ABSTRACT
Chapter 6 considers portfolio inference for the case where returns are independent (in time) and identically multivariate normally distributed. Connections are drawn between the (squared) Sharpe of the sample Markowitz portfolio and Hotelling's T2 statistic. Further parallels are drawn between the expected Sharpe under the conditional expecation model and the Hotelling-Lawley statistic. The latter is one of four statistics used in testing the Multivariate General Linear Hypothesis, which is discussed, along with approximate distributions of the various statistics for testing the same. The distribution and moments of the squared Sharpe of the Markowitz portfolio are given, along with less biased estimators. Frequentist inference is introduced, on both the optimal Sharpe as well as the weights of elements of the Markowitz portfolio. These tests are given for unhedged and hedged portfolio problems, as well as the conditional expectation model. Inference via the Likelihood and Bayesian paradigms are also considered.
