Smoothed Semicovariance Estimation for Portfolio Selection

Abstract

Minimizing the semivariance of a portfolio is an analytically intractable and numerically challenging problem due to the endogeneity of the parameters in the semicovariance matrix. We introduce a methodology for consistent estimation of the portfolio semivariance based on a smooth approximation of the empirical semicovariance matrix. Differently from existing methods, the new estimator does not rely on biased surrogate semicovariance models and enables the treatment of large problems with many assets. 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 iteratively reweighted algorithm, which is computationally efficient for high-dimensional problems with many assets. Our numerical studies confirm the theoretical convergence of the smoothed semivariance estimator to the true sample 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