Q: Why do we still use cap-weighted indices at all?
A: Because that’s the way we measure performance.

As old as the now-redundant argument as to whether passive investments are better than active over time is the argument as to whether capitalization-weighted indices, which remain the norm, represent the best yardstick for the average pension fund’s investment portfolio.

It is puzzling that report after report from eminent researchers have for years suggested different benchmarks, including bespoke ones, for institutional investors but there seems to be very little action.

In fact, with the onset of the financial crisis from 2008, there has likely been an aggregate swing away from benchmark-unaware portfolios. There also appears to have been only minor take-up of the value-oriented “real” or “fundamental” indices, “volatility” indices or other benchmarks, which have been shown to outperform the traditional cap-weighted ones over long periods.

Of course the work of Vanguard, in particular, and especially that of its still-active founder, Jack Bogle, is persuasive. Cap-weighted indices ARE the market; they are nothing more than an accurate representation of the performance and size of the total investable market. Why shouldn’t that be the main measurement yardstick?

Well, that is true, but cap-weighted indices are inefficient. And, if they are mirrored in an investment portfolio, as through an index fund, they have a major flaw: they can trap the investor in a bubble.

Lionel Martellini, the scientific director of the hedge fund research group EDHEC-Risk, produced an interesting paper recently which analysed “efficiency” with respect to benchmarks. He says the weight of evidence is that cap-weighted indices are inefficient, regardless of whether the markets themselves are efficient or inefficient.

The words “efficient” and “inefficient” have different meanings when used to describe a whole market or a specific portfolio, he says. When used describe a market it suggests that, at any given time, prices in the market fully reflect all available information about the stocks in the market. If that is 100 per cent true, then stock selection is pretty much a waste of time.

“While past research has unveiled empirical evidence suggesting that the efficient market hypothesis, at least in its purest versions, does not hold perfectly in the real world, there is a consensus regarding the fact that markets can still be regarded as somewhat efficient as a first-order approximation,” Martellini says.

But the word “efficient” for a portfolio refers to whether or not performance can be improved through diversification, say, without any increase in risk.

“While empirical evidence suggests that markets are approximately efficient and the average manager does not outperform the market, it turns out that empirical evidence also suggests that the average investor holds a severely inefficient portfolio…

“Intuitively, the fact that cap-weighted indices are inefficient and ill-diversified is perhaps not surprising as they are heavily concentrated in the largest market-cap stocks as a result of their one-dimensional construction mechanism, which only takes into account a stock’s market cap and thus does not allow for any mechanism that can enforce proper diversification.”

Martellini says that most of the new approaches looking to improve on cap-weighted indices do not rely on a particular assumption regarding whether or not the whole market is efficient, which is still open for at least some debate, but instead are based on “the more robust finding that cap-weighted indices are not in general adequately diversified portfolios”.