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It is common wisdom that luck plays a role in sports, along with skill. However, there is no consensus among researchers on what constitutes luck. One strand of the literature studied randomness in sports, most of which did the analysis at the levels of pitch actions, or at the match level. There is no empirical study to assess the role of luck in the determination of rank positions in football (soccer) leagues. In this paper, we define X-factor as unforeseen and unaccounted factors and quantify it as the difference between actual and predicted values of performance or outcome variables. For league football, we have perceived the difference between actual and expected goal difference as the X-factor effect in performance, and the difference between actual and expected points as the X-factor effect in outcome. Further, we have ideated that a plausible role of luck cannot be ruled out if the X-factor effect on outcome is significant while that on performance is not. Conducting analyses of variance on observations from seven seasons (2014–15 to 2020–21) in the top tier leagues of England, Spain, Germany, Italy, and France, we detected the presence of a significant and systematic X-factor effect. We have studied the role of luck using Tukey's HSD test. In general, luck does not play any significant role in determining the rank positions in league football. [ABSTRACT FROM AUTHOR]

The earliest documented analytical approach to portfolio selection is Markowitz’s mean-variance analysis, which attempts to find the portfolio with optimal performance by considering the tradeoff between return and risk. The performance of mean-variance analysis has been the subject of many studies and compared to other portfolio construction approaches such as a naïve equally-weighted allocation scheme. In recent years, several approaches have been proposed to improve the mean-variance model by reducing the sensitivity of the portfolio selection process in order achieve robust performance. Although robust portfolio optimization has been one of the most researched methods for improving portfolio robustness, the performance of robust portfolios has not been the major focus of studies. In this paper, a comprehensive analysis on robust portfolio performance is presented for equity portfolios constructed in the U.S. market during the period 1980 and 2014, and results confirm the advantage of robust portfolio optimization for controlling uncertainty while efficiently allocating investments. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new rank dependent utility approach, which unlike existing models, provides an SSD efficient portfolio as a function of the investors' quantified risk aversion degrees. A parametric family of distortion functions is considered to model various levels of risk aversion. Under assumptions of equally probable scenarios, for any distortion function the corresponding optimization models can be expressed as linear program and easily solved. An empirical study is performed to compare the performance of our proposed model to the previously proposed portfolio selection models in the literature. [ABSTRACT FROM AUTHOR]