  The asymptotic distribution of the Markowitz portfolio 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. Extensions of the main method to deal with hedged portfolios,
conditional heteroskedasticity, conditional expectation, and constrained
estimation are given. It is shown that the Hotelling-Lawley statistic
generalizes the (squared) Sharpe ratio under the conditional expectation model.
Asymptotic distributions of all four of the common `MGLH' statistics are found,
assuming random covariates. Examples are given demonstrating the possible uses
of these results.
