Is the Market Portfolio Efficient When Investors Are Not Utility Maximisers?
Authors: Véronique Le Sourd
Date: March 2010
The theoretical efficiency of the market portfolio is widely evoked by index providers to justify the setting of cap-weighting indices, as cap-weighting is, according to financial theory, bound to be the optimal investment choice. Indeed, the market portfolio, defined as the optimal risky investment by Sharpe (1964) and Lintner (1965) in the capital asset pricing model (CAPM), is set up as the cap-weighted combination of all available assets, including stocks, bonds, and not easily tradable assets such as human capital or real estate. However, the conclusion of market portfolio efficiency, and consequently of the efficiency of cap-weighted indices, appears to be questionable. The efficiency of the market portfolio, inherent to the CAPM, is obtained provided that strong assumptions hold. These assumptions, which serve to make the real world simpler, are the following. Investors have mean-variance preferences and seek to maximise their utility functions; there are no operational frictions; there are no restrictions on short sales or borrowing; all assets can be traded; and investors have homogeneous beliefs. As long as these assumptions hold, all investors choose the market portfolio as the risky part of their investments, as it is the optimal investment all rational investors seek to hold. This article is the first in a series of five in which we propose to study the impact of the violation of the CAPM assumptions on the model's central tenet, that the market portfolio is mean-variance efficient.
This first article deals with investors’ preferences. The CAPM assumes that investors have mean-variance preferences. In other words, when choosing their portfolios, investors consider only the first two moments of return distribution, that is, the expected return and the variance. The CAPM also assumes that investors seek to maximise expected utility, as defined in Von Neumann and Morgenstern (1944). The theory of maximum expected utility posits that investors always seek to maximise their terminal wealth. It also assumes that investors can compare alternatives, will establish a preference order, and will make consistent choices. The assumption that investors would rather have more than less underpins the choices it is assumed they make. This theory has been criticised by Allais (1953), Ellsberg (1961), Kahneman and Tversky (1979, 1992), and others. These critics point out that it is not always consistent with investors’ psychology and that investors often behave in keeping with what Kahneman and Tversky (1979) call prospect theory. Indeed, investors may not consider terminal wealth; instead, they look at gains and losses throughout the investment period. They also appear to be loss averse, a trait not without consequences for the CAPM theory. These consequences have been studied by Levy and Levy (2004), De Giorgi, Hens, and Levy (2004), and others. De Giorgi, Hens, and Levy (2004) established that the cumulative prospect theory, posited by Kahneman and Tversky (1992), does not allow the existence of financial market equilibrium, and, consequently, of the CAPM. A modification of utility function forms can, of course, make the theory compatible with financial market equilibrium. However, this compatibility is achieved only if asset returns are normally distributed. For Hearings and Kluber (2000), investor loss aversion may mean that the utility function is not concave and that market equilibria do not exist. Although the efficiency of the market portfolio relies on an equilibrium in which all investors use an identical and clearly-defined strategy of expected utility maximisation, a large and growing body of literature that takes into account investor behaviour concludes that equilibrium may not even be defined in the presence of more complex investor preferences. Thus, we see that if the CAPM assumption about investor preferences is violated, financial theory does not ensure that the market portfolio is efficient.
Indeed, it is not reasonable to assume that all investors have same investment preferences. In fact, investors often fail to seek utility maximisation (Barberis and Thaler 2003). This phenomenon has been described by Kahneman and Tversky (1979), who observed that people’s choices do not always tally with those that expected utility theory would suggest. An example of violation of utility maximisation principle is that typically the result of the choice by investors between two lotteries depends on whether their formulation is positive or negative. Individual investors may also seek risk after incurring losses, just as they may shed risk after posting gains (Jahnke 2006): investors will keep a losing position too long, hoping trends will reverse; they will also liquidate winning positions too early to secure their gains. Boyer, Mitton, and Vorkink (2009) argue that investor preferences can be described as a gamble in which investors seek exposure to lottery-like payoffs rather than as mean-variance preferences in which investors seek mean-variance efficiency.
Our review of the literature has shown that if the CAPM assumption of mean-variance investor preferences does not hold, the conclusion that the market portfolio is efficient is no longer valid. Moreover, recent empirical literature clearly makes the case against CAPM-type preferences; the implication is that the CAPM conclusion of an efficient market portfolio cannot be expected to carry through to financial markets.
Allais, M. 1953. Le comportement de l’homme rationnel devant le risque: critique des postulats de l’école américaine. Econometrica 21:503-546.
Barberis, N., and R. Thaler. 2003. A survey of behavioral finance. In Handbook of the economics of finance, ed. G. M. Constantinides, M. Harris and R. Stulz, 1051-120. Amsterdam: Elsevier.
Boyer, B., T. Mitton, and K. Vorkink. 2009. Expected idiosyncratic skewness. Working paper.
De Giorgi, E., T. Hens, and H. Levy. 2004. Existence of CAPM equilibria with prospect theory preference. Zurich NCCR-working paper, 85.
Ellsberg, D. 1961. Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics 75:643-65.
Hearings, J. J., and F. Kluber. 2000. The robustness of CAPM-A computational approach. METEOR working paper, Maastricht University.
Jahnke, D. 2006. Assetpreise – Traditionelle Theorie versus behavioral finance . Saarbrücken: VDM Verlag Müller.
Kahneman, D., and A. Tversky. 1979. Prospect theory: Analysis of decision under risk. Econometrica 47:263-91.
Kahneman, D., and A. Tversky. 1992. Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5:297-323.
Levy, H., and M. Levy. 2004. Prospect theory and mean variance analysis. Review of Financial Studies 17 (4): 1015-41.
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.
Sharpe, W. F. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19 (September): 425-42.
Von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.