An empirical analysis of intertemporal asset pricing models with transaction costs and habit persistence
Introduction
Transaction costs can play an important role in explaining the behavior of the returns of assets. While in most asset pricing models market frictions are assumed to be negligible, there is empirical evidence against this assumption, mainly within a CAPM or APT set-up (see, e.g., Schultz, 1983; Amihud and Mendelson, 1986, Amihud and Mendelson, 1989). Most intertemporal consumption-based asset pricing models without market frictions are empirically rejected (see Hansen and Singleton, 1982; Singleton, 1990Singleton, 1994). In a recent study, Cochrane (1996) obtains an estimate for the relative risk aversion coefficient using a CRRA consumption-based model without transaction costs that is extremely high, a result which reflects the equity premium puzzle. Moreover, the implied pricing errors for ten size-based portfolios are relatively high. Neglecting market frictions can be an explanation for the frequent rejections of the intertemporal models and it may provide an answer to the equity premium puzzle. Because transaction costs will make investors trade less frequently, investors are less able to hedge against consumption uncertainty, such that the presence of such market imperfections increases consumption volatility. The higher the transaction costs, the higher is the standard deviation of consumption growth.
In this paper, we incorporate transaction costs in intertemporal consumption-based asset pricing models. For intertemporal asset pricing models, empirical results incorporating market frictions are scarce. Among these are Fisher (1994), He and Modest (1995), Heaton and Lucas (1996) and Luttmer (1996), where only two of these studies actually estimate a model. The remaining two studies are based on the Hansen and Jagannathan (1991) volatility bounds. While most of the attention has been given to the theoretical impact of transaction costs, Fisher (1994) is one of the few who combines intertemporal asset pricing models with transaction costs in an empirical way. He finds that, using a market portfolio and a risk-free rate, the estimates of the transaction costs parameter are relatively high and significantly different from zero. In this paper we extend the work of Fisher in several directions. First, we use returns on ten size-based portfolios to analyze to what extent transaction costs help explaining the cross-section of expected returns. Second, we use monthly rather than annual data, and third, following Ferson and Constantinides (1991), Cochrane and Hansen (1992), and Heaton (1995) we also consider a time-nonseparable specification of utility. The idea behind this extension is that consumers get used to high levels of consumption and desire high consumption in period t when consumption in period t−1 was high. A positive effect of the consumption level of period t−1 on the marginal utility at time t is called habit persistence. In this paper, we will empirically examine the combined effect of habit persistence and transaction costs using US asset market data. Our main issue is to analyze the question whether ignoring market frictions and/or time-nonseparability of utility can provide an explanation for the frequent rejections of intertemporal asset pricing models and the corresponding equity premium puzzle. A possible explanation for the equity premium puzzle is that investors want to be compensated for relatively high transaction costs on the stock market. Standard asset pricing models do not account for these costs.
The remainder of this paper is organized as follows. Section 2presents the utility maximization problem with transaction costs in the stock market. The resulting asset pricing model is a generalization of the CRRA consumption-based asset pricing model as examined in Hansen and Singleton (1982) and many other articles. The method of estimation is explained in Section 3, while the empirical results using monthly US stock market data for 1959–1993 are presented in Section 4. Section 5extends the model to cover a time-nonseparable utility function with habit persistence. Following Cochrane (1996), the different models are evaluated statistically, in terms of specification tests, and economically, in terms of pricing errors. We conclude in Section 6by summarizing the main results.
Section snippets
The model
In this section we derive an intertemporal equilibrium model for asset prices, incorporating transaction costs in the stock market. This model is similar to the one in Fisher (1994), albeit that the specification discussed here is slightly more general. Our focus is an empirical analysis using monthly data for ten risky portfolios and a riskless asset, where Fisher only uses one aggregate risky asset, so that we can analyze to what extent transactions costs are helpful in explaining the
Estimation and evaluation
This section describes how the parameters of the model with transaction costs can be estimated by a one step and iterated generalized method of moments (GMM) procedure. In Section 3.1, we shall, starting from the two-step estimator of Hansen (1982), explain iterated GMM, which is likely to have better small sample properties. Next, it is argued that in some cases a one-step GMM estimator, where the weighting matrix equals the identity matrix, may be preferred. We also describe how the model can
Data and stylized facts
To estimate the intertemporal asset pricing models we use monthly real returns of ten size-based portfolios and a riskless asset for the period February 1959 to November 1993 (T=418). Data on the ten risky portfolios are supplied by the Center for Research in Security Prices (CRSP) at the University of Chicago, and are obtained by grouping all stocks listed at the New York Stock Exchange (NYSE). For these portfolios, we use return data with and without dividends. The riskless return is
Introducing habit persistence
Using the Hansen–Jagannathan volatility bounds, Gallant et al. (1990), Cochrane and Hansen (1992) and Luttmer (1996) show that habit persistence reduces the required risk aversion coefficient. The higher the degree of habit persistence, the larger the volatility of the stochastic discount factor. In this section, we look at the effects of relaxing the assumption of a time separable utility function by introducing habit persistence.
We use a particular specification of habit persistence, as in
Concluding remarks
In this paper, we developed a consumption-based asset pricing model in the presence of transaction costs in the stock market and habit persistence in consumption and estimated this model using monthly returns on ten size-based portfolios and a riskless return over the period 1959–1993. Our main goal was to analyze to what extent the introduction of transaction costs was able to explain the cross-sectional variation in expected returns. All models were estimated using both iterated and one-step
Acknowledgements
We would like to thank Peter de Goeij, Frans de Roon, Ramdan Dridi, Georges Hübner, Pascal Maenhout, Frans Spinnewyn and an anonymous referee for helpful comments and advice. The authors gratefully acknowledge the support of the Belgian Program “Interuniversity Poles of Attraction”, initiated by the Prime Minister's Office, Science Policy Programming.
References (24)
- et al.
Asset pricing and the bid–ask spread
Journal of Financial Economics
(1986) The relation between return and market value of common stocks
Journal of Financial Economics
(1981)- et al.
Habit persistence and durability in aggregate consumption
Journal of Financial Economics
(1991) - et al.
Finite sample properties of the generalized method of moments in tests of conditional asset pricing models: Empirical tests
Journal of Financial Economics
(1994) - et al.
Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution
Journal of Econometrics
(1990) On tests of representative consumer asset pricing models
Journal of Monetary Economy
(1990)- et al.
The equity premium: A puzzle
Journal of Monetary Economy
(1985) - et al.
The effects of beta, bid–ask spread, residual risk, and size on stock returns
Journal of Finance
(1989) - Clark, A.E., 1996. Are wages habit-forming? Evidence from Micro Data, DEELSA, OESO,...
A cross-sectional test of an investment-based asset pricing model
Journal of Political Economy
(1996)