  In the knowledge that the ex-post performance of Markowitz efficient
portfolios is inferior to that implied ex-ante, we make two contributions to
the portfolio selection literature. Firstly, we propose a methodology to
identify the region of risk-expected return space where ex-post performance
matches ex-ante estimates. Secondly, we extend ex-post efficient set
mathematics to overcome the biases in the estimation of the ex-ante efficient
frontier. A density forecasting approach is used to measure the accuracy of
ex-ante estimates using the Berkowitz statistic, we develop this statistic to
increase its sensitivity to changes in the data generating process. The area of
risk-expected return space where the density forecasts are accurate, where
ex-post performance matches ex-ante estimates, is termed the consistency
region. Under the 'laboratory' conditions of a simulated multivariate normal
data set, we compute the consistency region and the estimated ex-post frontier.
Over different sample sizes used for estimation, the behaviour of the
consistency region is shown to be both intuitively reasonable and to enclose
the estimated ex-post frontier. Using actual data from the constituents of the
US Dow Jones 30 index, we show that the size of the consistency region is time
dependent and, in volatile conditions, may disappear. Using our development of
the Berkowitz statistic, we demonstrate the superior performance of an
investment strategy based on consistent rather than efficient portfolios.
