Asymptotic Distribution of the Markowitz Portfolio

The asymptotic distribution of the Markowitz portfolio, Σ̂μ̂, is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect, one can estimate the proportion of error in the Markowitz portfolio due to mis-estimation of the covariance matrix. A likelihood ratio test is given which generalizes Dempster’s Covariance Selection test to allow inference on linear combinations of the precision matrix and the Markowitz portfolio. [12] Extensions of the main method to deal with hedged portfolios, conditional heteroskedasticity, and conditional expectation are given.