Penalized portfolio optimization
Yemin Shi · University of Southern California Digital Library · 2012
Penalization or regularization is an important integration to the traditional regression method to improve prediction accuracy, speed and adaptability for various problems. Lasso type L1-regularization methods and its variants can reduce the complexity of high dimensional data by feature selection as well as coefficient shrinkage. Fan et al. shows that using an L1-penalty, which he calls ?gross-exposure? constraint on the weights in a portfolio, has significant advantages. In particular it can reduce risk and because the L1 penalty sets coefficients to zero, many fewer assets are needed in the portfolio, and are therefore suitable for large-scale portfolio optimization problems. Fan et al. formulated this constrained portfolio risk minimization problem into a convex optimization problem and solved the problem by an efficient least angle regression (LARS) optimizer. However, the implementation of LARS used an approximation to the true optimization criterion. To address this problem, we propose a customized coordinate descent portfolio optimization procedure (CCDPO). The coordinate wise updating scheme can optimize all coefficients of the allocation vector faster than LARS. The warming-up and re-initialization steps in CCDPO prevent the dominant coefficients from growing to extreme values. CCDPO uses the advantage of coefficients scarcity to reduce the optimization load and achieves fast speed. To study the performance of CCDPO, we implement a factor-based covariance estimator for data simulation, and a data integration website for collecting real-life stock price quotes. The optimization results on the simulated data show that CCDPO significantly reduces the portfolio risk. And the penalty factor controls the diversity between empirical risk and actual risk in a similar fashion to the ?gross-exposure? constraint.