Higher Order Comoments Research Articles

Modeling dynamic higher-order comoments for portfolio selection based on copula approach

This paper introduces a novel approach to estimating time-varying higher-order comoments from a theoretical standpoint. We present how to estimate the dynamic higher-order comoments of asset returns under the copula framework, which builds on the ARCD and copula-DCC models to capture the time variation in higher-order moments and correlations of asset returns. Additionally, the elements in the coskewness and cokurtosis matrices are calculated by the double, triple, and quadruple integrals associated with the joint density function of asset returns. The empirical application to five international market indexes shows that the portfolio with time-varying higher-order comoments estimated by the copula approach significantly outperforms equally weighted and mean–variance strategies in economic performance. The robustness analysis verifies the validity and robustness of the proposed estimation method. Our research offers fresh insights for portfolio analysis and risk management decision-making in practical scenarios.

The football world upside down: Traditional equities as an alternative for the new fan tokens? A portfolio optimization study

This study provides a comprehensive analysis of the relationship between fan tokens and equities as investment vehicles in football clubs. Using the GO-GARCH methodology to account for time-varying higher-order co-moments, we examine the risk-return characteristics of these assets in different portfolio contexts over the period November 2021-March 2023. Our results show high diversification opportunities between fan tokens and equities, especially with investments in different leagues. Portfolio analysis shows that equities generally outperform fan tokens as an investment vehicle, highlighting the importance of active portfolio management. The study also shows that equities have broader diversification potential than fan tokens when added to a portfolio. Furthermore, Turkish fan tokens have better characteristics than Italian fan tokens, possibly due to the nonfinancial benefits for investors. The results are relevant for both retail and institutional investors, regardless of their risk tolerance profiles.

Exploring Downside Co-Skewness and Upside Co-Kurtosis: Implications for Asset Pricing Models

This study examines how the investors' preferences for downside co-skewness and upside co-kurtosis may influence the asset pricing. We analyze data from 2000 to 2021, encompassing 2874 companies listed on the Shanghai Stock Exchange. Our methodology includes both time series and cross-sectional analyses, employing the Fama-Macbeth approach. Our findings reveal that the estimated values for downside co-skewness and upside co-kurtosis contribute to a significant premium, one that remains unexplained by traditional market factors such as size, value, profitability, and investment. Furthermore, when these higher-order co-moments are incorporated into the Capital Asset Pricing Model (CAPM), they demonstrate significant explanatory power in understanding the variations in stock returns. This augmented CAPM, with downside co-skewness and upside co-kurtosis, exhibits a superior goodness-of-fit compared to conventional asset pricing models. This suggests a crucial link between these higher-order risk factors and stock valuation, offering new insights into the complexities of investor behavior and market dynamics.

Higher-order contagion effects in Russian fuel export markets: Evidence from COVID-19 pandemic and Russia-Ukraine war

This study investigates the transmission of financial contagion from energy markets, specifically focusing on Brent oil and natural gas, to the stock indices of 13 countries highly dependent on Russian fuel exports. The analysis encompasses two major crises: the COVID-19 pandemic and the 2022 Russia-Ukraine conflict. By employing six distinct second- and higher-order co-moment contagion tests, our findings reveal notable dynamics: 1) Both the COVID-19 pandemic and the Russia-Ukraine conflict exhibit significant evidence of contagion. 2) During the pandemic, Brent oil plays a more prominent role in transmitting contagion across different stock markets. In contrast, natural gas serves as the primary transmitter for Russian-Ukraine war. 3) Among the three regions analyzed, Asian countries demonstrate resilience against contagion in both crises, while European countries experience a substantial impact from the contagion. 4) Higher-order co-moment channels are more dominant in driving contagion than second-order co-moments. These empirical findings emphasize the importance of considering higher-order co-moments in elucidating the dynamics of financial contagion. They provide valuable insights for policymakers and decision-makers, aiding in the formulation of effective strategies and policies.

Conventional and downside CAPM with higher-order moments: Evidence from emerging markets

Research background: Conventional CAPM is a well-known and tested theory on various capital markets. It was also repeatedly rejected as a model of capital pricing. This article proposes a different approach to both CAPM testing and the use of other risk measures. In addition, research is global, including emerging countries. Purpose of the article: This paper investigates the standard CAPM, and this model is based on higher moments of the return distribution for the global emerging market. In addition, this paper aims to compare the conventional and downside CAPM versions using the beta coefficient and co-moments. Methods: Contrary to the classical unconditional tests for the risk premium, conditional relationships are also estimated considering the market portfolio condition. Moreover, the studies considered conventional and downside approaches to risk measures. The cross-sectional regressions are based on the Fama-MacBeth (F-M) procedure and panel models. Findings & value added: The findings contribute to the debate on whether beta coefficient and higher order co-moments in conventional and downside approaches can explain the cross-sectional emerging indices returns. The unconditional models using all measures do not significantly describe the cross-sectional volatility of returns. The cross-sectional regressions in up and down-market based on both the classic F-M procedure and panel models show that the beta and co-kurtosis risk premium is significant and depends on market conditions. The risk premium for co-skewness is not valid, and the direction of the relationships is opposite than expected. Research also demonstrates that the test results of CAPM relationships are not robust to the presence of outliers and shocks resulting from the Covid-19 pandemic in the context of risk-return space. Research provides strong support for the importance of downside risk in the context of standard CAPM and, above all, higher co-moments.

Are emerging Islamic equity markets immune from contagion effects during the COVID-19 pandemic crisis? Evidence from the higher-order comoment-based contagion tests

In this paper, we investigate the possible contagion effects of the COVID-19 pandemic on twenty-four emerging Islamic equity markets. To test for contagion, we use statistical tests based on changes in correlation and higher-order comoments. We also split the full sample into three sub-periods while identifying two phases of the COVID-19 crisis. Our main empirical findings indicate significant evidence of contagion during the two COVID-19 phases, especially through the coskewness, cokurtosis, and covolatility channels. Interestingly, we find that most emerging Islamic equity markets are not immune from the contagious effects of the COVID-19 pandemic. Furthermore, we draw on six behavioural indicators and construct a new index entitled ‘Feverish sentiment’ to examine the causal relationships between investor sentiment and emerging Islamic equity index returns during the COVID-19 pandemic. Using both traditional and frequency-domain Granger causality tests, we find significant causal linkages between investor sentiment and some emerging Islamic equity markets in low, medium, and high frequencies. In particular, the results highlight an increase in the predictive power of investor sentiment during the second phase of the COVID-19 pandemic.

Higher-order moments and co-moments' contribution to spillover analysis and portfolio risk management

Unlike volatility, the skewness and kurtosis of asset returns are often neglected in the analysis of spillovers and risk management, although they capture the return asymmetry and fat-tailedness, respectively, arising from the non-normality of returns. In this paper, we provide evidence of the relevance and utility of considering spillovers in volatility and higher-order moments (skewness, and kurtosis) and co-moments (covariance, co-skewness, and co-kurtosis), and their implications for hedging. Using high-frequency data on the US stock, crude oil, and gold markets, a time-varying spillover approach and portfolio analysis, we reveal the following results. Firstly, besides volatility and covariance, co-skewness and co-kurtosis are relevant spillover transmitters across the stock, crude oil, and gold markets. Secondly, the level of total spillover increases when including not only covariance but also co-skewness and co-kurtosis, suggesting the relevance of considering higher order co-moments beyond volatility when studying spillovers. Thirdly, the inclusion of co-moments in the spillover analysis generates a significant improvement in hedging for all pairs, which is reflected in the significant increase in the utility function when co-skewness and co-kurtosis are considered. This result is noted when the COVID-19 sub-period is considered separately, except for oil‑gold. Overall, the findings matter for the system of interconnectivity across various assets and emphasize the implications and contributions of higher-order moments and co-moments to portfolio allocation and financial risk management.

Estimating the higher-order co-moment with non-Gaussian components and its application in portfolio selection

The estimation of higher-order co-moments of asset returns play an important role in higher-order moment portfolio selection. We improve the estimation of higher-order co-moments by using non-Gaussian components in the observed factor models and construct a portfolio selection method, labelled as Non-Gaussian Component (NGC) portfolio. We assume the non-normality of asset returns is driven by the independent non-Gaussian components in the observed factors. Through identifying and extracting those non-Gaussian components, the parameters in the portfolio objective function have been significantly decreased. We show that the non-Gaussian components can be estimated consistently by the independent component analysis and higher-order cumulant tests. Simulation studies confirm the good finite sample properties of our estimation procedure and further the performance of the NGC portfolio. Empirical results show that the NGC portfolio outperforms the benchmark portfolios, and only a few non-Gaussian components are needed to optimize the objective function.

Do we need higher-order comoments to enhance mean-variance portfolios? Evidence from a simplified jump process

We consider a joint distribution that decomposes asset returns into two independent components: an elliptical innovation (Gaussian) and a systematic non-elliptical latent process. The paper provides a tractable approach to estimate the underlying parameters and, hence, the assets’ exposures to the latent non-elliptical factor. Additionally, the framework incorporates higher-order moments, such as skewness and kurtosis, for portfolio selection. Taking into account estimation risk, we investigate the economic contribution of the non-elliptical term. Overall, we find weak empirical evidence to support the inclusion of the non-elliptical term and, hence, the higher-order comoments. Nonetheless, our findings support the mean–variance (MV) decision rule that incorporates the elliptical term alone. Excluding the non-elliptical term results in more robust mean–variance estimates and, thus, enhanced out-of-sample performance. This evidence is significant among stocks that exhibit a strong deviation from the Gaussian property. Moreover, it is most pronounced during market turmoils, when exposures to the latent factor are highest.

A joint test of policy contagion with application to the solar sector

This paper examines the impact of China's 2005–2020 solar power energy policies on the stock performance of nine economic sectors in China, Japan, Germany, and the U.S. In order to model how policy shocks affect market performance, we develop a joint contagion test of higher-order co-moments, defining policy contagion as significant changes in the third- and fourth-order co-moments in the post-announcement period as compared to the pre-announcement period. The results show that eight Chinese solar energy policies have significant impacts on nine economic sectors in China, with weaker effects in Germany and the U.S., and the least significance in Japan. Among the eight energy policies, policy supporting plans (i.e., three national five-year plans from 2006 to 2020) provide stronger evidence of contagion to international markets than economic instruments (i.e., feed-in tariffs and subsidies).

Measuring financial interdependence in asset markets with an application to eurozone equities

A general measure of asset market interdependence based on higher order comoments is developed and applied to studying weekly U.S. and eurozone equity returns from 1990 to 2017. A new test of independence is also developed. The empirical results show that interdependence peaks during the global financial crisis with the covariance and covolatility comoments being the dominant factors. Conditioning the interdependence measure on volatility does not change the overall qualitative results. Implications of the results for constructing diversified portfolios reveal economic benefits from portfolios based on higher order comoments than the usual assumption of bivariate normality, especially during the GFC. The empirical results also provide evidence that European Union membership led to higher interdependence than did the adoption of the common currency.

Cokurtosis and the Ability of Mutual Fund Managers

In the present study we propose a new higher-order co-moment timing ability for fund managers. Top-performing fund managers successfully time higher-order co-moments of their investment portfolios, generating significantly positive abnormal returns. However, worst-performing funds show no abilities. The zero-trading strategy works well with all timing ability models, where the zero-cost trading profit of the cokurtosis timing model generates the 0.091% per month abnormal return. The bootstrap test shows that the higher-order co-moment timing ability is not purely driven from luck. The robustness test ensures the main findings.

Identification of structural multivariate GARCH models

The class of multivariate GARCH models is widely used to quantify and monitor volatility and correlation dynamics of financial time series. While many specifications have been proposed in the literature, these models are typically silent about the system inherent transmission of implied orthogonalized shocks to vector returns. In a framework of non-Gaussian independent structural shocks, this paper proposes a loss statistic, based on higher order co-moments, to discriminate in a data-driven way between alternative structural assumptions about the transmission scheme, and hence identify the structural model. Consistency of identification is shown theoretically and via a simulation study. In its structural form, a four dimensional system comprising US and Latin American stock market returns points to a substantial volatility transmission from the US to the Latin American markets. The identified structural model improves the estimation of classical measures of portfolio risk, as well as corresponding variations.

Realized higher-order comoments

We propose a new realized third-order comoment and new realized fourth-order joint cumulants, which are standardized comoments. They are obtained from sub-period returns and lower-order comoments and satisfy A. Neuberger’s (Realized skewness. Rev. Financ. Stud., 2012, 25(11), 3423–3455) aggregation property. Different from other realized higher-order comoments obtained from sub-period returns only, those in this study reflect characteristics of the volatility of volatility as well as jump contributions. As a result, our realized kurtosis and coskewness can reflect well-known phenomena such as the positive autocorrelation of volatility or negative correlation between returns and covariances.

Conditional relation between return and co-moments – an empirical study for emerging Indian stock market

Due to many theoretical and practical shortcomings of the traditional CAPM model, this study aims at analyzing the CAPM with possible extensions. The analysis aims to know the empirical soundness of Conditional Higher Moment CAPM in emerging India’s capital market. The sample consists of 69 company’s daily stock price data from April 2004 to March 2019 from NSE 100. Panel data analysis is used on 21 cross-sections. The overall results show that when both up and down markets are incorporated separately, all three moments, namely, co-variance, co-skewness, and co-kurtosis, are priced during the normal Indian economy phase. Further, this study states that including higher moments (co-skewness and co-kurtosis) in the two-moment model provides symmetry in both the up and down markets. This is one of the first studies in the Indian Stock market explaining the variation in portfolio returns through panel data analysis by extending CAPM with conditional higher-order co-moments. The portfolio managers should consider skewness and kurtosis along with variance in constructing the optimal portfolios.

Capital Market Liberalization and Equity Market Interdependence

This paper uses tests drawn from the literature on financial market contagion measured by changes in higher-order comoments to establish the patterns in the interdependence between equity markets in Shanghai and Shenzhen with Hong Kong as mainland China liberalized their capital market. On the announcement of the opening of the Shanghai market correlations rise, but subside by the launch. Following the launch changes in coskewness, cokurtosis and covolatility emerge. The liberalization process is complete by mid-September 2016.

Higher-order comoments and asset returns: evidence from emerging equity markets

This article examines the role of co-skewness and co-kurtosis in explaining portfolio excess returns utilizing time-series and Fama–Macbeth cross-sectional regression methods in the context of an emerging market. The sample consists of listed firms in Vietnam stock market covering the period from September 2011 to December 2016. This paper reports that co-skewness and co-kurtosis are not important in explaining stock returns in Vietnam stock market. More importantly, we find that market risk premium is the most important factor while other popular factors such as SMB, HML and UMD have minor impact on stock returns. This finding is crucial in identifying factors significantly influencing stock returns in emerging equity markets. This paper also supports the proposition that findings from advanced markets might not be able to generalize into the context of emerging markets. The finding has direct implications for portfolio analysis and risk management.

A Parsimonious Approach for Higher-Order Moments in Portfolio Selection

We propose a joint distribution that decomposes asset returns into two independent components: an elliptical innovation (Gaussian) and a systematic non-elliptical latent process. The paper provides a tractable approach to estimate the underlying parameters and, hence, the assets' exposures to the latent non-elliptical factor. Additionally, the framework incorporates higher-order moments, such as skewness and kurtosis, for portfolio selection. Taking into account estimation risk, we investigate the economic contribution of the non-elliptical term. Overall, we find weak empirical evidence to support the inclusion of the non-elliptical term and, hence, the higher-order comoments. Nonetheless, our findings support the mean-variance (MV) decision rule that incorporates the elliptical term alone. Excluding the non-elliptical term results in more robust mean-variance estimates and, thus, enhanced out-of-sample performance. This evidence is significant among stocks that exhibit a strong deviation from the Gaussian property. Moreover, it is most pronounced during market turmoils, when exposures to the latent factor are highest. Overall, our paper advocates for shrinking away from the non-elliptical term, which is associated with higher estimation risk.

Nearest comoment estimation with unobserved factors

We propose a minimum distance estimator for the higher-order comoments of a multivariate distribution exhibiting a lower dimensional latent factor structure. We derive the influence function of the proposed estimator and prove its consistency and asymptotic normality. The simulation study confirms the large gains in accuracy compared to the traditional sample comoments. The empirical usefulness of the novel framework is shown in applications to portfolio allocation under non-Gaussian objective functions and to the extraction of factor loadings in a dataset with mental ability scores.

Nearest Comoment Estimation with Unobserved Factors

We propose a minimum distance estimator for the higher-order comoments of a multivariate distribution exhibiting a lower dimensional latent factor structure. We derive the influence function of the proposed estimator and prove its consistency and asymptotic normality. The simulation study confirms the large gains in accuracy compared to the traditional sample comoments. The empirical usefulness of the novel framework is shown in applications to portfolio allocation under non-Gaussian objective functions and to the extraction of factor loadings in a dataset with mental ability scores. Supplementary appendix with code examples: https://ssrn.com/abstract=3269127.