Empirical Gram Matrix Estimation Using High-Frequency Data for Portfolio Optimization and Gross Exposure: Evidence from Emerging Stock Markets

The contribution of this paper is to examine and develop a new methodology in terms of precision matrix estimation and its validity on Markowitz portfolio framework. We consider nodewise regression with lasso penalty to cope with the singularity problem of the high-dimensional sample covariance matrix estimation on the portfolio optimization framework in emerging stock markets. We estimate the portfolio variance and the gross exposure of the constructed portfolios through simulation studies and empirical applications. For main purpose we use penalized estimators and Lasso penalty. For the comparisons, we apply POET, factor modelling and shrinkage estimators. We expect to show that increasing number of assets in a portfolio decreases estimation error for the portfolio variance. Under sparsity conditions, many off- diagonal elements of the approximate inverse matrix truncate to zero that also enables to improve the constructed optimal portfolio performance in terms of estimated risk.