Mean-reverting Behavior Research Articles

Optimal trading and competition with information in the price impact model

Information drives trading and hence affects price dynamics. We study how an informed trader optimally trades, how multiple traders compete with each other, and how their competition affects price dynamics as well as their inventories in the linear price impact model framework. We formulate the informed trading problem as a stochastic optimal control problem and a stochastic differential game in different cases. By virtue of different methods, problems are solved explicitly in all cases. In the case of a single trader, the risk-averse informed trader trades less in the beginning and then speeds up to reduce exposure to the volatility of dynamic information. In addition, the risk-averse trader reveals information more slowly and thus contributes less to price efficiency. When multiple risk-neutral traders compete with information, regardless of the competition structure, they tend to trade more rapidly in the early stage to fill orders at a good price. Competition and the presence of a leader help promote price efficiency, and competition also leads to the empirically observed mean-reverting behavior of price dynamics and order flows. Furthermore, among risk-averse informed traders, inventory management triggers predatory trading and active information leakage during informed trading, and the positions of traders with the same level of risk aversion tend to be identical and mean-reverting to zero under multiple rounds of competition.

Towards A Debt-Overhanged Economy: Causes and Consequences for the Economy of Pakistan

The reliance on debt is not only essential but also a key factor in economic growth of poor countries like Pakistan because of a meager tax base and an annuity of fiscal deficit. Trade surplus is a common tool that covers the budget deficit but twin deficit makes the economic conditions worst. The excessive borrowing can stimulate the economic cycle in the short run but in the in the long-run it creates the issues of debt-overhang. This timely study is an attempt to investigate the short-run and long-run dynamics of debt on the economy of Pakistan. The empirical results (ARDL co-integration) suggests that long-run relationships exist among the variables under consideration such as Exports and Remittances have negative effects on debt, while other variables have positive effects. The Error-Correction-Model (ECM) analysis indicates mean-reverting behavior, where the dependent variable returns to its long-run equilibrium. Post-estimation tests support the model's assumptions. The Jarque–Bera test shows that residuals exhibit normal distribution. CUSUM and CUSUMsq tests indicate reliability and stability of the regression model. There is a long-run relationship between exports of goods and services (EGS), imports of goods and services (IGS), gross fixed capital formation (GFCF), net official development assistance (NOD), personal remittances (PRR), and debt in Pakistan. In the long-run, Exports of goods and services have a negative impact, Imports of goods and services have a significantly positive impact, Gross fixed capital formation has a positive impact, Net official development assistance has a positive impact, Personal remittances have a negative impact on debt respectively. However, Trade as a percentage of GDP has an insignificant impact on debt in the long run. The study also found that the impact of each variable on Debt is different in the short run. Overall, the study provides valuable insights into the factors that affect Debt in Pakistan.

Persistence in the Realized Betas: Some Evidence from the Stock Market

This paper examines the stochastic behaviour of the realized betas in the CAPM model for the ten largest companies in terms of market capitalisation included in the U.S. Dow Jones stock market index. Fractional integration methods are applied to estimate their degree of persistence at daily, weekly, and monthly frequencies over the period July 2000–July 2020 over time spans of 1, 3, and 5 years. On the whole, the results indicate that the realized betas are highly persistent and do not exhibit weak mean-reverting behaviour at the weekly and daily frequencies, whilst there is some evidence of weak mean reversion at the monthly frequency. Our findings confirm the sensitivity of beta calculations to the choice of frequency and time span (the number of observations).

VOLATILITY ANALYSIS OF CRUDE OIL PRICES IN NIGERIA

This study investigates the symmetric and asymmetric characteristics as well as the persistence of shocks in the Nigerian crude oil returns, utilizing monthly and daily crude oil prices spanning from January 2006 to September 2022 and November 3, 2009, to November 4, 2022, respectively. Descriptive statistics, normality measures, time plots, and the Dickey-Fuller Generalized Least Squares unit root test were employed to analyze the series properties. Symmetric ARMA (1,1)-GARCH (2,1) and asymmetric ARMA (1,1)-TARCH (2,1) models for monthly and daily returns, with varying innovation densities, were utilized, alongside symmetric GARCH (1,1) and asymmetric TARCH (1,1) models. Model selection criteria including AIC, SIC, HQC, and log likelihood guided the order and error distribution selection. Results revealed non-normal distributions for both monthly and daily prices and returns, non-stationarity in prices, and weak stationarity in log returns with ARCH effects detected in both returns. Symmetric models exhibited volatility clustering, high shocks persistence, mean-reverting behaviour, and predictability in both returns. Asymmetric models identified asymmetry with leverage effects in both returns, indicating that negative shocks induce greater volatility than positive shocks of the same magnitude. Mean reversion and volatility half-life findings suggested that crude oil prices tend to revert to their long-run averages. The study recommended promoting market information flow and aggressive trading to enhance market depth and mitigate the volatile nature of the Nigerian crude oil market.

Overview of an alternative trigger for DCL

In this research letter, we suggest a novel trigger for Dynamic Control of Leverage (DCL). These instruments are analogous to conventional Contingent Convertible (CoCo) bonds, employed to constrain a firm’s leverage within specified limits, thus minimizing the likelihood of default. Our proposed trigger enables continuous leverage monitoring, bringing in the desired flexibility allowing the conversion to be triggered ahead of the cash payment. This alternative design, building upon the DCL mechanism, has been shown to further reduce the probability of default while preserving the desirable mean-reverting behaviour of the leverage dynamic. We provide evidence of the model’s effectiveness and discuss the implications of its implementation.

The “Perpetually” Efficient Stock Market Nonsense: The Gaslighting Effects

Abstract One of the conventional and commonly accepted assumption in the financial world is the Efficient Market Hypothesis (Fama, 1970). However, the intellectual dominance of the efficient-market revolution has more been challenged by economists who stress psychological and behavioral elements of stock-price determination and by econometricians who argue that stock returns are, to a considerable extent, predictable (Malkiel, 2003). “Boom-bust” patterns are the empirical evidence of the efficient market nonsense. We suggest a theoretical linkage between the EMH and the Reflexivity Theory focusing mainly on the psychological profile. We suppose that, during stages of market exuberance/panic, the market pricing produces “gaslighting effects” and that mean-reverting behavior (i.e., contrarianism) is the result of participants’ awareness of psychological deviation from reality. We suspect that investors “benchmarking” plays a primary role on this latter aspect. Outside bubbles episodes, the market pricing is generally efficient and reflects the fundamental value evolution, without producing gaslighting effects. JEL classification numbers: G10, G11, G14. Keywords: Efficient Market Hypothesis (EMH), Reflexivity Theory, Gaslighting Effects.

Comparison of the Performances for the Mean-Reversion Strategy for Exchange Rate

Mean-reversion theory predicts that historical returns and asset price volatility will eventually return to the long-run mean or average level of the entire dataset. The mean-reversion strategy applies the fundamental idea of selling high and attracting low to stock market investment. Researchers studying the international exchange market have shown that foreign exchange rates display momentum and mean reversion behavior. This study aims to assess the effectiveness of the mean-reversion approach on exchange rates and improve it. Using historical data, the author assessed the mean-reversion method's impact on the exchange rate. According to the study, the method offers a risk-to-reward ratio that is conservative. The clear disadvantage is that for most of the exchange rate, mean-reversion methods yield lesser profits. Furthermore, the return is significantly influenced by the mean-reversion lookback period. Quantitatively, exchange rates with significant volatility and variation often outperform when using the mean-reversion approach. Overall, these results shed light on guiding further exploration of mean-revision strategy.

What determines the mean reversion speed of NAV spreads?

ABSTRACT In this paper, we study the mean reversion behaviour of NAV spreads for a global sample of 219 listed real estate stocks. We find NAV spreads for companies trading at a high discount to mean revert fastest. Remarkably, we also provide evidence that online search attention impacts the mean reversion speed of NAV spreads: Stocks with lower levels of online search attention mean-revert significantly faster than those with higher levels. Our global research setting allows us to show that a country’s average NAV spread has an impact on the NAV spreads of individual stocks. Ultimately, we find that the NAV spread of companies receiving high levels of online search attention has a disproportionately high impact on the NAV spreads of other companies.

On the persistence of shocks to global CO2 emissions: a historical data perspective (0 to 2014).

Anthropogenic emissions of carbon dioxide (CO2) are the most important greenhouse gas. However, until now, no research has investigated the persistence of global CO2 emissions over a very long period of time. This work aims to fill this gap by examining the persistence of shocks to global CO2 emissions with a dataset of more than 2000years. To this end, the study applies a battery of unit root tests by considering sharp and smooth structural shifts as well as the frequency domain properties of the series. Lee-Strazicich method results reveal that sharp break dates relate to the influenza pandemic of 1557 and the invention of the steam engine in 1712, and these historical events led to changes in the trend function of CO2 emissions. The findings of the Fourier Lagrange Multiplier and Fourier wavelet unit root tests illustrate that global CO2 emissions contain a unit root and do not exhibit mean-reverting behavior, thus external shocks have permanent effects on CO2 emissions. The results suggest that a reduction in global CO2 emissions is possible if effective environmental and energy policies established in international meetings such as Rio Conference, Kyoto Protocol Paris Agreement, and the United Nations Sustainable Development Summit are properly implemented.

Modelling housing market fundamentals and the response to economic and political events: empirical evidence from Kuwait

PurposeThe purpose of this paper is to examine the sensitivity of the Kuwait housing market to major local and regional geo-political and economic events.Design/methodology/approachThis paper examines the market dynamics of the housing market in Kuwait. Kuwait provides an interesting market to consider owing to its position as a major oil producer, its sensitivity to geo-political events and its unusual demographic characteristics.FindingsThe error-correction model highlights that market is relatively volatile, with evidence of mean-reverting behaviour. Only when the data is smoothed are their more consistent findings with respect to underlying fundamentals. This paper also examines the response of the market to seven regional and local events. Of particular interest is that the one event that results in a consistent significant response is domestic legislation directly concerned with housing. This has a far greater impact than local or regional geo-political events.Originality/valueVery few papers have considered how economic and political shocks directly impact housing markets using an event study approach. Given its geographic location and also its economic dependence on oil, Kuwait is an interesting market to consider.

How fearful are commodities and US stocks in response to global fear? Persistence and cointegration analyses

This paper deals with the analysis of long-run relationships of fear indices for US stocks, commodities, and the energy sector with global fear indices for stocks and oil. Departing from the classical literature, fractional integration, and cointegration techniques are used to determine the degree of persistence in the long-run relationship of the indices. Our results are threefold. We first established a fractional cointegrating relationship between each of the global and oil fear indices and other fear indices. However, the long-run relationship tends to be weak for the technology stocks. In addition, the cointegrating framework reveals a nonstationary mean-reverting behaviour in the long-run relationship, implying that the effect of shocks from financial, economic, or other exogenous sources will be temporary though with long-lasting effects. These findings have crucial policy inferences for portfolio managers concerning investment decisions.

Investigating efficiency of frontier stock markets using multifractal detrended fluctuation analysis

PurposeThe investigation of the fractal nature of financial data has been growing in the literature. The purpose is to investigate the multifractal behavior of frontier markets using multifractal detrended fluctuation analysis (MFDFA).Design/methodology/approachThis study used daily closing prices of nine frontier stock markets up to 31-Aug-2020. A preliminary analysis reveals that these markets exhibit fat tails and clustering patterns. For a more robust analysis, a combination of Seasonal and Trend Decomposition using Loess (STL) and MFDFA has been employed. The former method is used to decompose daily stock returns, where later detected the long rang dependence in the series.FindingsThe results confirm varying degree of multifractality in frontier stock markets, implying that they exhibit long-range dependence. Based on these multifractality levels, Serbian and Romanian stock markets are the ones exhibiting least long-range dependence, while Slovenian and Mauritius stock markets indicating highest dependence in their series. Furthermore, the markets of Kenya, Morocco, Romania and Serbia exhibit mean reversion (anti-persistent) behavior while the remaining frontier markets show persistent behaviors.Practical implicationsThe information given by the detection of the fractal measure of data can support for investment and policymaking decisions.Originality/valueFrontier markets are of great potential from the perspective of international diversification. However, most of the research focused on other emerging and developed markets, especially in the context of multifractal analysis. This study combines the STL method and a physics-based robust technique, MFDFA to detect the multifractal behavior of frontier stock markets.

Gender Diversity Index. Measuring persistence

This paper deals with the analysis of the Gender Diversity Index (GDI), which is an Index developed by Solactive AG and is calculated and distributed by this provider. The index tracks the performance of developed world companies that are successfully working towards gender diversity as part of their CSR (Corporate Social Responsibility) strategy, and we measure its degree of persistence by using fractional integration or I(d) techniques. Using daily data from 8 December 2010 until 16 December 2020, the results indicate that the series is highly persistent with an order of integration lower than, though very close to 1. However, an interesting result is obtained by estimating d recursively across subsamples. The differencing parameter moves around 0.92 until 23 March 2020, with the series displaying a very small degree of mean reversion behaviour until that date. After that period, however, we observe an increase in the estimate of d, which stabilizes around 0.97 after 5 May 2020, though now the series presents evidence of a lack of mean reversion, with the shock having a permanent effect on the series. Thus, it seems that the sanitary crisis due to Covid-19 has had a clear effect in the degree of persistence of the GDI data.

The Effects of Structural Breaks on Energy Resources in the Long Run. Evidence from the Last Two Oil Price Crashes before COVID-19

The course of events since 2014, including the worldwide pandemic of a coronavirus disease, have shown that oil market fundamentals have not always been clearly anticipated and that additional external factors, rather than those related to supply and demand, do play important roles in signaling future price changes. Within that complex setting, this study examined the influences of structural breaks on the long-term properties of Brent crude oil, gasoil, low-sulfur fuel oil, natural gas, and coal over the period 2002–2018. In an effort to assess the impacts of these structural changes, we identified time points at which structural break changes occurred and unit root properties using a representative variety of unit root testing alternatives. From the estimation results, we observed that only fuel oil and national balancing point (NBP) prices show evidence of mean-reverting behavior, suggesting that shocks to these two markets are short-lived when allowing for structural breaks. Although the idea of market forces bringing the non-renewable markets to their equilibrium in the long run makes the role of policy-making more challenging, it highlights the importance of the policy mix in the transition to a low-carbon energy system.

Persistence, mean reversion, and non-linearities in inflation rates in the GCC countries: an eclectic approach

ABSTRACT The inflation rate is a key variable in many macroeconomic models that are used to guide policy analysts and lead to effective decisions. However, achieving this outcome depends, to a large extent, upon the validity of these macroeconomic models whose successes, in turn, critically depend on whether inflation is stationary or not. In this paper, we investigate the dynamics of inflation in the Gulf Cooperation Council countries using both linear and non-linear tests. To add an extra layer of robustness to our results, we avoid the pitfalls of the econometrics of stationarity by applying the MS-ADF and Fourier ADF tests. After using a battery of tests, the analysis provides more reliable inferences on the question of whether the inflation rates of these countries are I(0) or I(1). The findings convincingly support the view that not only are the inflation rates of these countries non-linear, but they are also characterized by mean-reversion behaviour. The policy implication of our findings is that random shocks will not have permanent effects and that active monetary policies are not needed, as these effects will eventually disappear in the long run.

Differentiation Strategies in the Adoption of Environmental Standards: LEED from 2000 to 2014

We study the role of vertical differentiation in the adoption of LEED (Leadership in Energy & Environmental Design), a multitier environmental building certification system. Our identification strategy relies on the timing of adoption and shows that builders seek to differentiate from each other by choosing a different certification level from previously certified buildings. A common concern in this framework is that mean-reverting behavior could be mistaken for differentiation. We develop a new method for establishing the importance of strategic interactions based on simulating from a model with independent choice and unobserved heterogeneity, and showing that such a model cannot generate the level of interaction that we observe. Finally, we estimate a model that incorporates both differentiation incentives and correlated market-level unobservables and use our estimates from this model to simulate the impact of reducing the number of LEED tiers from four to two. The simulations indicate that environmental investments depend on the location of the threshold between tiers. This paper was accepted by Bruno Cassiman, business strategy.

Robust and Interpretable Liquidity Proxies for Market and Funding Liquidity

We introduce a method to create two interpretable liquidity measures, which we associate with market and funding liquidity. The construction is based on creating two parsimonious linear combinations of the many liquidity proxies often used in the liquidity literature, both displaying mean-reverting behavior, but characterized by very different reversion speeds. Our construction does not require transaction-level data (such as volume or bid-offer spreads), but correlates well both with other measure that do, and with other liquidity proxies (liquidity as ‘noise’, liquidity as broker-dealer leverage) recently introduced in the literature. TOPICS:Fixed income and structured finance, Statistical methods, risk management Key Findings • We introduce two interpretable liquidity measures that can be obtained from publicly available prices, and correlate well with liquidity measures that require transaction-level information. • Our measures have distinct reversion speeds, which sort and mirror the different reversion speeds of the input liquidity proxies. • We interpret our measures as relating to market and funding liquidity, and we justify this interpretation. • We present a brief application (to the extraction of inflation expectations from the break-even yield) to give an idea of how our measures can be used.

Maximum Likelihood Estimation of Continuous-time Diffusion Models for Exchange Rates

Five diffusion models are estimated using three different foreign exchange rates to find an appropriate model for each. Daily spot exchange rates expressed as the prices of 1 euro, 1 British pound and 100 Japanese yen in US dollars, respectively denoted by USD/EUR, USD/GBP, and USD/100JPY, are used. The maximum likelihood estimation method is implemented after deriving an approximate log-transition density function (log-TDF) of the diffusion processes because the true log-TDF is unknown. Of the five models, the most general model is the best fit for the USD/GBP, and USD/100JPY exchange rates, but it is not the case for the case of USD/EUR. Although we could not find any evidence of the mean-reverting property for the USD/EUR exchange rate, the USD/GBP, and USD/ 100JPY exchange rates show the mean-reversion behavior. Interestingly, the volatility function of the USD/EUR exchange rate is increasing in the exchange rate while the volatility functions of the USD/GBP and USD/100Yen exchange rates have a U-shape. Our results reveal that more care has to be taken when determining a diffusion model for the exchange rate. The results also imply that we may have to use a more general diffusion model than those proposed in the literature when developing economic theories for the behavior of the exchange rate and pricing foreign currency options or derivatives.

Maximum Likelihood Estimation of Continuous-time Diffusion Models for Exchange Rates

Five diffusion models are estimated using three different foreign exchange rates to find an appropriate model for each. Daily spot exchange rates expressed as the prices of 1 euro, 1 British pound and 100 Japanese yen in US dollars, respectively denoted by USD/EUR, USD/GBP, and USD/100JPY, are used. The maximum likelihood estimation method is implemented after deriving an approximate log-transition density function (log-TDF) of the diffusion processes because the true log-TDF is unknown. Of the five models, the most general model is the best fit for the USD/GBP, and USD/100JPY exchange rates, but it is not the case for the case of USD/EUR. Although we could not find any evidence of the mean-reverting property for the USD/EUR exchange rate, the USD/GBP, and USD/ 100JPY exchange rates show the mean-reversion behavior. Interestingly, the volatility function of the USD/EUR exchange rate is increasing in the exchange rate while the volatility functions of the USD/GBP and USD/100Yen exchange rates have a U-shape. Our results reveal that more care has to be taken when determining a diffusion model for the exchange rate. The results also imply that we may have to use a more general diffusion model than those proposed in the literature when developing economic theories for the behavior of the exchange rate and pricing foreign currency options or derivatives.

Persistence in the Realized Betas: Some Evidence for the Spanish Stock Market

This paper examines the stochastic behaviour of the realized betas within the one-factor CAPM for the six companies with the highest market capitalization included in the Spanish IBEX stock market index. Fractional integration methods are applied to estimate their degree of persistence at the daily, weekly and monthly frequency over the period 1 January 2000 – 15 November 2018 using 1, 3 and 5-year samples. On the whole, the results indicate that the realized betas are highly persistent and do not exhibit mean-reverting behaviour. However, the findings are rather sensitive to the choice of frequency and time span (number of observations).