Index Semantics

June 16, 2011

The debate over index weighting methodologies rumbles on. Who’s right?



[This article previously appeared on our sister site,]

Vanguard’s investment boss, Gus Sauter, told the audience at an event held by the firm in London last week that capitalisation-weighted indices represent “the market portfolio”.

William Sharpe’s 1964 Capital Asset Pricing Model (CAPM) provides the basis for Sauter’s assertion. Under CAPM, which you’ll be taught in any business school, a portfolio in which each stock is held in the same proportions as it is in the wider market should be considered optimal.

It’s no coincidence that index funds—which are the foundation of Vanguard’s US$1.8 trillion asset management business—started to become popular at around the same time as CAPM established itself as the leading financial theory.

And capitalisation-weighting still provides the basis for the portfolio holdings of the vast majority of passive funds, as measured by the assets allocated to them. Beyond the index and exchange-traded fund market, cap-weighted indices are also used as benchmarks by most active funds.

In the last ten years, however, CAPM has come under sustained attack. Some (less serious) criticisms relate to the model’s unrealistic assumptions: that trading is frictionless, that short-selling is possible at no cost, and that you can borrow without limit, for example.

But other, weightier assaults on CAPM dismiss its central tenets as essentially worthless.

James Montier (then strategist at Société Générale, now asset allocator at fund manager GMO) argued in early 2007 that CAPM’s categorisation of stocks into low and high beta (stocks with lower and higher sensitivity to moves in the overall market, in other words) doesn’t work. Over time, shows Montier, low-beta stocks actually outperformed high-beta stocks in a rising market; the opposite of what you should expect.

And—anticipating a criticism often levelled at proponents of alternative weighting methodologies by defenders of CAPM—it’s not just a question of a “value tilt” causing the unexplained performance divergence. In fact, says Montier, even within the growth category of the market (with “growth” stocks defined as those with a low book value/price ratio) you find that low beta stocks have historically outperformed those with high beta.

An attack from a different angle is offered by those who focus on CAPM’s (and finance theory’s) inaccurate measure of risk. CAPM is based on a mean-variance framework, which defines the distribution of stock returns over time as a bell curve, implying that risk (measured as standard deviation from the mean) can be measured precisely and predictably.

Nothing could be further from the truth, argued Benoît Mandelbrot in a 2005 book with a tongue-in-cheek title, “The Misbehaviour of Markets”. Those damn markets (those messy human beings acting in aggregate, in other words) keep refusing to fit into our nice mathematical models, says Mandelbrot, going on to show conclusively that the actual behaviour of stocks is far wilder than classical finance theory presupposes.

At our recent Inside ETFs Europe conference in Amsterdam you could hear this debate being re-enacted in person. Indexing should be based on the (CAPM-inspired) market portfolio, said Paul Kaplan, chief investment officer at Morningstar. Any other methodologies represent an active bet against the market and should be recognised as such, Kaplan went on. Not so, said Denis Panel, CIO of BNP Paribas Investment Partners; cap-weighted indices are only efficient under a CAPM framework, whereas in reality this model doesn’t work. Alternative approaches to risk-based indexation are the future for the passive funds business, said Panel.

It’s worth remembering that there are also business reasons for the differences in index approach. By virtue of its sheer size, you’d expect Vanguard to stick to cap-weighting, since any other strategy would cause the firm immediate liquidity and capacity problems when managing portfolios. By contrast, smaller market participants have every incentive to try innovative index methods to gain market share.

But who’s right? In my opinion, treating any index methodology as a neutral starting point is a value judgement that risks being misleading. Just as you wouldn’t suggest that any stock portfolio was intrinsically “right”—you’d expect to judge it later on its performance, risk, and relative to competitors—neither should you do so when it comes to an index.

Perhaps we’re all just indulging in “index semantics”, in the words of Rob Arnott. But for some reason we don’t seem to tire of hearing the arguments pro and con, however often they are replayed.

We may still be short of a full comparative study of index methodologies, involving not only obvious things like security selection and concentration, risk and return, but also less widely followed metrics like index premia, tax efficiency and rebalancing costs. One thing’s for sure, though—the index debate is leading to an increasing variety of choice. And that must be a good thing for investors.



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