Before revision:  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 .
After revision:  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 .