On Mean Variance Portfolio Optimization: Improving Performance Through Better Use of Hedging Relations

In portfolio optimization, the inverse covariance matrix prescribes the hedge trades where a portfolio of stocks hedges each one with all the other stocks to minimize portfolio risk. In practice with finite samples, however, multicollinearity makes the hedge trades too unstable to be reliable. By reducing the number of stocks in each hedge trade to curb estimation errors, we motivate a “sparse” estimator of the inverse covariance matrix with multiple zero off-diagonal elements. Comparing favorably with those under no-short-sale constraints and using shrunk covariance matrix, a portfolio formed on this estimator achieves significant risk reduction out-of-sample. By improving hedge trades, the portfolio delivers higher certainty equivalent returns after transaction costs in a range of situations. Mean variance portfolio optimization relies on covariances to transform expected returns into optimal portfolio weights. Consider a portfolio of N stocks. A portfolio manager uses an asset pricing model to predict a vector of expected returns, denoted by μ, and employs a risk model to predict the covariance matrix, denoted by Σ. Then, it is well known that her optimal portfolio weights are summarized by