Can consumption-based asset pricing models explain the cross-section of investment funds returns?

Abstract

Using the parametric Generalized Method of Moments (GMM) methodology of Hansen (1982) and the nonparametric approach of Hansen and Jagannathan (1991), this note investigates the ability of Consumption-based Asset Pricing Models (CCAPMs) to explain the cross-section of investment funds returns in the German market. The parametric analysis shows that both the classic power utility model of Hansen and Singleton (1982) and the habit formation extension of Campbell and Cochrane (1999) are not rejected, but require high risk-aversion to be consistent with the data. Furthermore, only the power utility model suffers from a risk-free rate puzzle. The nonparametric results are not accompanied by a risk-free rate puzzle for both models but the models still show high risk aversion. So using adequate test assets and evaluation methods, this note fully supports Cochrane (2006) saying that work explaining asset returns with consumption-based models should be dying out since there are preferences that can coherently describe the data with high risk-aversion.

Keywords:

• CCAPM
• habit formation
• stochastic discount factor
• GMM
• volatility bounds
• investment funds returns

JEL Classification:

• E21
• G12

Acknowledgements

I thank Frank Schuhmacher for helpful comments and the BVI for supplying the investment funds database for the analysis.

Notes

¹ Cochrane (2005) devotes his excellent textbook ‘Asset Pricing’ entirely to this fact.

² There are of course studies that explain investment funds performance within the stochastic discount factor framework (e.g. Fletcher and Ntozi-Obwahle, 2008, 2009; Bessler et al., 2009). However, their stochastic discount factors are linear or nonlinear functions of asset or portfolio returns and therefore do not reflect classic consumption-based models.

³ Note that shocks to consumption growth are modelled to have a direct impact on the surplus consumption ratio, and for φ close to one, habit responds slowly to these shocks.

⁴ Thus, the model solves the equity premium puzzle by high risk aversion, but without facing a risk-free rate puzzle.

⁵ See Campbell and Cochrane (1999) or Campbell (2003) for details.

⁶ Note that this does not mean that the moments are weighted equally (a mistake stated in many recent papers). Furthermore, identity weighting does not ignore the correlation structure of the model errors (Cochrane, 2005, Chap. 11).

⁷ Following Møller (2009), the returns are not scaled with instruments so that only the unconditional implications of the model are analyzed. This has the advantages of keeping the number of moment conditions manageable and of avoiding the problem of weak identification.

⁸ So in contrast to Engsted and Møller (2010), the parameters g, and φ are estimated outside the GMM system because this gives unbiased estimates.

⁹ The BVI offers more than seven groups. The other groups, however, do not contain funds with a sufficient data history, so they cannot be used here.

¹⁰ These results are consistent with the findings of Engsted et al. (2010) for equity, bond and money market returns that are obtained using the iterative procedure of Engsted and Møller (2010).

¹¹ Following Hyde et al. (2005), for both models δ is set to 0.97. The parameters g, and φ for the habit formation model are estimated as in the GMM estimation. The starting value of s_t is again set to .

¹² Detailed test results are available from the author.

¹³ This is a typical result when using this test as an additional diagnostic tool (e.g. Engsted, 1998; Hyde et al., 2005).

¹⁴ Another possibility is to use the distance measure of Hansen and Jagannathan (1997) because this measure can be given an intuitively appealing pricing error interpretation in the sense that it measures the maximum pricing error per unit norm induced by the stochastic discount factor.