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In order to examine whether the early results are not unique to a specific subperiod and to provide a robustness tests for Equation (7), the monthly hedge portfolio returns are also regressed on the macro variables in each of the 5-year subperiods. The length of the subperiod is based on comprise to obtain meaningful estimated parameters and to capture the time-varying properties in stock returns. For brevity, Table 3-7 only reports the test results based on formation and testing period (12, 6). All regressions are carried out independently and the tratios in the brackets are calculated using the Newey-West (1987) heteroscedasticity and autocorrelation consistent standard errors with lags equal to 6. Panel A excludes the January dummy variable and in Panel B a January dummy variable is included that takes value of 1 in January and 0 otherwise.
Regardless whether to consider the January effect, the intercepts from the regression based on the size premium tend to have higher absolute values relative to the value portfolios, suggesting that the explanatory power of Equation (9) is weaker for the size premium than for value premiums. It is noticed that the regression coefficients on variable def and term are consistently positive for value premiums in post-1993 subsamples (except for term based on PC in 2003-2004).
Also the R2 are much higher when considering the January effect.
Overall, the results are consistent with those of Table 3-6 and it is safe to conclude that the early results are not driven by specific sample periods.
In summary, the empirical results in this section show that the underlying driving forces affecting the style spreads are much controversial. The size premium and the value premiums on company characteristics PC and MTBV are mainly driven by the cross-sectional pricing error from the multifactor business cycle model, suggesting that the outperformance of small stocks and PC- and MTBV-based value stocks may be caused by investors’ irrational trading behaviour to such stock groups that results from cognitive biases such as underreaction to firm-specific news. Conversely, the divergent return patterns between value and growth stocks on DY is attributed to the cross-sectional differences in conditionally expected returns predicted by the business cycle model, and therefore is the compensation for bearing business cycle risk.
3.4.6 Contemporaneous relations between equity characteristics, common risk factors and the pricing error of the business cycle model In the previous sections a set of macroeconomic variables are used to model the expected stock returns. Such variables are state variables that have forecasting power for future investment opportunities that represents the slope of the yield curve and the conditional distribution of stock returns. By decomposing stock returns into predicted and unpredicted components from the business cycle model, it is suggested that the value premium based on equity characteristics DY is mainly captured by the predicted risk premias, while value premiums based on characteristics PC and MTBV and the size premium may result from the model mispricing unrelated to the business cycle, and may be best described by investors’ underreaction to the firm-specific information in behavioural finance.
The different mechanisms company characteristics predict the crosssectional average stock returns is intriguing. The characteristics used in this study are price-related variables. The empirical literature suggests that these variables are associated with the variation on average stock returns. Fama and French (1989) emphasize that the price variables that forecast returns are correlated with business cycles. In addition, authors such as Estrella and Hardouvelis (1991) and more recently Ang et al. (2004) document that the price variables that forecast returns are also able to forecast economic activity. If the business cycle model is empirically well specified, rational asset pricing argues that the evidence of strong size and value premiums would suggest that the underlying characteristic proxies for risk factor.
Alternatively it should proxy for the information of mispricing.
However, as discussed in section 3.4.4, the existence of style premiums on firm characteristics would still be consistent with traditional finance theory if the underlying characteristic associated with higher average returns is cross-sectionally correlated with risk factors. Under this condition, the style premium simply reflects compensation for risk.
Given the seeming evidence that macroeconomic variables do not capture the style premiums on firm characteristics PC, MTBV and MV in this chapter, it is motivated to examine what underlies the mispricing of the business cycle model. Under the assumptions that 1) the multifactor asset pricing model is well specified; 2) significant style premium found on the underlying characteristic based on raw stock returns; and 3) the underlying characteristic neither proxies for the risk factor nor has the cross-sectional correlation with the risk factor loadings in the asset pricing model, it follows that the style premium is mainly driven by the cross-sectional pricing errors, which are determined by other factors orthogonal to risk factors in the asset pricing process. Moreover, if such factors predict stock returns, one would expect to see a significant correlation between the mispricing and the underlying characteristic. Now consider factors such as the underlying firm characteristic, the CAPM beta and the loadings on Fama and French (1993) three factors, the null hypothesis of business cycle risk proxy story or correlation with risk factor argument can be rejected if these factors do not predict the cross-sectional pricing errors of the business cycle model.
For this investigation, this section examines the contemporaneous relations between the equity characteristics, common risk factors and the business cycle adjusted returns from Equation (7). Thus crosssectional regressions are tested for individual stock i in each month t starting from January 1982 to December 2004. The cross-sectional
OLS regression takes the form of:
(7) and acts as the dependent variable in regression (10). Z t is a vector of firm characteristics including the log of market value, the log of the value-growth style indicators (PC, DY and MTBV), the CAPM beta, the loadings on Fama-French three factors. To be consistent with the estimation of Equation (7), the CAPM beta for the underlying stock is estimated using a rolling window of its previous 24-60 month observations. Thus stocks must have at least 24-month return data to be considered. The loadings on Fama-French three factors are obtained using exactly the same methodology as CAPM betas.
Equation (10) links the time-series data with the cross-sectional data and some of the independent variables are observed while others are estimated. A combination of firm characteristics and risk factor loadings is used as regressors in Equation (10), yielding a total of 11 regressions (except for size portfolios)14. In each month, regression (10) is estimated and the vector of monthly estimators of cm obtained. The average time-series of such estimated cm and the Newey-West (1987) heteroscedasticity and autocorrelation consistent standard errors with lags of 36 are calculated to obtain the t-ratios15.
Table 3-8 reports the result for such cross-sectional regressions. Panel 1 is the result for stocks with size information only. Only the CAPM betas or the loading on Fama and French market risk factor significantly tracks the variation on the cross-sectional average pricing
Only the market value (MV) and the underlying characteristic variables (PC, DY
and MTBV) used to sort stocks will be used in regression (10). This is because not every stock has all the four available characteristic values. Due to this reason, for size portfolios, characteristic variables PC, DY and MTBV are not included, hence yielding only 5 cross-sectional regressions in each month.
It is reasonable to use 36 as the number of lags in the Newey-West (1987) test.
U.K. listed companies generally disclose the financial results on a quarterly basis.
The time-series test of return series (not reported here) suggests that in most cases there are autocorrelations up to around 40 months.
errors from the business cycle model. When augmented by stock’s market value information or using market value alone as independent variable, the intercepts become significant, suggesting that firm characteristic MV does not predict the average pricing errors, although it does have the correct sign.
Panel 2 and 4 report the results for stocks with characteristic PC and MTBV. Notice that the size information is also included in the regression because of its availability. Consistent with Panel 1, the pricing errors from the business cycle model is explained by the CAPM betas, or the market risk exposure and/or SMB but not HML of Fama and French three factor model. Augmenting equity characteristics or using such characteristics along as regressors will result in significant intercepts, indicating that company characteristic variable PC and MTBV do not explain the mispricing of the business cycle model. It is also noted that SMB or MV has the right sign to demonstrate the size effect impounded in pricing errors. The sign of PC is correct while that of MTBV is relatively noisy. Interestingly, the coefficients on HML factor are all negative (but not significant), suggesting that the mispring of business model is perhaps more severe for growth stocks.
This result is consistent with recent research such as Finn et al. (1999) who argue that equity mispricing is mostly on the short side (growth stocks).
The results in Panel 4 based on characteristic DY tell a very different story. Although the sign of DY is correct, the regression intercepts are all significant regardless which set of variables is combined as regressors. This is consistent with the argument that DY-based value premium is mainly captured by business cycle risk, and hence common factors such as CAPM beta and the loading on Fama and French market factor do not explain the model mispricing. Naturally, since DY is associated with average returns, it does not track the cross-sectional variation on pricing errors.
In summary, it is suggested that in the U.K. stock market the value premium on firm characteristic DY is compensation for the business cycle risk and hence DY is a proxy for macroeconomic risk factor in stock returns. While the size premium and value premiums on firm characteristic PC and MTBV are not directly captured by the business cycle effects, under the assumption that the underlying multifactor business cycle model accurately describes stock returns, they are mainly driven by factors that are unrelated with the business cycle risk. Specifically, this chapter finds that the pricing errors are crosssectionally captured by exposures to other common risk factors such CAPM betas or loadings on market factor or SMB of Fama and French (1993) three-factor model. Moreover, equity characteristics PC, MTBV and MV have no explanatory ability in such mispricing when augmented or used alone as independent variables. Given the fact that these variables are associated with the cross-sectional variation on average stock returns, the null hypothesis that these variables do not proxy for risk factors or have no cross-sectional correlation with the factor loadings can be rejected. Overall, the empirical research in this chapter supports the rational risk-based argument that style premium reflect compensation for risk, although such risk may not directly business cycle related.
Table 3-8 Regressions of unpredicted stock returns on firm characteristics and risk factors Stock returns are modelled by.
def is the default spread of the lower and higher yield bond. yld is the short-term interest rate proxied by the 3-month Treasury bill yield. div is the dividend yield on the overall market and term is the term spread representing the difference between the 20-year gilt and 3-month Treasury bill yield. The parameters of the above regression are estimated by 60-month rolling window samples containing stocks with minimum 24 months of observations. In each month and cross-sectionally, all the one-month-ahead unpredicted returns from the above regression (i.e. the estimated intercept plus the residual) of individual stocks are regressed on a combination of a set of equity characteristics such as the market capitalisation (MV), the price to cash flow ratios (PC), the dividend yield (DY), the market to book ratios (MTBV) and the common risk factor loadings such as CAPM beta and the FamaFrench three-factor loadings. The CAPM beta and the loadings for Fama-French three factors of an individual stock are also estimated using a 60-month rolling window with stocks having minimum 24 months of observations. The table below presents the regression results and the t-ratios in the brackets are calculated using the Newey-West (1987) heteroscedasticity and autocorrelation consistent standard errors with lags equal to 36. *, ** and *** denote significance at the 10%, 5% and 1% levels, respectively.
3.5 Summary and conclusions Expected returns vary over time and across asset groups. The size and value premium are widely referred to market anomalies, but the precise paradigm for which they present an anomaly is far from clear.
The interpretations of the relative performance across styles remain an ongoing debate in the financial literature. Rational asset pricing theory argues that style spreads are compensation for the risk, behavioural finance links style premiums to mispricing of assets groups caused by investors’ irrational trading behaviour that are unrelated to fundamentals. This chapter contributes to the literature by investigating the relative importance of common risk factors and the firm-specific information in explaining the return differentials across equity styles. Understanding the relative importance of the underlying driving forces that affect the relative performance across asset classes is of obvious interest for portfolio managers and those who pursue style investing. This is because different driving forces would point to the different guidelines for investors to capitalise on the relative style performance to enhance their investment returns.