Evaluating the Performance of Factor Pricing Models for Different Stock Market Trends: Evidence from China

ABSTRACT

This paper examines the performance of three famous factor pricing models in markets of bull, bear, and consolidation in China. Empirical results show that these models explain the time-series variations in portfolio returns in bearish market reasonably well, but fail to explain the cross-sectional variations. Another two findings are revealed by instability tests. First, the three models are more unstable in trending (i.e., bearish and bullish) markets under time-series regression due to the higher stock price synchronicity. Second, greater instability causes the unitary parameter estimates less reliable and brings about difficulties in explaining the cross-sectional portfolio returns in trending markets.

KEYWORDS:

• Asset pricing
• factor models
• market trends
• chinese stock market

JEL:

• C52
• C58
• G11
• G12

Notes

1. Hou, Xue, and Zhang (2015) also present an empirical justification for excluding Carhart’s momentum factor from their model.

2. See http://db.resset.com.

3. See http://cn.gtadata.com/Home.

4. Although examining the factor models based on monthly returns is more conventional, using daily returns is also very common nowadays. Faff (2004) and Kozak, Nagel, and Santosh (2018) are the examples among others where the daily returns are employed for the tests on asset pricing models similar to ours. Moreover, Kenneth R. French has already provided daily, weekly, and monthly data for factors and portfolio returns on his website.

5. Fama and French (2015, 2016) and Hou, Xue, and Zhang (2015) suggest that the two new profitability and investment factors could challenge the role of the value factor, but the evidence in the current literature is not strong enough to exclude the value factor from the models. Studies examining the FF5 model are just in their infancy, and the evidence is still relatively limited compared to that for the FF3 model.

6. The term regular stocks here is the opposite of the term ST stocks in the Chinese stock market. The latter refer to the stocks of companies under special treatment (ST), where the company has reported repeated losses and is therefore deemed to be at risk. In such cases the letters ST are added by the stock exchanges in front of the company abbreviation. As well as potentially being delisted, such stocks are subject to a tighter daily price variation restriction (±5%) than the 10% for regular shares.

7. The rule for choosing the lag parameter q is that q = 0.75 ×$\sqrt[3]{\mathrm{T}}$, rounded to an integer, where T is the number of observations used in the regression (Stock and Watson 2007, 607).

8. In the recent studies, Wang et al. (2020) and Kong, Shi, and Zhang (2021) provide some microeconomic explanations for the causes of stock crashes in China.

9. These results are not explicitly reported in this paper for brevity.

10. To estimate the cross-sectional dispersion in average returns missed by a model, Fama and French (2015) define $R_i$ as the time-series average excess return on portfolio i, $\bar{R}$ as the cross-sectional average of ${\bar{R}}_i$, and ${\bar{r}}_i$ as portfolio i’s deviation from the cross-sectional average, ${\bar{r}}_i={\bar{R}}_i-\bar{R}$.

11. The inconsistent ranking of the factor models based on the metrics focusing on the intercepts is also reported by Fama and French (2018).

12. Fama and French (1988) claim that stocks have weak time-series autocorrelation in daily and weekly holding periods, but that autocorrelation is stronger over long horizons.

13. The typically reported standard errors and t-statistics will, of course, not be the same, because in Equation (7)(7) $E_T(R_i-R_f)={\gamma }_0+{\gamma }_M{\hat{\beta }}_{iM}+{\gamma }_S{\hat{\beta }}_{iS}+{\gamma }_H{\hat{\beta }}_{iH}+{\gamma }_R{\hat{\beta }}_{iR}+{\gamma }_C{\hat{\beta }}_{iC}+{\epsilon }_i,i=1,\mathrm{K},N$(7) the factor premiums, $\gamma$s, are not estimated with the same time-averaging techniques as the Fama–MacBeth method. Remember that the Newey–West (HAC) standard errors should be used to test the significance of $\hat{\gamma }$s. Equation (7)(7) $E_T(R_i-R_f)={\gamma }_0+{\gamma }_M{\hat{\beta }}_{iM}+{\gamma }_S{\hat{\beta }}_{iS}+{\gamma }_H{\hat{\beta }}_{iH}+{\gamma }_R{\hat{\beta }}_{iR}+{\gamma }_C{\hat{\beta }}_{iC}+{\epsilon }_i,i=1,\mathrm{K},N$(7) is only used to obtain the cross-sectional adjusted R².

14. Note that the distribution of the test statistic is different if the data are nonstationary (e.g., unit root, deterministic trend; for more details, see Hansen 2002). Our data for the 25 portfolio returns and the five factor premiums do not suffer from the problem of nonstationarity.

15. The graphs of the recursive regressions for the remaining 23 portfolios exhibit similar patterns as those in this paper and are omitted for the sake of brevity. They are readily available upon request.

16. Note that the residuals outside of the error bars are either outliers or are associated with changes in ${\hat{\sigma }}_t$.

Additional information

Funding

This work was supported by the the Fundamental Research Funds for the Central Universities [JBK190951,JBK2101060].