Long-horizon consumption risk and the cross-section of returns: new tests and international evidence

Abstract

This paper investigates whether measuring consumption risk over long horizons can improve the empirical performance of the consumption-based capital asset pricing model (CCAPM) for size and value premia in international stock markets (USA, UK, and Germany). In order to account for commonalities in size and book-to-market sorted portfolios, we also include industry portfolios in our set of test assets. Our results show that, contrary to the findings of Parker and Julliard [2005. Consumption risk and the cross- section of expected returns. Journal of Political Economy 113, no. 1: 185–222], the model falls short of providing an accurate description of the cross-section of returns under our modified empirical approach. At the same time, however, measuring consumption risk over longer horizons typically yields lower risk-aversion estimates. Thus, our results suggest that more plausible parameter estimates – as opposed to lower pricing errors – can be regarded as the main achievement of the long-horizon CCAPM.

Keywords:

• consumption-based asset pricing
• long-run consumption risk
• value puzzle
• international stock markets

Jel Classification :

• G12
• G15

Acknowledgements

The authors are indebted to Martin Bohl, Bernard Dumas, Halit Gonenc, Christian Salm, Stephan Siegel, Tao Wu, two anonymous referees, and audiences at the 43rd meeting of the Euro Working Group on Financial Modelling (London), 15th annual meeting of the German Finance Association (Münster), 6th International Meeting of the French Finance Association (Paris), 11th Symposium on Finance, Banking, and Insurance (Karlsruhe), the Tübingen-Konstanz empirical finance seminar as well as seminar participants at University of Münster, University of Tübingen, and ZEW Mannheim for useful comments and suggestions. We also thank Kenneth French and Stefan Nagel for making portfolio data available on their websites.

Notes

The consumption-based asset pricing model has its roots in the original articles by Rubinstein (1976), Lucas (1978), and Breeden (1979).

Research on the long-run implications of the consumption-based asset pricing framework has constituted a rather prominent field in recent literature (Jagannathan and Wang 2007; Bansal, Dittmar, and Kiku 2007; Hansen, Heaton, and Li 2008; Rangvid 2008). More detailed information on how our paper is related to the extant literature is provided in Section 2.2.

Several authors focus on consumption and investment decisions of stockholders versus nonstockholders. In particular, a recent contribution by Malloy, Moskowitz, and Vissing-Jørgensen (2008) studies the long-run consumption risk of US stockholders. A detailed study using microlevel consumption data for all three countries under consideration is beyond the scope of this paper.

The existence of a persistent component in consumption and dividends is empirically confirmed by Bansal, Kiku, and Yaron (2007).

For a detailed discussion of this issue see Cochrane (2005, Chapter 13) and Yogo (2006, Appendix C).

The computation of the cross-sectional R 2 in the GMM framework follows the extant literature (e.g., Lettau and Ludvigson 2001; Parker and Julliard 2005): , where denotes a cross-sectional variance, is the time series average of the excess return on asset i, and is the fitted mean excess return for asset i implied by the model.

For computational details and the simulations for the model test based on the HJ-distance, the reader is referred to the Appendix in Parker and Julliard (2005).

Additional estimations (not shown) confirm that our main conclusions are largely unaffected if total consumption expenditure is used instead of nondurables and services consumption.

Returns on the 16 portfolios as well as Market, HML and SMB factors can be downloaded from Stefan Nagel's webpage: http://faculty-gsb.stanford.edu/nagel

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/

Notice that the overall sample period, however, is longer due to the LH consumption growth (up to S) aligned to the returns: USA (2004:Q3), UK (2003:Q4), GER (2003:Q4).

CPI data for the USA, the UK, and Germany are available from the BEA, the IMF International Financial Statistics, and the OECD Economic Outlook, respectively.

In order to render our results comparable across countries, we limit the horizon at which long-run consumption risk is measured to 11 quarters.

The overlap of observations of long-run consumption growth induces serial correlation, which must be accounted for when conducting inference in case of the LH-CCAPM. Our estimate of the covariance matrix of GMM estimates is computed by the procedure of Newey and West (1987) with S+1 lags.

This is a common finding in the empirical asset pricing literature: even the best performing models such as the Fama–French three-factor model are often rejected by formal statistical tests [e.g., Lettau and Ludvigson 2001).

An exception is the work of Gao and Huang (2004), who use UK value and size portfolios, whereas other papers such as Hyde and Sherif (2005a, 2005b) for the UK and Lund and Engsted (1996) for Germany estimate consumption-based models separately for each industry sector or market index.

We discuss pricing errors on individual portfolios in more detail below.

This result is remarkable given the poor performance of the standard CAPM documented in the paper by Schrimpf, Schröder, and Stehle (2007), which is based on an evaluation of the model on monthly data.

A major disadvantage of Fama and French's three-factor model is that there is still no full agreement in the literature about what the true risks underlying SMB and HML actually are. See, e.g., Petkova (2006) for a risk-based explanation in an empirical implementation of an ICAPM in the spirit of Merton (1973).

However, models using macroeconomic factors will always be at a disadvantage to models using financial factors (Cochrane 2007, 7) due to a less precise measurement of macroeconomic variables. Moreover, these models allow for a more structural analysis of the economic determinants of risk premia, which typically cannot be delivered by models using merely financial factors.