Decomposition of durable consumption and equity returns

ABSTRACT

In this paper, we investigate the risks of cash flow news and discount rate news exposed to durable consumption. When utility is nonseparable in nondurable and durable consumption, the optimal portfolio allocation implies a linear factor model in nondurable and durable consumption growth. Using 30 portfolios sorted by book-to-market, momentum and size, we find that the differences in these betas account for more than 70% of the cross-sectional variation in the risk premia.

KEYWORDS:

• Durable consumption
• cross-sectional returns
• beta decomposition
• consumption beta

JEL CLASSIFICATION:

• G12
• C21

Disclosure Statement

No potential conflict of interest was reported by the authors.

Notes

¹ The household stock of durable goods $D_t$ is related to its expenditure by $D_t=(1-\delta )D_{t-1}+E_t$, where $\delta \in (0,1)$ is the depreciation rate and $E_t$ is the expenditure of durable goods; Since the value of $M_t$ is close to 1, $M_t\approx 1+m_t=1+\kappa log\beta -b_1\mathrm{\Delta }{c}_t-b_2\mathrm{\Delta }{d}_t-b_{3}r{w}_t$. Taking the log of both sides and approximating around $\rho =1$, $-m_t\approx -\kappa log\beta +b_1\mathrm{\Delta }{c}_t+b_2\mathrm{\Delta }{d}_t+b_3{r}_{wt}$, where $r_w$ is the log of $R_w$ and $b_1$, $b_2$, and $b_3$ are constant coefficients.

² We also find that our explanatory variables are not soaked up by the Fama-French three or five factors empirically. The detailed results are available upon request.:

³ The linearization parameters $k_{i,0}$ and $k_{i,1}$ are defined as $k_{i,1}\equiv \frac{exp(\overline{p{d}_i})}{1+exp(\overline{p{d}_i})}$ and $k_{i,0}\equiv -log(k_{i,1})-(1-k_{i,1})log(1/k_{i,1}-1)$, respectively, and $\overline{p{d}_i}$ is the time-series average of $p{d}_{i,t}$.

⁴ If we set ${\beta }_d=0$ and ${\beta }_w=0$, our analysis reduces to the model in Bansal, Dittmar, and Lundblad (2005).

⁵ Due to space limitations, we do not report the results for the decomposition of characteristic-sorted portfolios here.

⁶ We also run the out-of-sample regression for each portfolio, and find that our model can obtain a satisfactory $R_{os}^2$, defined in Campbell and Thompson (2008). Due to space limit, we do not report them in details.

Additional information

Funding

Ren's research is supported by the National Natural Science Foundation of China (71771192, 71631004, 71301135). Wang's research is supported by Ministry of Education in China (MOE) Project of Humanities and Social Sciences (18YJC790166), the Fujian Provincial Key Laboratory of Statistics (Xiamen University) and the Fundamental Research Funds for the Central Universities (Zhongnan University of Economics and Law(2722020JCG026)).