«Equity Style Investing RONG, WU How to cite: Equity Style Investing, Durham theses, Durham University. RONG, WU (2013) Available at Durham E-Theses ...»
The predicted and unpredicted returns from the business cycle model play a very different role in affecting the relative performance of stocks in extreme quintiles based on different equity characteristics. First, for stocks sorted on characteristics PC, MTBV and MV, controlling for the mispricing from regression (7) generally reduces style premiums, and the number of months with positive hedge portfolio returns is reduced sharply. For example, consider the (6,12) strategy, after controlling for the unpredicted returns (i.e. use Equation (8) to calculate the hedge portfolio returns), in the 12-month testing period the percentage of outperformance of small stocks declines from 57.4% to 12.2% in the entire sample period. Similarly, the outperformance of value stocks decreases from 79.2% (PC) and 67.7% (MTBV) to 46.1% (PC) and 33.8% (MTBV), respectively. Such return patterns also exhibit in both January and non-January months. Hence, after controlling for the pricing errors of the business cycle model, the return differentials between stock group Q1 and Q5 decrease in most sample periods and are no longer significant. It is also noted that the value premium for MTBV stocks or size premium becomes negative after controlling the model mispricing, suggesting that model pricing errors are responsible for the observed returns spread. In contrast, however, consistent with Figure 3-3, value premiums based on characteristics DY seem to tell a different story.
Second, even after controlling for the business cycle risk, there is still MTBV-based value premium found, and the size premium is even more pronounced. The number of months with positive style spreads is still reasonably high. While there is no PC-based value premium during subperiod January 1994 to December 2004, 59% of the months see higher returns of value stocks relative to growth stocks.
This suggests that business cycle effects are unlikely the dominant factors that affect the size premium and value premiums based on stocks sorted on PC and MTBV. However, the business cycle model seems to capture the divergent performance of stocks across DY quintiles. Controlling for the explained portion of Equation (7) would result in growth premium instead. Overall, consistent with Figure 3.3, Table 3-5 suggests that in the U.K. market, common stocks sharing similar characteristics tend to commove together. The size premium and value premiums based on equity characteristics PC and MTBV are not captured by the business cycle. On the contrary, business cycle fluctuations are able to capture the cross-sectional average return of extreme stocks characterised by DY.
The finding of different underlying mechanism driving value premiums on firm characteristics is intriguing. The characteristic variables used to classify assets are price-related financial ratios and empirical literature has found that such characteristics are associated with the cross-sectional average returns (e.g. Stattman (1980); Rosenberg et al., (1985); Fama and French (1992, 1996); Lakonishok et al. (1994)).
Given significant size and value premiums found in this study, asset pricing theory would well argue that these firm characteristics proxy for a risk factor in returns. Alternatively they provide information about stock mispricing. Arguably, as Chordia and Shivakumar (2002) suggests, if the exposures to the risk factors of each stock are well known and the pricing model is empirically well specified, sorting can take place on either the risk premiums or the pricing errors instead of raw returns. A risk-based explanation can be rejected if these sorts on pricing errors still exhibit style premiums, or style spreads disappear when the sorting is on the predicted risk premiums. For this reason, the preliminary results in this section would suggest that firm characteristics PC, MTBV and MV may proxy for mispricing from the business cycle model, while DY is a proxy of business cycle risk factor.
However, if Equation (7) accurately describes the stock returns, and PC, MTBV and MV are cross-sectionally associated with the factor loadings, the variation in expected returns across stocks based on these characteristics would still be consistent with traditional finance theory. Thus style premiums on such characteristics still reflect compensation for risk. Chan and Chen (1991) and Fama and French (1993) argue that size and BM proxy a distress factor that explains the variation in average stock returns. Berk (1995, 1996) shows that in the cross-section, market value or BM is theoretically inversely related to expected returns. Liew and Vassalou (2000) find that the size and the BM factors forecast GDP output growth, indicating that they are already business cycle variables. A number of other studies including Estrella and Hardouvelis (1991) and more recently Ang et al. (2004) all document that such price variables that forecast returns also forecast macroeconomic activity. If such characteristic variables have already impounded business cycle risk information, sorting stocks into quintiles on these variables is an abundant procedure simply because all stocks in the universe have been already properly sorted (just like in a single quintile of similar business cycle risk premia). Hence the cross-sectional variation in returns across stock groups cannot be business cycle risk related, and hence are unpredictable by the business cycle model.
★Note: for style based on DY, the hedge portfolios are Q5 – Q1.
3.4.5 Style premiums regressed on macroeconomic variables Previous section suggests that U.K. size and value premiums on characteristics PC and MTBV sorted stocks are mainly driven by firmspecific mispricing rather than the conditional macroeconomic risk factors, one may be concerned with the explanatory power of the business cycle model under consideration. Equation (7) is based on the individual stock level. Prior studies such as Ferson and Harvey (1991, 1998 and 1999) have focused on the portfolio level to relate with the macroeconomic variables. Avramov and Chordia (2006a) argue that the use of individual stocks in a model reduces the datasnooping biases of Lo and MacKinlay (1990) and avoids the loss of information in the portfolio sorting process of Litzenberger and Ramaswamy (1979). Equation (7) is based on the assumption that the exposures to the risk factors of each stock are known, and hence the pricing errors can be used to examine the model’s explanatory ability.
The null hypothesis of a rational risk-based explanation can be rejected if after controlling for the predicted risk premiums there are still significant return divergence exhibited across styles. However, rejecting the risk-based interpretation may also be caused by failing to properly identifying the underlying risk factors. In particular in the individual stock level, the exposures to the risk factors are in general unknown and can be hard to estimate (Swinkels, 2004).
To have a better understanding regarding the relation between the style spreads based on such characteristics and the macroeconomic conditions, this section directly examines the relation between style spreads for stocks classified by different characteristics PC, DY, MTBV and MV with the macroeconomic variables as described in Equation (7):
(9) Where ri (i = 1, 2, 3, 4) is the hedge portfolio returns based on characteristic variables PC, DY, MTBV and MV.
To allow for the time-varying nature impounded in Equation (9), the parameters are estimated using the previous 60-month rolling window that contains stocks with at least 24 months return observations. The estimated coefficients from (9) are then used to forecast the onemonth-ahead style spreads. Identical to Equation (7), each month the unpredicted portion of regression (9) is calculated as the sum of the intercept and residuals. To account for the possible autocorrelations caused by the rolling windows, the t-statistics are calculated based on Newey-West (1987) heteroscedasticity and autocorrelation consistent standard errors. Given the evidence of size and value premiums found in previous sections, it is hypothesized that, if Equation (9) fails to capture the business cycle effect in the expected style spreads, the pricing error of Equation (9) is expected to be significantly positive.
Table 3-6 reports the time-series average of the intercept and the style spreads that are predicted and unpredicted by Equation (9) in different sample periods. The time-series average of the coefficients of the macroeconomic variables is also presented. For comparison the raw hedge portfolio returns are also listed. Panel A presents the results for the regressions without including the January dummy variable, while Panel B includes the January dummy to consider the seasonality of style premiums.
Table 3-6 Style Investing Profits Regressed on the Business Cycle Variables Style portfolios are formed in the same manner as in Table 3.3. This table
reports the average coefficients for the regression:
Hedge portfolio returns (Q1-Q5) based on PC 01/1982-12/1993 0.018 0.038 -0.018 43.5 -0.019 0.027 -0.824 0.165 0.948 -0.205 0.216
Hedge portfolio returns (Q5-Q1) based on DY 01/1982-12/1993 0.010 -0.023 0.033 75.0 0.035 0.005 -0.663 0.198 -0.379 -0.152 0.127 t-value (4.17)*** (-2.503)*** (3.616)*** (3.982)*** (2.599)*** (-3.309)*** (2.093)** (-2.216)** (-4.452)*** 01/1994-12/2004 0.007 0.067 -0.059 24.8 -0.062 0.008 2.129 0.797 1.367 0.913 0.220
Hedge portfolio returns (Q1-Q5) based on MTBV 01/1982-12/1993 0.015 -0.010 0.025 70.4 0.030 0.020 0.261 0.174 -0.373 -0.189 0.140
Hedge portfolio returns (Q1-Q5) based on MV 01/1982-12/1993 0.011 -0.188 0.200 100.0 0.203 -0.003 -0.898 0.888 -4.005 0.287 0.394 t-value (2.13) (-14.001)*** (18.648)*** (22.969)***(-1.105) (-2.608)** (5.269)*** (-15.99)*** (3.452)*** 01/1994-12/2004 0.008 -0.150 0.158 74.4 0.162 0.052 0.012 1.197 -4.962 0.807 0.353
01/1982-12/2004 0.010 -0.185 0.195 96.7 0.199 0.022 -0.672 0.688 -4.973 0.690 0.352 t-value (2.78)*** (-9.291)*** (9.977)*** (10.188)***(5.350)*** (-1.458) (2.505)** (-7.812)*** (3.817)*** Consistently, it is found that business cycle variables do not explain the size premium in the U.K. market. It is shown that all intercepts of size portfolios are significantly positive over all sample periods, and the unpredicted portion of the size premium is statistically significant regardless whether the January effect is considered or not. Besides, the coefficients for variable div are always significantly negative in different testing periods, and those for def are significantly negative during period 1993:01-2004:12, suggesting that in market conditions with high dividend yields on aggregate level and small default spreads, small stocks tend to underperform large stocks. The negative coefficients on default spread and the overall market dividend yield should imply that controlling for these two variables could increase the size premium.
However, the business cycle effect has some ability in explaining value premiums on the portfolio level. All coefficients on the macroeconomic variables are positive based on whole sample periods although some may be noisy in subperiods. The unexplained portions of the regression are not significantly positive, and the percentage of positive signs is less than 50% on characteristics PC and DY. The dummy variables in Panel B are generally significant in different testing periods too. Thus both size and value premiums exhibit some kind of January effect, which is consistent with Table 3-3. It is shown that adding January dummy variable generally increases the explanatory ability of macro variables. The t-ratios are higher in absolute value and the R2 are higher in Panel B as compared to those in Panel A.
It is interesting to see that the default spread has largest coefficients compared to other variables. It also remains as the only variable that is significant regardless whether to consider January effect. Since default spread measures the credit market conditions, an increase in this variable is commonly interpreted to signal the market’s expectation of worsening credit market conditions. Chan and Chen (1991) and Perez-Quiros and Timmermann (2000) suggest that small firms are more vulnerable to variation of credit market conditions over the business cycle. Hence there should be interaction between value premiums and the size premium. Further, Fama and French (1989) and Hahn and Lee (2006) show that the term spread tends to be low near business cycle peaks and high near troughs. Hence, consistent with Table 3.4, Equation (9) predicts that value premiums are higher in an economic environment with higher short-term interest rates, wider default spread and higher term spreads, which is typically the case in economy recessions.
Overall, while previous sections find that on the individual stock level the relative performance of stocks sorted on PC and MTBV are not driven by the business cycle risk, this section suggests that on the portfolio level the business cycle model partly explains the time-series expected value premiums. Hence equity characteristics PC, DY and MTBV contain information in predicting the time-variation in expected style returns. This result is consistent with findings of recent empirical studies to focus on the time-series relations among expected returns, risk and equity characteristics. For example, Kothari and Shanken (1997) and Pontiff and Schall (1998) find that DY and BM forecast stock returns at the aggregate level. Similarly, Lewellen (1999) reports that BM predicts economically and statistically time-variation in expected returns at the portfolio level. These studies aim to distinguish between risk and characteristics stories and generally support the risk-based argument.