Sorting vs. Optimizing: Holding the Largest N Names Is Less Efficient than Minimizing Tracking Error Using Only N Names

The author documents the superior risk-adjusted performance (IR) of a hedged portfolio constructed by minimizing tracking error to a parent benchmark while holding at most N names (the Optimal N portfolio) over a portfolio that cap-weights the largest N names in a parent benchmark (the Top N portfolio). Both portfolios have large size (market-cap) biases, so the absolute performance is consistent with the historical performance of the size factor: poor performance prior to 2015, excellent performance since 2015. Nevertheless, across different N (50, 100, 200), universes (large/mid cap, small cap; developed, emerging), and time periods (both when size is and is not working), the IRs for the Optimal N portfolio generally are better than those of the Top N portfolio. He shows that the outperformance is not driven by other well-known, nonsize factors such as value, quality, industries, or countries, as those active exposures are small. He shows that the outperformance can be attributed to a Selection Effect for the non-Top N names using performance attribution. He suggests that the outperformance may be driven by market participants preferring the non-Top N names when they hedge their own portfolios, but he has no direct evidence to support this. The superiority of the Optimal N approach over the Top N approach is a useful insight that can be taken advantage of by portfolio managers.