The aim of this study is threefold; first, the study investigates the symmetric impact of trade openness, financial development, and institutional quality on environmental degradation and environmental sustainability. Second, the study examines the asymmetric relationship between financial development, institutional quality, and environmental degradation. Third, the study examines the asymmetric relationship between financial development, institutional quality, and environmental sustainability. For this purpose, the study utilized the data of Pakistan from 1996 to 2018. The study applied Augmented Dickey–Fuller (ADF), Phillips Parron (PP) and Zivote, and Andrews unit root test to check the properties of stationarity of the data. This study applied the Auto Regressive Distributive Lags (ARDL) model to investigate symmetric relationships while the Non-Linear Auto Regressive Distributive Lag Model (NARDL) approach is utilized to investigate the asymmetric relationship among variables. ARDL bounds testing approach utilized to investigate long-run co-integration while short-run dynamics have been investigated by applying the error correction method (ECM). This study found the significant long-run symmetric and asymmetric association of institutional quality (IQ) and financial development (FD) with environmental degradation (ED) and environmental sustainability. However, IQ- has an insignificant association with environmental sustainability. Moreover, dynamic multiplier analysis indicates that positive shock to FD and IQ has a stronger impact on environmental degradation while a positive or negative shock to FD; both have a stronger impact on environmental sustainability. However, a positive or negative shock to IQ has a smaller impact on environmental sustainability. Moreover, the study also found a significant long-run symmetric association of trade openness with environmental degradation and environmental sustainability. This study suggests that the quality of institutions, financial development, and trade openness is necessary to enhance the quality of the environment.

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COVID-19 is certainly the first sustainability crisis of the 21st century. The paper examines the impact of COVID-19 on the Indian stock and commodity markets during the different phases of lockdown. In addition, the effect of COVID-19 on the Indian stock and commodity markets during the first and second waves of the COVID-19 spread was compared. A comparative analysis of the stock market performances and sustainability of selected South Asian countries is also included in the study, which covers the lockdown period as well as the time frame of the first and second waves of COVID-19 spread. To examine the above relationship, the conventional Welch test, heteroskedastic independent t-test, and the GMM multivariate analysis is employed, on the stock return, gold prices, and oil prices. The findings conclude that during the different phases of lockdown in India, COVID-19 has a negative and significant impact on oil prices and stock market performance. However, in terms of gold prices, the effect is positive and significant. The results of the first wave of COVID-19 infection also corroborate with the above findings. However, the results are contradictory during the second wave of coronavirus infection. Furthermore, the study also substantiates that COVID-19 has significantly affected the stock market performances of selected South Asian countries. However, the impact on the stock market performances was only for a short period and it diminished in the second wave of COVID-19 spread in all the selected South Asian countries. The findings contribute to the research on the stock and commodity market impact of a pandemic by providing empirical evidence that COVID-19 has spill-over effects on stock markets and commodity market performances. This result also helps investors in assessing the trends of the stock and commodity markets during the pandemic outbreak.

The environmental degradation and the concern for sustainable development have garnered extensive attention from researchers to evaluate the prospects of green bonds over other traditional assets. Against this backdrop, the current study measures the asymmetric relationship between green bonds, U.S. economic policy uncertainty (EPU), and bitcoins by employing the Nonlinear Autoregressive Distribution Lag (NARDL) estimation technique recently developed by Shin et al., (2014). The outcome of the empirical analysis confirms an asymmetric cointegration between EPU, bitcoins, the clean energy index, oil prices, and green bonds. The NARDL estimation substantiates that positive shock in EPU exerts a negative impact on green bonds, whereas a negative shock in EPU increases the performance of green bonds. It implies, in the long run, a 1 percent increase (decrease) in EPU decreases (increases) the performance of green bonds by 0.22 percent and 0.11 percent, respectively. Likewise, the study also confirms a bidirectional relationship between bitcoins and green bonds. A positive shock in bitcoin increases the performance of green bonds and vice versa. In addition, our study also reveals a direct co-movement between clean energy, oil prices, and green bonds. This outcome implies that green bonds are not a different asset class, and they mirror the performance of other asset classes, such as clean energy, oil prices, and bitcoins. The findings offer several implications to understand the hedging and diversification properties of bitcoins, and assist in understanding the role of U.S. economic policy uncertainty on green bonds.

The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were proposed by researchers. ARCH, GARCH or EGARCH models, among others, are very popular to model volatility autocorrelation. In this paper, a new simple method called HP is introduced to measure the co-movement between two time series. This method, based on the Hurst exponent of the product series, is designed to detect correlation, even if the relationship is weak, but it also works fine with cointegration as well as non linear correlations or more complex relationships given by a copula. This method and different variations thereaof are tested in statistical arbitrage. Results show that HP is able to detect the relationship between assets better than the traditional correlation method. 2 of 24 multivariate GARCH, to estimate large covariance matrices, and Hafner [26] developed the GDCC model which is able to capture the asset-specific heterogeneity in the correlation structure.In this paper, an alternative way to look at correlations and co-movements is proposed by using the Hurst exponent. Along the paper, correlations, co-movements, etc. refer to cross-correlation, i.e., correlation between two different series (or assets). Introducing the HP of Two Series Hurst Exponent of a Time SeriesHurst exponent can be used to measure persistence as well as mean reversion properties in a time series. Introduced by H.E. Hurst in 1951 [27] to study the frequency of rain and drought in order to size the Nile River Dam, its application was extended not only to social sciences (see [28] for an interesting review) but also to meteorology [29], astrophysics [30], geography [31], medicine [32] or culturomics [33]. The first method to estimate the Hurst exponent was the R/S analysis [34]. However, as a consequence of a lack of accuracy of this methodology claimed by several authors [35-38] and its limited validity mainly for fractional Brownian motions [39], there has been an effort in the literature to provide new algorithms to improve the estimation. Some of these techniques are the Hudaks Semiparametric Method (GPH) [40], the Quasi Maximum Likelihood analysis (QML) [41], the Generalized Hurst Exponent (GHE) [42], Wavelets [43], the Centered Moving Average (CMA) [44], the Multifractal Detrended Fluctuation Analysis (MF-DFA) [45], the Lyapunov Exponent [46,47], Geometric Method-Based Procedures (GM) [48] and Fractal Dimension Algorithms (FD) [49].Among all of them, in this paper we will use the GHE algorithm, because it does not require to calculate ranges, it is not biased when applied to short series [49,50] and the calculation is simple.The GHE algorithm is based on the scaling properties of the following statistic [50]:

The main goal of the paper is to introduce different models to calculate the amount of money that must be allocated to each stock in a statistical arbitrage technique known as pairs trading. The traditional allocation strategy is based on an equal weight methodology. However, we will show how, with an optimal allocation, the performance of pairs trading increases significantly. Four methodologies are proposed to set up the optimal allocation. These methodologies are based on distance, correlation, cointegration and Hurst exponent (mean reversion). It is showed that the new methodologies provide an improvement in the obtained results with respect to an equal weighted strategy.

In this paper, we use a statistical arbitrage method in different developed and emerging countries to show that the profitability of the strategy is based on the degree of market efficiency. We will show that our strategy is more profitable in emerging ones and in periods with greater uncertainty. Our method consists of a Pairs Trading strategy based on the concept of mean reversion by selecting pair series that have the lower Hurst exponent. We also show that the pair selection with the lowest Hurst exponent has sense, and the lower the Hurst exponent of the pair series, the better the profitability that is obtained. The sample is composed by the 50 largest capitalized companies of 39 countries, and the performance of the strategy is analyzed during the period from 1 January 2000 to 10 April 2020. For a deeper analysis, this period is divided into three different subperiods and different portfolios are also considered.