  We apply the procedure of Lee et al. to the problem of performing inference
on the signal-noise ratio of the asset which displays maximum sample Sharpe
ratio over a set of possibly correlated assets. We find a multivariate analogue
of the commonly used approximate standard error of the Sharpe ratio to use in
this conditional estimation procedure. We also consider several alternative
procedures, including the simple Bonferroni correction for multiple hypothesis
testing, which we fix for the case of positive common correlation among assets,
the chi-bar square test against one-sided alternatives, Follman's test, and
Hansen's asymptotic adjustments.
  Testing indicates the conditional inference procedure achieves nominal type I
rate, and does not appear to suffer from non-normality of returns. The
conditional estimation test has low power under the alternative where there is
little spread in the signal-noise ratios of the assets, and high power under
the alternative where a single asset has high signal-noise ratio. Unlike the
alternative procedures, it appears to enjoy rejection probabilities montonic in
the signal-noise ratio of the selected asset.
