ABSTRACT
Chapter 7 considers portfolio inference for the case where returns are not i.i.d. normally distributed. The second moment matrix, which collects the first two moments into one matrix, is introduced. The asymptotic distribution of the sample analogue is given. From this the distribution of the Sharpe of the Markowitz portfolio is considered for elliptical returns, for heteroskedastic normal returns, and for autocorrelated returns. It is found that the heteroskedasticity has little effect on the sample statistic, but autocorrelation introduces both bias and increased standard error. The distribution of the second moment matrix for subspace and hedging constraints is given, as well as for the conditional expectation model. Frequentist inference is considered for the case of general returns, both for the Sharpe of the Markowitz portfolio and for elements of the Markowitz portfolio. A trick using the Cholesky factorization of the inverse second moment is used. Inference via likelihood and Bayesian inference are considered.
