Investing in Global Markets: Big Data and Applications of Robust Regression

Abstract

In this analysis of the risk and return of stocks in global markets, we apply several applications of robust regression techniques in producing stock selection models and several optimization techniques in portfolio construction in global stock universes. We find that (1) that robust regression applications are appropriate for modeling stock returns in global markets; and (2) mean-variance techniques continue to produce portfolios capable of generating excess returns above transactions costs and statistically significant asset selection. We estimate expected return models in a global equity markets using a given stock selection model and generate statistically significant active returns from various portfolio construction techniques.Keywords: outliers, big data, robust regression, portfolio selection, portfolio management INVESTING IN GLOBAL MARKETS: BIG DATA, OUTLIERS, AND ROBUST REGRESSIONIn this study, we apply robust regression techniques to model stock returns and create stock selection models in a very large global stock universe. We employ Markowitz portfolio construction and optimization techniques to a global stock universe. We estimate expected return models in the global market using a given stock selection model and generate statistically significant active returns from various portfolio construction techniques. In the first section, we introduce the reader to the risk and return trade-off analysis. In second section, we introduce the reader to modeling expected returns and make extensive use of robust regression techniques. In the third section, we examine the relationship of the (traditional) Markowitz mean-variance (MV) portfolio construction model with a fixed upper bound on security weights. In fourth section, we discuss portfolio construction and simulation, and present the empirical results. In fifth section, we offer conclusions and a summary. We report that mean-variance techniques using robust regression-created expected returns continue to produce portfolios capable of generating excess returns above transactions costs and statistically significant asset selection in a global stock market offer the potential for high returns relative to risk. The stock selection model used in this analysis is the "public form" of the McKinley Capital Management proprietary model. The public form model produces highly statistically significant asset selection and similar factor risk exposures to our proprietary model.

Do corporate governance structure and capital structure matter for the performance of the firms? An empirical testing with the contemplation of outliers

“…Robust regression can be used in any case in which we use OLS regression [106]. After applying the OLS regression, we may find some outliers or high leverage data points.…”

A Case Study of Forecasted Earnings Acceleration and Stock Selection in Global and Emerging Stock Markets

“…Constraints are an integral part of portfolios optimization construction process because the error in the estimation of expected return, and variances, and covariances. 10 Guerard [54] reported the effectiveness of the Blin and Bender APT and Sungard APT systems in portfolio construction and management. Blin et al [55] used a 20-factor beta model of variance and covariances based on 3.5 years of weekly stock returns data.…”

“…The Blin and Bender Arbitrage Pricing Theory (APT) model followed the Roll factor theory, but Blin and Bender estimated at least 20 orthogonal factors. The trade-off curves in Guerard [54] were created by varying lambda, a measure of risk-aversion, as a portfolio decision variable. As lambda rises, the expected return of the portfolio rises and the number securities in the portfolio declines.…”

“…As lambda rises, the expected return of the portfolio rises and the number securities in the portfolio declines. The Guerard [54] application minimized risk in terms of a "tracking error at risk" concept in which portfolio risk is three parts systematic tracking variance and one part specific tracking variance. The reader is referred to Blin et al [55] and Guerard [54] for more explanation of the multi-factor risk model and optimization process.…”

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