[lutusp]

> This is a common misunderstanding, but actually 50% will do better than the median not the average.

If the market were skewed to the degree that a symmetrical normal distribution wasn't a realistic model, then (assuming a particular skew) beating the median would be child's play, but it also wouldn't produce returns different than the average portfolio -- that average portfolio that sits at or near the mean, not the median.

Another way to say this is that, if a skewed distribution peaked at some mean value M (the value on the curve that has a zero first derivative), and if there was a pathological, nonsymmetrical tail at the right or left that shifted the median value, the majority of portfolios would remain at the mean value in spite of the asymmetry.