11 May
2023
Smoothed Semicovariance Estimation for Portfolio Selection
Minimizing the semivariance of a portfolio is analytically intractableand numerically challenging due to the endogeneity of the semicovariance matrix. In this paper, we introduce a smoothed estimator fort he portfolio semivariance. 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 optimization 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.