Academic literature on the topic 'Co-skewness and co-kurtosis'

This article proposes a new method for the estimation of the parameters of a simple linear regression model which is based on the minimization of a quartic loss function. The aim is to extend the traditional methodology, based on the normality assumption, to also take into account higher moments and to provide a measure for situations where the phenomenon is characterized by strong non-Gaussian distribution like outliers, multimodality, skewness and kurtosis. Although the proposed method is very general, along with the description of the methodology, we examine its application to finance. In fact, in this field, the contribution of the co-moments in explaining the return-generating process is of paramount importance when evaluating the systematic risk of an asset within the framework of the Capital Asset Pricing Model. We also illustrate a Monte Carlo test of significance on the estimated slope parameter and an application of the method based on the top 300 market capitalization components of the STOXX® Europe 600. A comparison between the slope coefficients evaluated using the ordinary Least Squares (LS) approach and the new Least Quartic (LQ) technique shows that the perception of market risk exposure is best captured by the proposed estimator during market turmoil, and it seems to anticipate the market risk increase typical of these periods. Moreover, by analyzing the out-of-sample risk-adjusted returns we show that the proposed method outperforms the ordinary LS estimator in terms of the most common performance indices. Finally, a bootstrap analysis suggests that significantly different Sharpe ratios between LS and LQ yields and Value at Risk estimates can be considered more accurate in the LQ framework. This study adds insights into market analysis and helps in identifying more precisely potentially risky assets whose extreme behavior is strongly dependent on market behavior.

ABSTRACT This article aims to analyze the relation between third- and fourth-order conditions and risk factors and their adequacy to return, performance, and net fundraising. The factors used to determine fund performance and, consequently, their relation with fundraising are: market return, size, book-to-market, profitability, investment, co-skewness, and co-kurtosis. The funds constituting the sample are those classified as Free Stocks (within the period from April 2001 to April 2015). Methodologically, this study has two phases. The first one refers to estimating the parameters that represent fund sensitivity to the factors and the comparison of the capital asset pricing models (CAPM), Fama-French-Carhart 4-factor (FFC), Fama-French 5-factor (FF5), Fama-French 5-factor with momentum (FF5M), added or not with co-moments, by means of the fixed-effects procedure. The second one deals with verifying the relation between performance and net fundraising. The models were reestimated through moving time windows, so that the alpha calculated on each of them represented fund performance within the immediately subsequent period. We also estimated the relation fundraising-performance through cross-section regressions, with rates and age as control variables. The results showed that the co-skewness and co-kurtosis coefficients are not that relevant for determining performance and net fundraising of investment funds. Among the risk factors, market, size, and momentum are the significant parameters for fund returns. The FFC and FF5M models are those with greater explanatory power regarding return specification. There is also evidence of convexity in the relation between performance and fundraising.

Interactions between stock and cryptocurrency markets have experienced shifts and changes in their dynamics. In this paper, we study the connection between S&P500 and Bitcoin in higher-order moments, specifically up to the fourth conditional moment, utilizing the time-scale perspective of the wavelet coherence analysis. Using data from 19 August 2011 to 14 January 2022, the results show that the co-movement between Bitcoin and S&P500 is moment-dependent and varies across time and frequency. There is very weak or even non-existent connection between the two markets before 2018. Starting 2018, but mostly 2019 onwards, the interconnections emerge. The co-movements between the volatility of Bitcoin and S&P500 intensified around the COVID-19 outbreak, especially at mid-term scales. For skewness and kurtosis, the co-movement is stronger and more significant at mid- and long-term scales. A partial-wavelet coherence analysis underlines the intermediating role of economic policy uncertainty (EPU) in provoking the Bitcoin-S&P500 nexus. These results reflect the co-movement between US stock and Bitcoin markets beyond the second moment of return distribution and across time scales, suggesting the relevance and importance of considering fat tails and return asymmetry when jointly considering US equity-Bitcoin trading or investments and the policy formulation for the sake of US market stability.