It is not possible to refute the existence of skilful investors, as explained in my previous post. So, can we test whether there are investment managers with skill by analysing their investment returns? Investment performance can only be judged on a relative basis. The two candidates to evaluate performance against are either a peer group or a defined benchmark. We consider the merits of both.

An investment track record should only be measured against a peer’s track record if the peer uses the same investment universe and manages her portfolio under the same constraints. The peer should have comparable liquidity requirements and mandate restrictions, such as, for example, the amount of risk allowed.

Even if a fund performs well relative to similar funds, it remains difficult to judge whether this was due to skill or luck simply by comparing their long-run track records. It could be that no manager in the peer group has skill and that the outperforming managers are merely lucky. To distinguish skilful managers from lucky and incompetent managers, persistence studies can, for example, be used, as we will show in future posts.

It is more sensible to compare a fund’s track record against a benchmark that has been specified ex-ante. But, which benchmark is the best for measuring investment skill?  An unbiased benchmark will be most suitable for making any statistical inferences.

The only unbiased benchmark for performance evaluation is the market portfolio which is made up of all listed securities weighted by market capitalisation – the market-cap-weighted index. Every market security is in someone’s portfolio. Therefore the aggregate money-weighted return of all market participants will, over any period, equal the return of the market as a whole.  Relative to the market portfolio, investing is a zero-sum game. On a money-weighted basis, for every outperforming portfolio, one or more portfolios are underperforming.

Furthermore, as explained by Laurence Segal (2003)1,  the market-cap-weighted index has macro-consistency: ”if everyone held a market-cap-weighted index fund and there were no active investors, all stocks would be held with none left over”. It is also the only weighting scheme consistent with a buy-and-hold strategy because no trading is required to deal with price moves. Trading is only required for dividend reinvestments and changes in the number of listed securities due to buybacks or new issues.

We have, though, made the implicit assumption that all the securities are liquid. Also, refer to Segal’s paper1 for additional requirements of an appropriate benchmark.

As the return of any other benchmark would differ from that of the market-cap-weighted index, a typical portfolio’s performance will be biased if measured against such a benchmark. Whether the bias is towards outperforming or underperforming the benchmark depends on the performance of the benchmark constituents during the measurement period.

For example, an equal-weighted stock market benchmark up-weights small-cap stocks and down-weights large-cap stocks. If small-cap stocks underperform large-cap stocks during a period,  more portfolios will outperform the equal-weighted benchmark.  This is because, in aggregate,  portfolios would be underweight small-cap stocks relative to the equal-weighted benchmark.

For this reason, one should take more care when attempting to proof skill or incompetence versus a benchmark that differs from the market-cap-weighted index. The observed out- or underperformance could be an artefact of the benchmark’s construction, rather than the result of skill or incompetence. A methodology for testing skill against such benchmarks are discussed in a following post.

1Siegel, Laurence B. (2003).Benchmarks and Investment Management. Research Foundation of AIMR Publication 2003(1). (Available here.)