2013/12/02 by Steven E. Pav, Pav, Steven E. · 1 citation
Economics, Econometrics and Finance · #91G10 #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #G.3 #Portfolio Management (q-fin.PM) #Statistical Finance (q-fin.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1312.0557
openalex publication_date 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.