Robust Estimation of Skewness and Kurtosis in Distributions with Infinite Higher Moments

2010 ◽  
Author(s):  
Matteo Bonato
Keyword(s):  
Robust Estimation ◽  
Higher Moments ◽  
Skewness And Kurtosis

FLUCTUATIONS OF CLUSTER NUMBERS IN PERCOLATION

2002 ◽  
Vol 13 (06) ◽  
pp. 777-781
Author(s):  
DANIEL TIGGEMANN
Keyword(s):  
Power Law ◽  
Higher Moments ◽  
The Mean ◽  
Large Clusters ◽  
Small Clusters ◽  
Skewness And Kurtosis

In order to study fluctuations in percolating systems, lattices for sizes up to L = 100 000 have been simulated several thousand times using the Hoshen–Kopelman algorithm. Distributions of cluster numbers are Gaussians for small clusters and half-sided quasi-Gaussians for large clusters. The variance of cluster numbers is proportional to the mean, with power-law deviations for small clusters. Higher moments like skewness and kurtosis were also studied.

scholarly journals Abnormal Portfolio Asset Allocation Model: Review

2020 ◽  
Vol 1 (1) ◽  
pp. 46-54
Author(s):  
Nurfadhlina Bt Abdul Halima ◽  
Dwi Susanti ◽  
Alit Kartiwa ◽  
Endang Soeryana Hasbullah
Keyword(s):  
Asset Allocation ◽  
Asset Returns ◽  
Higher Moments ◽  
Investment Portfolio ◽  
Allocation Model ◽  
Model Review ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis ◽  
Normally Distributed

It has been widely studied how investors will allocate their assets to an investment when the return of assets is normally distributed. In this context usually, the problem of portfolio optimization is analyzed using mean-variance. When asset returns are not normally distributed, the mean-variance analysis may not be appropriate for selecting the optimum portfolio. This paper will examine the consequences of abnormalities in the process of allocating investment portfolio assets. Here will be shown how to adjust the mean-variance standard as a basic framework for asset allocation in cases where asset returns are not normally distributed. We will also discuss the application of the optimum strategies for this problem. Based on the results of literature studies, it can be concluded that the expected utility approximation involves averages, variances, skewness, and kurtosis, and can be extended to even higher moments.

Realized Skewness and the Return Predictability

2016 ◽  
Vol 24 (1) ◽  
pp. 119-152
Author(s):  
Myounghwa Sim
Keyword(s):  
Stock Returns ◽  
Cross Section ◽  
Realized Volatility ◽  
Return Predictability ◽  
Higher Moments ◽  
Firm Characteristics ◽  
Realized Variance ◽  
Negative Relation ◽  
Intraday Data ◽  
Skewness And Kurtosis

We explore the cross-section of realized variance, skewness, and kurtosis for stock returns obtained from intraday data. We investigate the properties of the realized higher moments, and more importantly, examine relations between the realized moments and subsequent stock returns. We find evidence of a negative relation between realized skewness and next week’s returns. A strategy buying stocks in the lowest realized skewness quintile and selling stocks in the highest realized skewness quintile earns 0.79 percent per week a risk-adjusted basis. Our results on the realized skewness are robust to controls for various firm characteristics such as size and book-to-market. Little evidence exists that either the realized volatility or the realized kurtosis is significantly related to next week’s returns.

On more robust estimation of skewness and kurtosis

2004 ◽  
Vol 1 (1) ◽  
pp. 56-73 ◽  
Author(s):  
Tae-Hwan Kim ◽  
Halbert White
Keyword(s):  
Robust Estimation ◽  
Skewness And Kurtosis

scholarly journals Do average higher moments predict aggregate returns in emerging stock markets?

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sumaira Chamadia ◽  
Mobeen Ur Rehman ◽  
Muhammad Kashif
Keyword(s):  
Quantile Regression ◽  
Stock Markets ◽  
Higher Order ◽  
Higher Moments ◽  
Excess Returns ◽  
Market Returns ◽  
Content Type ◽  
Emerging Stock Markets ◽  
The Impact ◽  
Skewness And Kurtosis

PurposeIt has been demonstrated in the US market that expected market excess returns can be predicted using the average higher-order moments of all firms. This study aims to empirically test this theory in emerging markets.Design/methodology/approachTwo measures of average higher moments have been used (equal-weighted and value-weighted) along with the market moments to predict subsequent aggregate excess returns using the linear as well as the quantile regression model.FindingsThe authors report that both equal-weighted skewness and kurtosis significantly predict subsequent market returns in two countries, while value-weighted average skewness and kurtosis are significant in predicting returns in four out of nine sample markets. The results for quantile regression show that the relationship between the risk variable and aggregate returns varies along the spectrum of conditional quantiles.Originality/valueThis is the first study that investigates the impact of third and fourth higher-order average realized moments on the predictability of subsequent aggregate excess returns in the MSCI Asian emerging stock markets. This study is also the first to analyze the sensitivity of future market returns over various quantiles.

scholarly journals Higher-Order Risk–Returns to Education

2020 ◽  
Vol 13 (11) ◽  
pp. 253
Author(s):  
Daniel J. Henderson ◽  
Anne-Charlotte Souto ◽  
Le Wang
Keyword(s):  
Returns To Education ◽  
Expected Returns ◽  
Higher Moments ◽  
Investment Risk ◽  
Educational Decisions ◽  
Trade Off ◽  
Risky Assets ◽  
Nonparametric Models ◽  
The Relationship ◽  
Skewness And Kurtosis

In the traditional human capital framework, education is often considered as an investment, rather than consumption, while consumption is not necessarily precluded. Whether education is an investment is empirically unclear and relatively under-explored. We shed light on this issue by estimating the risk–return trade-off in the context of education. If education is indeed an investment, risk could play an important role in individual educational decisions just as with risky assets. As portfolio theory predicts, there could be a trade-off between returns to education and risks concerning those returns: higher risks are generally associated with higher returns. We contribute to the literature by proposing various measures of risk based on the entire distribution of returns to education recovered by our nonparametric models. Our results confirm a trade-off between returns and variance. We also found statistically significant impacts for the higher moments: skewness and kurtosis. Interestingly, we found the relationship between mean returns and variance to be linear, and the relationship between expected returns and higher-moments (skewness and kurtosis) is non-linear.

On the relevance of higher-moments for portfolio-management within Islamic finance

2020 ◽  
Vol 13 (3) ◽  
pp. 533-552
Author(s):  
Omar Shaikh
Keyword(s):  
At Risk ◽  
Portfolio Management ◽  
Value At Risk ◽  
Risk Measure ◽  
Statistical Moments ◽  
Islamic Finance ◽  
Higher Moments ◽  
Tail Risk ◽  
Content Type ◽  
Skewness And Kurtosis

Purpose Using a convenient tail-risk measure of performance, this paper aims to explore the extent to which incorporating higher statistical moments such as an assets skewness and kurtosis, provides further insight into the potential benefits of asset-class diversification within the realm of Islamic finance. Design/methodology/approach The authors use Engle’s (2002) DCC-GARCH model to study the dynamic conditional correlations between asset classes. Furthermore, the authors use the modified value-at-risk (Favre and Galeano, 2002), which incorporates higher statistical moments, to measure the performance of portfolios during both crisis and bullish regimes. Findings The most important finding relates to the estimation of portfolio tail-risk. In particular, the authors find that using a standard two-moment value-at-risk (VaR) measure, which assumes normally distributed returns, rather than a four-moment VaR, which incorporates an asset skewness and kurtosis, can lead to a substantial underestimation of portfolio risk during the most extreme market conditions. Originality/value This paper contributes to the extremely limited research considering higher-moments within the realm of Islamic portfolio-management. The results suggest that Islamic portfolio managers should remain cognisant of the skewness and kurtosis parameters of their assets. Ignoring higher-moments could induce misleading inferences and would, therefore, constitute imprudent risk-management.

On the Usefulness of Risk-Neutral Skewness and Kurtosis for Forecasting the Higher Moments of Stock Returns

2016 ◽  
Vol 24 (2) ◽  
pp. 185-220
Author(s):  
Sol Kim
Keyword(s):  
Stock Returns ◽  
Stock Index ◽  
Higher Moments ◽  
Overlapping Data ◽  
Information Contents ◽  
Risk Neutral ◽  
Alternative Measures ◽  
Measures Of Risk ◽  
Skewness And Kurtosis

In this paper, we examine whether the risk neutral skewness and kurtosis from S&P 500 options have information for predicting the higher moments of the stock returns called skewness and kurtosis, which contain the important information for forecasting potential crash, spike upward and the fluctuations of stock index. We find that the implied risk neutral skewness and kurtosis does not provide the information contents for predicting the higher moments of S&P 500 index return, after eliminating the overlapping data. All the results are robust to the alternative measures of risk neutral moments from options prices, the sub-periods and forecasting periods.

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