Smoothed Semicovariance Estimation

Abstract

Investors might prefer to consider the problem of minimizing the semivariance of a portfolio given a certain benchmark rather than the variance, as in such case only the downside volatility is considered as risk. However, such optimization framework has received limited attention compared to the variance minimization framework as the problem is analytically intractable due to the endogeneity of the semicovariance matrix. To solve this issue, we introduce a smoothed semicovariance estimator (SSV) and a simple re-weighting scheme to compute the optimal portfolio weights. Beside relying on a fast estimation algorithm, the SSV has appealing theoretical properties: by tuning a single parameter, controlling the trade-off between bias and variance, the SSV allows to span the entire set of portfolios from the minimum sample semivariance to the minimum sample variance portfolio. Simulations confirm the theoretical and convergence properties of the SSV estimator, while empirical results on real-world data show its out-of-sample properties in comparison to state-of-art optimal portfolio approaches.