Smoothed semicovariance estimation for portfolio selection
提出一种基于平滑近似半协方差矩阵的方法，用于一致估计投资组合的半方差，解决了传统方法在大规模资产问题中的计算难题，并通过数值研究验证了其收敛性和样本内外表现。
Abstract Downside risk measures, such as semivariance, are essential for evaluating investment risk. Focusing on semivariance allows investors to emphasize loss mitigation without considering upside volatility as risk. However, 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 traditional sample semivariance. The resulting minimum smoothed semivariance portfolio performs well in- and out-of-sample compared to other popular selection rules.