Smoothed Semicovariance Estimation for Portfolio Selection
24 Pages Posted: 23 Mar 2021 Last revised: 26 May 2022
Date Written: May 25, 2022
Minimizing the semivariance of a portfolio is analytically intractable and numerically challenging due to the endogeneity of the semicovariance matrix. In this paper, we introduce a smoothed estimator for the portfolio semivariance and use it as an objective for portfolio selection. The extent of smoothing is determined by a single tuning constant, which allows our method to span an entire set of optimal portfolios with limit cases represented by the minimum semivariance and the minimum variance portfolios. The methodology is implemented through an interatively reweighted algorithm, which is found to be computationally efficient in large problems with many assets. Our numerical studies confirm the theoretical convergence of the smoothed semivariance estimator to the true semivariance. The resulting minimum smoothed semivariance portfolio performs well in- and out-of-sample compared to other popular selection rules.
Keywords: semivariance, smoothed semicovariance, portfolio optimization, skewness
JEL Classification: G11, D81
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