Abstract

Portfolio allocation strategies, and notably the mean-variance approach, use past returns to assign optimal weights. Even though both past and expected returns should come from the same distribution, a formal test of whether this holds in practice has not been conducted yet. Thus, the study examines if the daily returns of 242 companies with continuous trading in the S&P index come from the same distribution using the Kolmogorov-Smirnov, Cramér-Von Mises, and Wilcoxon rank-sum tests. The tests suggest that generally stock returns do come from the same distribution. However, the hypothesis is rejected during the Great Recession, with the rejection rate increasing as the forecast horizon increased. The rejection rate, using an array of macroeconomic variables, is found to record high levels of persistence. Although macroeconomic variables were not found to be statistically significant determinants of the rejection rate, market distress has a small but significant effect.

Highlights

  • The exact specification of the stock market returns distribution has intrigued both academics and practitioners as it holds a prominent role in portfolio construction

  • The study examines if the daily returns of 242 companies with continuous trading in the S&P index come from the same distribution using the Kolmogorov-Smirnov, Cramér-Von Mises, and Wilcoxon rank-sum tests

  • This study examines if the daily returns of 242 companies with continuous trading in the S&P index during 2000-2014 come from the same distribution using the Kolmogorov-Smirnov, Cramér-Von Mises, and Wilcoxon rank-sum tests

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Summary

INTRODUCTION

The exact specification of the stock market returns distribution has intrigued both academics and practitioners as it holds a prominent role in portfolio construction. Given the large available sample of stock returns and, most importantly, if past and future returns belong to in the same distribution, practitioners can find the optimal weights for their desired portfolio mix of risk and return based on the Markowitz procedure. Existing studies (e.g., Egan, 2007; Malevergne, Pisarenko, & Sornette, 2005; Aparicio & Estrada, 2001) utilize aggregate indices and do not focus on portfolio allocation in individual stocks As such, they do not require the distribution to be the same in the estimation and forecast samples. The optimal weights for their desired portfolio mix In his seminal paper, he supports that investors of risk and return, only if past and future returns make base their decisions for portfolio selection belong to the same distribution.

METHODS
The Wilcoxon rank-sum test
RESULTS
Equality rejection and macroeconomic conditions
Findings
DISCUSSION
CONCLUSION
Full Text
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