University of Tasmania
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Realized skewness and kurtosis in asset markets

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posted on 2023-05-28, 00:31 authored by Ahadzie, RM
The recent advent of high-frequency data has given rise to the notion of realized skewness and realized kurtosis. Unlike sample skewness and sample kurtosis which is normally computed from long samples of low-frequency return series (daily, weekly, monthly return series, and so on), realized skewness and realized kurtosis is computed from high-frequency return series (1-second, 1-minute, 5-minute return series, and so on). The relevance of high-frequency return data has been extensively documented in the extant financial literature. Researchers have shown that with high-frequency return data, realized variance converges to the sample variance and is an efficient estimator of the quadratic variation. However, realized skewness and realized kurtosis do not converge to the sample skewness and sample kurtosis values. This is because the second realized moments depend on both the diffusion and jump components of the observed price, whereas, the third and fourth realized moments depend exclusively on just the jump component. This implies that information embedded in realized skewness and realized kurtosis is different from that of sample skewness and sample kurtosis. This thesis contributes to the body of literature by adopting, deducing, and following various theoretical methodologies, simulation techniques and empirical procedures to offer a new perspective, which cautions researchers to be observant of the optimal sampling frequency for their country of investigation when using high-frequency return series. Primarily, researchers should also be aware of the effects of sampling-interval and holding-intervals on the estimated realized skewness and realized kurtosis and its implication to high-frequency finance. Researchers need to be critical of the type of volume used for information flow, and its relationship with realized skewness and realized kurtosis. Finally, it is important to note the significance of high-order moment pricing models in capturing the cross-section of asset returns under various market conditions (upturn and downturn markets) and sample-periods (pre-crisis, crisis, and post-crisis period). The second chapter of this thesis investigates the optimal sampling frequency for computing realized variance for the DJI30 index and its component stocks, and also whether the obtained sampling frequency could be extended to the Australian framework. To the best of my knowledge, this study is the first to investigate the preferred sampling frequency with a focus on the Australian stocks, and not naively extending the 5-minutes rule of thumb from the US framework. Using 1-second (high-frequency) raw prices downloaded from Thomson Reuters Tick History/Securities Industry Research Centre of Asia-Pacific (TRTH/SIRCA) database from 2010 to 2015, this study computes daily RVs and find that the standard 5-minute interval for the US market holds, a '10-' to '30-minute' sampling frequency is the preferred interval for the Australian framework. The third chapter of this thesis investigates theoretically and empirically, how realized skewness and realized kurtosis are affected by holding-interval and sampling-interval. In particular, before any computations of realized skewness and realized kurtosis are carried out, one often predetermines the holding-interval and sampling-interval and thus implicitly influencing the actual magnitudes of the computed values of the realized skewness and realized kurtosis (i.e. they have been found to be interval-variant). To-date, little theoretical or empirical studies have been undertaken in the high-frequency finance literature to properly investigate and understand the effects of these two types of intervalings on the behaviour of the ensuring measures of realized skewness and realized kurtosis. This chapter fills this gap by theoretically and empirically analyzing as to why and how realized skewness and realized kurtosis of market returns are influenced by the selected holding-interval and sampling-interval. Using simulated and price index data from the G7 countries, this study then proceeds to illustrate via count-base signature plots, the theoretical and empirical relationships between the realized skewness and realized kurtosis and the sampling-intervals and holding-intervals. The fourth chapter of this thesis investigates empirically volume-higher order moment relationship by employing various proxies of information flow. The relationship between volume and realized volatility has been extensively documented in the extant financial literature. However, minimal attention has been accorded to volume-realized skewness and volume-realized kurtosis relationships. The insight in this chapter is that these additional higher-order realized moments hold volume-dependent relationships that have been neglected. The empirical analysis employs 142 Australian stocks from 2003 to 2017 downloaded at 15-minute sampling-intervals from the TRTH/SIRCA database and compute their weekly and monthly realized high-order moments. It is found that the volume proxy influences the signage of the ensuring volume-higher-order realized moment regression coefficients. This study then attempts to explain the empirical findings via three common volume-related hypotheses cited in the extant volume literature and conclude that the DOH (Difference of Opinion) hypothesis implicitly encompasses or nests both the SIAH (Sequential Information Arrival) and MDH (Mixture of Distribution) hypotheses. These two subtle but significant findings have yet to be reported in extant volume or trading-related studies. The fifth chapter follows a set of methodologies documented in the extant literature for investigating the higher-order co-moment risk-return relationship for the Australian stock market. Using 142 stocks from 2003 to 2017 downloaded from TRTH/SIRCA database. For this study, monthly realized return and monthly higher-order co-moment estimates are computed from 15-minute series. The high-frequency return data will ensure robust estimates for the empirical analysis. The empirical results show that the average return for standard beta and kappa risks are asymmetric and diametrically opposite in upmarket and downmarket periods, while gamma risks yield significant gains to the investor regardless of the market condition (the results are consistent for the three methodologies considered: (i) the single sorting of excess return on risk measures, (ii) double sorting of excess returns on risk measures, and (iii) the Fama-MacBeth cross-sectional regression). Additional results from the Fama-MacBeth cross-sectional regression shows that gamma and kappa risk factors remain priced, even in the presence of continuous beta and jump beta. It is found that not only the normalized covariance risk factor is important in asset pricing but also normalized co-skewness and co-kurtosis risk factors are also priced separately. This study further splits the full-sample data into sub-periods and observes that the level of significance of the risk premium varies across the sub-periods. The results contribute to the debate on whether systematic realized higher-order co-moments can explain the cross-sectional Australian stock returns. To conclude, this thesis brings to light some research questions and answers related to realized skewness and realized kurtosis that are yet to be considered in the existing high-frequency finance literature and hence contributes to the body of knowledge in field of finance.


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Copyright 2021 the author Chapter 3 appears to be the equivalent of an accepted manuscript of an article published by Taylor & Francis in Quantitative finance on 7 April 2020, available online: Chapter 4 appears to be the equivalent of a post-print version of an article published as: Ahadzie, R .M., Jeyasreedharan, N., 2020. Trading volume and realized higher-order moments in the Australian stock market, Journal bf Behavioral and experimental finance, 28, 100413

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