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The Efficiency of Capitalisation-Weighted Indices

Cap-weighted indices are widely used by institutional investors in general, and pension funds in particular, as benchmarks for investment performance. Proponents of cap-weighted stock market indices often argue that such indices provide efficient risk/return portfolios.

In recent research at EDHEC Risk Institute[1], we reviewed the evidence in the academic literature and concluded that only under very unrealistic assumptions would such indices be efficient investments. In the presence of realistic constraints and frictions, cap-weighted indices cannot, according to the academic literature, be expected to be efficient investments.

Pioneering work in financial theory (Markowitz 1952; Sharpe 1964; Lintner 1965) led to the development of an elegant theory, the capital asset pricing model (CAPM), formulated by Sharpe (1964), which held that the portfolio made up of all existing risky assets, weighted by their market capitalisation, named the market portfolio, offered an efficient risk/return trade-off. In other words, no other combination of risky assets makes it possible to obtain a better return for the same degree of risk, or a lower risk for the same expected return. Any risky portfolio other than the market portfolio will introduce some unsystematic, and hence unrewarded risk, and thus will not be a valuable investment.

According to the tenets of the CAPM, all investors will choose to build their portfolios by dividing their wealth between the market portfolio and a risk-free asset (two-fund separation theorem), with the relative split between the two assets allowing them to adjust the risk of their global portfolios. Index providers relied heavily on this theory to present cap-weighted indices as the best media for indexation management, a technique that, for financial theory, could not be outperformed by any other management technique.

Like many theories, however, the CAPM relies on assumptions that seek to simplify reality and thus that do not resemble real market conditions. In addition, indexation could not use the true market portfolio. Indeed, this portfolio is not observable, since it would have to include traded assets (stocks, bonds, and so on), as well as non-traded assets (human capital) or illiquid assets (real estate). Investment managers use cap-weighted stock market indices as a proxy for the market portfolio.

The objective of our research was thus to answer two questions. Is the market portfolio still efficient if one of the assumptions on which the model relied does not bear out? Can a market index serve as a valid proxy for the market portfolio?

A detailed review of the literature allowed us to conclude that, as soon as one of the CAPM assumptions no longer holds, financial theory does not predict that the market portfolio is efficient. Therefore, it seems important to ask whether the assumptions of the theory are at all realistic.

The theory that has it that the cap-weighted market portfolio will be efficient assumes that investors have identical preferences and that they all have the same investment horizons. It also assumes unlimited borrowing, tradability of all existing assets, and no taxes or transaction costs. From this list, it becomes clear that it is unreasonable to expect that all these assumptions hold. After all, investors are unlikely to have the same preferences and the same investment horizons. In addition, the existence of taxes and transaction costs is quite real. Nor is unlimited borrowing feasible for most investors. Likewise, not all assets are tradable, and investors may invest significant portions of their wealth in non-tradable assets (human capital, for example) or illiquid assets such as real estate. So it is hardly surprising that the model frequently fails in empirical tests, as a detailed review of the empirical literature shows.

The second key point of our research was to establish whether an index could serve as a good proxy for the market portfolio. According to the CAPM, only the market portfolio is efficient. Stock market indices appear to be very poor proxies for the market portfolio. Though the true market portfolio is assumed to contain a vast collection of assets, including unlisted and illiquid assets, stock market indices include only a small fraction of listed assets. Thus, the many empirical studies done to test the CAPM have attempted to come up with reasonable proxies for the market portfolio, including not only many more stocks than indices do, but also bonds, real estate, and non-tradable assets such as human capital.

To conclude, it turns out that stock market indices are far from being the market portfolio. Stock market indices in reality reflect only a fraction of wealth in the economy, ignoring the share of wealth represented by human capital, social security benefits and illiquid assets. Even if it were possible to build and hold the market portfolio that includes all these assets, the market portfolio would be efficient only if a set of highly unrealistic assumptions held. And not even under more realistic assumptions does financial theory necessarily conclude that the market portfolio is efficient. In view of these arguments, it seems that financial theory alone does not justify the current practice of using cap-weighting indices.

References

- Goltz, F., and V. Le Sourd, 2010. Does finance theory make the case for capitalisation-weighted indexing”, EDHEC-Risk Institute Publication, January.

- Lintner J. 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47 (1): 13-37.

- Markowitz, H. M. 1952. Portfolio Selection. Journal of Finance 7: 77-91.

- Sharpe, W. F. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19 (September): 425-42.