Here is a graph from the paper.
There are two contrary conclusions we can reach from this. From the paper:
These results reaffirm the importance of portfolio diversification, particularly for those investors who view performance in terms of the mean and variance of portfolio returns...The results here show that underperformance can be anticipated more often than not for active managers with poorly diversified portfolios, even in the absence of costs, fees, or perverse skill.
At the same time, a preference for positive skewness in portfolio returns is not necessarily irrational, and it is known that diversification tends to eliminate skewness from portfolio returns. The results reported here also highlight the fact that poorly diversified portfolios occasionally deliver very large returns. As such, the results can justify a decision to not diversify by those investors who particularly value positive skewness in the distribution of possible investment returns, even in light of the knowledge that the undiversified portfolio will more likely underperform.The lesson for diversification is clear. But, it seems like there is an additional factor here having to do with rebalancing. For the fully diversified investor, rebalancing would be important - even a source of profit. But, for the less diversified investor, the positive skew would favor momentum.
I wonder, for the non-diversified investor if the idea that there is a tradeoff between positive skew and average underperformance is necessarily true. It would depend on the balance between winners and losers. If an investor took a sort of barbell approach, only investing in equities with highly variable potential outcomes, it seems that there could be a large advantage created by that skew for portfolios that maintained positions without rebalancing. It would come down to skill, in the end. Small differences in the ability to pick winners - say, picking 60% winners instead of 40% - would make a huge difference in returns.
This seems like another piece of evidence that the real losers are the sort of reputation-based, semi-active portfolios that basically follow the indexes, with minor adjustments, or a sort of middle-of-the-road safe basket of tactical portfolio adjustments that are fairly conventional. These are the sorts of portfolios over time that tend to have net losses after costs. But, both fully passive and highly selective portfolios can do well. Fully passive is certainly recommended for most investors, but highly selective seems to be a reasonable choice, if the risks are known, with tremendous potential upside, and I suspect the benefits of that kind of portfolio tend to be underappreciated because it gets lumped in with "active" portfolios, which sophisticated observers who appreciate EMH are supposed to understand are a loser's bet.