The following is in response to Jason Hsu and Vitali Kalesnik’s commentary, Measuring the "Skill" of Index Portfolios, which was published on February 28:
To the Editor:
Jason Hsu and Vitali Kalesnik’s commentary is one of a series of papers over a period of years, often by the same authors, that have argued for an impossible – indeed absurd – conclusion. Their aim appears to be to discredit a capitalization-weighted index by claiming that practically any strategy – even one chosen at random – will beat it. They have, unfortunately, gained traction in the media with their efforts.
The paper's argument is that those who invest using traditional indexing – that is, cap-weighted indexing – "systematically deliver returns that are inferior to the expected returns of uninformed investors." This amounts to saying that the average investor outperforms the average. This is possible only if the word "average" is used with two different meanings in the same sentence.
That is in fact the case. What Hsu and Kalesnik refer to as "the expected returns of uninformed investors" is in fact the return on an equal-weighted index. The Hsu-Kalesnik article conflates two averages. One is the weighted average return on all stocks, which is the average return on the total market. The other is the unweighted average return, which is the return on an equal-weighted index. Relative to the total market, it weights smaller-cap, lower-price stocks more heavily. These stocks outperformed large stocks over the time period that Hsu and Kalesnik used for their measurements, on a risk-unadjusted basis. Through clever wording the Hsu-Kalesnik piece not only evades risk-adjustment, but tries to imply a mathematically-proven general fact from a historical period of observation. All of the arguments the piece uses are, however, no more than a result of this conflation of the average return of an equal-weighted index with the average return on the market as a whole.
Michael Edesess
