Can the seasonal pattern of consumption growth reproduce habits in the cross-section of stock returns? Evidence from the European equity market

Abstract

This paper examines the prevalence for Europe of some well-documented seasonal patterns in consumption data, which allow classic consumption-based asset pricing models to omit an explicit habit specification. We use the Campbell-Cochrane habit model as a reference, proxying habit persistence by the serial correlation of consumer sentiment. Our results show that consumption data for the third and fourth quarters allow the classic power utility function to perform very similarly to the Campbell-Cochrane model, while the serial correlation of consumer sentiment helps improve the explanatory power of habits.

KEYWORDS:

• European equity market
• habits
• power utility function
• CCAPM
• consumption dynamics
• consumer confidence index

JEL classifications:

• E32
• E44
• G12
• G15

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

Notes: We use Kenneth French return data for Europe, for the period from January 1990 to December 2018, to estimate the annual returns of 25 portfolios sorted by size and book-to-market equity (size-BE/ME portfolios) and 25 portfolios sorted by size and the past one-year return (size-momentum portfolios). Portfolios comprise all stocks listed in the following countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom. In order to determine excess returns, when appropriate we use the interest rate of the Treasury Bill for the region under consideration, as provided by Kenneth French. Panel A shows the summary statistics for size-BE/ME portfolios, while Panel B does the same for size-momentum portfolios. Additionally, we compile return data for Fama-French factors from Kenneth French’s website, namely, the value-weighted market return minus the risk-free rate (RMRF), the excess return of the portfolio that comprises the small minus big market value firms (SMB), the excess return of the portfolio that comprises the high minus low book-to-market equity firms (HML), the excess return of the most profitable stocks minus the least profitable (RMW), and the excess return of firms that invest conservatively minus aggressively (CMA). We compile quarterly chained volume estimates for consumption in nondurables and services, non-seasonally adjusted, in national currency, for the 16 countries under consideration, as provided by the OECD. We estimate the average consumption growth for the economies under consideration weighting by population. Q1-Q1 consumption growth shows annual consumption growth, determined using exclusively consumption data for the first quarter, and similarly for the other quarters. Panel C shows the summary statistics for Fama-French factors and consumption growth. All results are annual percentages.

Notes: We use Kenneth French return data for Europe, for the period from January 1990 to December 2018, to estimate the annual returns of 25 portfolios sorted by size and book-to-market equity (size-BE/ME portfolios) and 25 portfolios sorted by size and the past one-year return (size-momentum portfolios). Additionally, we compile return data for Fama-French factors from Kenneth French’s website, namely, the value-weighted market return minus the risk-free rate (RMRF), the excess return of the portfolio that comprises the small minus big market value firms (SMB), the excess return of the portfolio that comprises the high minus low book-to-market equity firms (HML), the excess return of the most profitable stocks minus the least profitable (RMW), and the excess return of firms that invest conservatively minus aggressively (CMA). We compile quarterly chained volume estimates for consumption in nondurables and services, non-seasonally adjusted, in national currency, for the countries under consideration, as provided by the OECD. We estimate the average consumption growth for the economies under consideration weighting by population. Q1-Q1 consumption growth shows annual consumption growth, determined using exclusively consumption data for the first quarter, and similarly for the other quarters. The table shows the correlations of consumption growth with the excess returns of the portfolios and factors under consideration.

Notes: We compile monthly series for the consumer confidence index (CCI), as provided by the OECD, for the period from January 1990 to December 2018, for the European countries under consideration. We estimate the average CCI weighting by population. We compile return data from Kenneth French’s website. Panel A shows the regression results for the AR(1) process of the CCI using lags of 3, 12 and 24 months. First and second rows show the coefficient estimates and the standard errors, respectively. Third row shows $t$-statistics, while the fourth row shows the $R^2$ statistics for the time-series regressions. Panel B shows the results of the forecasting regressions for the excess return of the value-weighted market portfolio (RMRF), using the CCI as the predictor at lags of 3, 12 and 24 months. First and second rows show the coefficient estimates and the standard errors, respectively. We correct standard errors for the autocorrelation that results from overlapping returns, following the Hansen and Hodrick (1980) methodology. Third row shows $t$-statistics, while the fourth row shows the $R^2$ statistics for the time-series regressions.

Notes: We use Kenneth French return data for Europe, for the period from January 1990 to December 2018, to estimate the annual returns of 25 portfolios sorted by size and book-to-market equity (size-BE/ME portfolios) and 25 portfolios sorted by size and the past one-year return (size-momentum portfolios). We use these portfolios to study the performance of different asset pricing models, namely, the Campbell-Cochrane habit model (Panel A), the power utility model (Panel B), the linear consumption-capital asset pricing model (CCAPM, Panel C), and the Fama-French three- and five-factor models (Panel D). Models 1–3 comprise the results of the Campbell-Cochrane model, with models 1 and 2 determining the serial correlation of the surplus consumption ratio using that of the consumer sentiment index (CCI), and model 3 using the serial correlation of the log price/dividend ratio, as in Campbell and Cochrane (1999). Models 1 and 3 assume that the first value of the log surplus ratio $s_0$ matches the log steady state $\overline{s}$, while model 2 sets $s_0$ to −1.4 in order to maximize the $R^2$ statistic. Models 4–8 comprise the results provided by the power utility model, using different aggregation procedures to determine consumption growth. Specifically, model 4 uses annual consumption growth, determined using exclusively consumption data for the first quarter. Similarly, models 5–7 do the same, using second, third and fourth quarter consumption data, respectively. Model 8 use annual consumption data to determine consumption growth. Models 9–13 comprise the results of the linear CCAPM, using the same aggregation procedures for consumption data as those described for models 4–8. Models 14 and 15 show the results of the Fama-French three- and five-factor models, respectively. We use GMM to estimate all models. We use a spectral density matrix with zero leads and lags both to determine standard errors and for the $J$-test for overidentifying restrictions. The table displays two rows for each model, where the first row shows the coefficient estimates and the second row the standard errors. Gamma estimates ($\gamma$) represent the relative risk aversion coefficients that result from the Campbell-Cochrane habit model and the power utility model, while lambda estimates ($\lambda$) represent the prices of risk of linear asset-pricing models, determined as the slope coefficients of the cross-sectional regression of expected returns on betas. Additionally, the $R^2$ statistic of Campbell and Vuolteenaho (2004), the mean absolute pricing error (MAE) and the standard deviation of absolute pricing errors (SDAE) are provided.

1 This literature is too large to summarize here. Cochrane (2008) provides a complete review of the mechanics of macroeconomic asset pricing models.

2 All data is publicly available at Rojo-Suárez, Alonso-Conde, and Ferrero-Pozo (2020).

Additional information

Funding

This work was supported by the European Social Fund and the Education and Research Service of the Madrid regional government through grants PEJ16/SOC/AI-1627 PEJD-2018-PRE/SOC-8898.