A study has come out of Cass Business School that investigates a number of ways of building equity indices. Andrew Clare, Nicholas Motson and Stephen Thomas, of course, include market capitalization weighting. A number of schemes that fall under the name of “smart beta” are also included.
They compare the indices not only among themselves but to a cohort of random portfolios. When I say “random portfolio”, I mean that there are constraints to be obeyed. But the only constraints that the random portfolios in the paper obey is that the weights are non-negative and sum to 100%.
My favorite part is Figure 7 of Part 1 that shows the proportion of random portfolios — monkeys, as they say — that outperform the cap-weighted index over three-year rolling windows.
This puts the cart and the horse in the proper order, I think. It is presenting cap-weighting as just another strategy (which does have some interesting properties) rather than as the market. Interestingly it is almost always completely outperforming the random portfolios or completely outperformed by them (but see below). There is much more of the latter than the former.
You might hypothesize that flows into and out of index funds would have a big impact on the performance of cap-weighting. If it does, I don’t think it is evident from the picture. Cap weighting did well in the early 70’s and then poorly for a decade.
I’m concerned that ignoring constraints isn’t the best thing to do. (I would say that, wouldn’t I?) Fair enough that cap-weighting is compared to portfolios with no specific constraints.
But some of the other strategies — while not created with constraints — rather imply constraints. For example, minimum variance sort of implies that wildly high volatilities wouldn’t be desireable. Likewise, maximum dispersion would imply that large concentrations wouldn’t be tolerated well.
Another concern with the lack of constraints is that what “random portfolio” means when there are minimal constraints becomes quite philosophical. For instance, the way that the “monkeys” were generated is to have a little noise around equal weighting.
Adding practical constraints makes the problem much harder computationally, but easier conceptually.