical areas (US, Europe, Asia/Pacific, the Rest of the World and Total) and investment types (Buyout & Growth Equity, Venture Capital & Fund of Funds, Infrastructure, Natural Resources, Real Estate, Subordinated Capital & Distressed as well as the aggregate category All Types). The results support the hypothesis of stationarity and mean reversion in all cases; however, there are differences in the degree of persistence across regions, the series for Europe being the closest to a short-memory process, while those for the US exhibit long memory, which implies that shocks have long-lived effects. Differences are also found in the results by asset class. The implications of these findings for private equity management, profit smoothing and return benchmarking are briefly discussed.

TESTING VOLATILITY PERSISTENCE WITH FRACTIONAL INTEGRATIONAND COINTEGRATION IN WORLDWIDE COMMODITY MARKETS

In this paper, we examine the volatility of commodity prices around the world using monthly data for the time period 1960–2022. During this period, there were significant economic crises that increased the prices of both energy and non-energy commodities in the short term. These past crises may provide insights into the behavior of current crises, as they generally exhibit similar patterns. We use fractional integration methods and find that the volatility for each variable exhibits mean reversion, with the effect of the shocks disappearing in the long run. While this may seem obvious, our paper is the first to empirically demonstrate this significant process of convergence using a flexible time series model. As an additional contribution, we complement our analysis by incorporating a fractional cointegration test to examine potential relationships among the commodity prices. Our findings reveal the existence of four distinct cointegrating relationships within the set of ten commodity prices. This implies that these commodities are not entirely independent and may share underlying connections that contribute to their price movements over time. This valuable insight further enriches our understanding of the intricate interactions within the commodity market. We conclude that although countries do not have effective policies for mitigating volatility, it is only a short-term phenomenon that will disappear in the long term.

Hourly Energy Prices in Spain: Evidence of Persistence Across Different Months

We examine the hourly structure of energy prices in Spain using 12 one-month-long series (from November 2020 to October 2021) of samples of hourly pricing (from 00:00 to 23:00) for each day of the month and applying a long memory approach with fractional integration analysis. Our results indicate that the series are highly persistent, with shocks having permanent effects with non–mean reversion properties, with no month-specific effects on the data series.

Dissecting Idiosyncratic Earnings Risk

Abstract This paper examines whether nonlinear and non-Gaussian features of earnings dynamics are caused by hours or hourly wages. Our findings from the Norwegian administrative and survey data are as follows: (i) Nonlinear mean reversion in earnings is driven by the dynamics of hours worked rather than wages since wage dynamics are close to linear, while hours dynamics are nonlinear—negative changes to hours are transitory, while positive changes are persistent. (ii) Large earnings changes are driven equally by hours and wages, whereas small changes are associated mainly with wage shocks. (iii) Both wages and hours contribute to negative skewness and high kurtosis for earnings changes, although hour-wage interactions are quantitatively more important. (iv) When considering household earnings and disposable household income, the deviations from normality are mitigated relative to individual labor earnings: changes in disposable household income are approximately symmetric and less leptokurtic.

Anchor Reversion: The Case of the 52-Week High and Asset Prices

This study attempts to jointly identify the effects of anchoring and mean reversion on asset prices. In particular, we define “anchor reversion” as the tendency for stock prices to revert back toward an anchor, for example, the 52-week high. Our results show that the further a stock moves away from its 52-week high, the more likely it is to revert back toward that 52-week high in the following month. Conversely, if a stock moves toward its 52-week high in a given month, it is less likely to experience a large movement toward that 52-week high in the following month. Portfolios constructed according to a long-short anchor reversion strategy result in future returns that range from 1.40% to 1.62% per month. These results are robust to controls for various risk factors as well as several cross-sectional stock characteristics, such as the monthly reversal phenomena.

The impact of long memory in mortality differentials on index-based longevity hedges

AbstractIn multi-population mortality modeling, autoregressive moving average (ARMA) processes are typically used to model the evolution of mortality differentials between different populations over time. While such processes capture only short-term serial dependence, it is found in our empirical work that mortality differentials often exhibit statistically significant long-term serial dependence, suggesting the necessity for using long memory processes instead. In this paper, we model mortality differentials between different populations with long memory processes, while preserving coherence in the resulting mortality forecasts. Our results indicate that if the dynamics of mortality differentials are modeled by long memory processes, mean reversion would be much slower, and forecast uncertainty over the long run would be higher. These results imply that the true level of population basis risk in index-based longevity hedges may be larger than what we would expect when ARMA processes are assumed. We also study how index-based longevity hedges should be calibrated if mortality differentials follow long memory processes. It is found that delta hedges are more robust than variance-minimizing hedges, in the sense that the former remains effective even if the true processes for mortality differentials are long memory ones.

A parsimonious enhanced Newell’s model for accurate reproduction of driver and traffic dynamics

This paper investigates the stimulus–response behavior between leader and follower in car-following, based on vehicle trajectories in the prevailing field experiments. The analysis result indicates that the follower’s reaction time is time-varying, which can change significantly or keep a constant value for some time; and the follower cannot accurately track the leader in car following, which results in a residual from the follower’s speed. Inspired by the findings, this paper proposes a parsimonious enhanced Newell’s car-following model incorporating the stochastic reaction time and the fluctuation around the vehicle’s desired speed subject to the mean reversion process. The numerical experiment is carried out. It is shown that the proposed model can qualitatively and quantitatively reproduce the following important field observations: (i) the spontaneous formation and evolution of traffic oscillations, (ii) the concave growth pattern of traffic oscillations, (iii) the oscillations’ amplitude and frequency, (iv) the stochastic reproduction of individual trajectories, and (v) the linear speed-capacity relationship. The robustness of the proposed model is demonstrated, compared with the state-of-the-art model. Finally, the sensitivity analysis is carried out to evaluate the effect of each parameter of the proposed model.

Variational inequality arising from variable annuity with mean reversion environment

In this paper, we study a variational inequality arising from variable annuity (VA) to find the optimal surrender strategy for a VA investor when the underlying asset follows a mean reverting process. We formulate the problem as a free boundary partial differential equation (PDE) to obtain the optimal strategy. The PDE is solved analytically by the Mellin transform approach. Using the Mellin transform, we derive the integral equations for the value of the VA and the optimal surrender boundary. Since the solutions are obtained as the integral equations, we use the recursive integration method to determine the optimal surrender strategy. Finally, we provide the optimal surrender boundaries and values of VA with respect to some significant parameters to show the impacts of mean reversion.

Mean Reversion of Low and High Stock Returns

Mean Reversion of Low and High Stock Returns

Prediction of mineral product price based on mean reversion model

Prediction of mineral product price based on mean reversion model

Debt dynamics and credit risk

We investigate how the dynamics of corporate debt policy affect the pricing of corporate bonds. We find empirically that debt issuance has a significant stochastic component that is imperfectly correlated with shocks to asset value. As a consequence, the volatility of leverage is significantly higher than asset volatility over short horizons. At long horizons, the relation between leverage and asset volatility is reversed due to mean reversion in leverage. We incorporate these stochastic debt dynamics into structural models of credit risk, both standard diffusion models as well as newer models with stochastic volatility and jumps. Including stochastic debt gives more accurate predictions of credit spreads in both the cross-section and the time series.

Forecasting Volatility Persistence: Evidence from International Stock Markets

Volatility persistence represents a notable feature of financial markets and is a widely studied phenomenon that explores the clustering and leverage effects of stock market returns. Recognizing and incorporating volatility persistence into risk management, asset pricing, and portfolio management strategies provide valuable insights for market participants enabling them to navigate and capitalize on the dynamics of market volatility. The aim of this study was to empirically investigate whether the current high volatility in stock markets are temporal or will persist in the future. An ARCH model and a GARCH model were employed to achieve the aim of this study for the JSE, CAC 40, DAX, Nasdaq and Nikkei 225 from May 29, 2023 to May 29, 2018. The findings revealed that stock market volatility will persist at least for some time from the ARCH and GARCH output results. Active traders and market makers need to adapt their strategies in response to the expected volatility persistence. Higher levels of persistence may call for adjustments such as widening stop-loss orders to accommodate larger price swings or using more extended timeframes to capture sustained trends. Portfolio managers may also opt for strategies that thrive in volatile market conditions such as breakout trading or mean reversion strategies

Conditional mean reversion of financial ratios and the predictability of returns

While traditional predictive regressions for stock returns using financial ratios are empirically proven to be valuable at long-term horizons, evidence of predictability at few-month horizons is still weak. In this paper, based on the empirical regularity of a typical dynamic of stock returns following the occurrence of a mean reversion in the US Shiller CAPE ratio when the latter is high, we propose a new predictive regression model that exploits this stylized fact. In-sample regressions approximating the occurrence of mean reversion by the smoothed probability from a regime-switching model show superior predictive powers of the new specification at few-month horizons. These results also hold out-of-sample, exploiting the link between the term spread and the credit spread as business cycle variables and the occurrence of mean reversion in the US Shiller CAPE ratio. For instance, the out-of-sample R-squared of the new predictive regression model is ten (four) times bigger than that of the traditional predictive model at a 6 (12) month horizon. Our results are robust with respect to the choice of the valuation ratio (CAPE, excess CAPE or dividend yield), and countries (Canada, Germany and the UK). We also conduct a mean–variance asset allocation exercise which confirms the superiority of the new predictive regression in terms of utility gain.

Mean‐reversion risk and the random walk hypothesis

AbstractThe nature of risk and long‐term returns is not fully understood. There is need for a measure of long‐term risk at multiple horizons. Frequency domain digital signal processing, with an additive noise model, tests the random walk hypothesis for individual firm total and idiosyncratic risk at 2‐month to 4‐year periods. All firms have significant 12‐month risk. Monthly effects influence small firms. Large firm total risk and mid‐cap firm idiosyncratic risk are influenced by annual and 8‐year mean reversions. Large firm idiosyncratic risk has 4‐year mean‐reversion risk. Results suggest that single‐period risk is composed of multiple long‐term calendar and non‐calendar‐length variances.

Nominal and real wages in the UK, 1750–2015: mean reversion, persistence and structural breaks

This paper analyses the stochastic properties of UK nominal and real wages over the period 1750–2015 using fractional integration techniques. Both the original series and logged ones are analysed. The results generally suggest that nominal wages exhibit a higher degree of persistence, which reflects relatively long lags between inflation and wage adjustments. Endogenous break tests are also carried out and various structural breaks are identified in both series. On the whole, the corresponding subsample estimates imply an increase over time in the degree of persistence of both series.

Asymmetric persistence in Turkish interest and inflation rates: New evidence from quantile unit root test with structural shifts

AbstractThis study investigates the persistence in Turkish interest and inflation rates since the implementation of inflation‐targeting monetary policy, covering the period from January 2006 to July 2022. We focus on accounting for asymmetric persistence by benefiting from recent developments in quantile unit root analysis. The findings indicate that while the conventional unit root tests support the persistence of shocks to interest rates and inflation, the quantile unit root test demonstrates an asymmetric behaviour of the persistence, implying a time‐varying structure with mean reversion (persistency) of the shocks in low (high) inflation periods. Furthermore, the half‐lives increase with the positive shocks, indicating a longer speed of adjustment in the high inflation regime. These findings provide new insights into the relationship between interest rates and inflation and have sound policy implications.

The isotropy of cryptocurrency volatility

AbstractWe examine the fractal volatility and long‐range dependence of Bitcoin, Ethereum, Tether and USD Coin by employing the continuous wavelet transform, maximal overlap discrete wavelet transform and rescaled range. Our dataset consists of daily prices spanning from January 2017 through to October 2022, encapsulating pre‐ and post‐epidemic eras. Generally, our findings suggest that Tether presents the least overall volatility throughout the time‐frequency spectrum. USD Coin demonstrates ephemeral turbulence, contrary to Tether's maturity in influencing market equilibrium through token issuance and trade responses. In the post‐epidemic sample, both stablecoins indicate mean reversion, with USD Coin showing marginally better efficiency. Conversely, investment tokens display persistent clusters due to retail traders and long‐term fundamental institutions. Although both tokens illustrate multifractal volatility, Ethereum unveils more essence of self‐similarity than Bitcoin. Hence, there is no evidence that Ethereum truly duplicates Bitcoin since policy‐related events differ between them, as both return series move incongruously. Conditional dynamics signify that all cryptocurrencies, except Tether, were affected by the pandemic transition of COVID‐19 and subsequent macroeconomic news. The unconditional volatility of stablecoins evinces zero‐mean errors, antithetical to investment tokens exhibiting annual cycles. The fractal geometry suggests that investment tokens simulate one‐dimensional lines, whereas stablecoins mimic two‐dimensional planes.

A COMPARISON OF THE WEAK-FORM EFFICIENCY OF THE ASEAN STOCK MARKETS BEFORE AND DURING THE COVID-19 PANDEMIC

This paper aims to examine the weak-form efficient market hypothesis (EMH) for the ASEAN stock markets before and during the outbreak of the COVID-19 pandemic. The pandemic is a tremendous threat to the health condition and mortality of the world population. An important prevention step undertaken was to have social distancing at different levels of strictness. The ongoing pandemic has caused some negative consequences, including businesses enduring a period of hardship and stock market declines. It seems to be expected that a recession is coming ahead and therefore some people are unwilling to invest in the stock market. On the other hand, some people are optimistic about the economy of ASEAN countries and may think that the declines in stock markets are opportunities to invest. They believe in mean reversion that the falls in stock prices are only temporary and the prices will rebound after some time. If this is true, the market is inefficient and stock prices can be predicted. Conversely, if stock price movements are random walks, shocks to prices will be permanent and prices will reach new equilibrium aftershocks. Hence the market is efficient and stock prices are unpredictable. This study analyses the movements of ASEAN stock markets’ composite indices before and during the outbreak of the COVID-19 pandemic to find out whether the markets are efficient and thus cannot be predicted. We found that some ASEAN stock markets were efficient in both periods, while some others were showing decreased or increased efficiency from the period before the pandemic to the period during the pandemic.

Valuing Forestry Agronomic Potential under Seasonal Mean-Reverting Prices

In the valuation of forest resources, the alternative use of the land is one of the central themes. In most cases it is made without taking into account the uncertainty and the possible flexibility of the alternative use. Within these alternatives, the strategy of shifting to a more profitable and sustainable crop is a well-studied topic in forest research. Although the transformation opportunity could add great value to the project, the valuation of this flexibility is obviated by traditional discounted cashflow criteria (NPV). The application of real options theory (ROT) makes it possible to assess this flexibility based on the uncertainty that the transformation entails. However, the hypotheses that are made about the future evolution of the underlying asset, in this case the value of the new crop, may condition the precision of the result. Usually some researchers model these conversions under the hypothesis of geometric Brownian motion (GBM), hypotheses that are not plausible when the new crop has a strong seasonal component. In this work, an adapted model framework is proposed to evaluate forest transformation opportunity into another crop when land use has both high agronomic potential and high seasonal component, a context in which classic real options framework is not applicable. As a work based on a theoretical model, after methodological motivation, the strawberry crop is chosen as alternative due to its seasonal component. Using private data for this crop, we model through the Ornstein–Uhlenbeck process, with mean-reversion (MR) to a seasonal component, and then we use of Longstaff and Schwartz’s algorithm to calculate the option value. The results show that when considering flexibility in option valuation it leads to an increase on the return of more than 4%. Furthermore, robustness analysis evidence shows that option value is very sensitive to seasonal component, reinforcing previous evidence that suggests that the MR process offers a more accurate and appropriate valuation over the traditional GBM in the arena of agronomic potential valuation. Specifically, the result of valuing this transformation through the MR process is between 1.5 and 1.7 times the value of the NPV, which results in approximately a 13% annual return. If GBM had been used, the valuation would have been a 72% annual return, an unrealistic result in this context, due to the non-consideration of the seasonal mean-reverting prices process.