Style premiums after adjusting for the predicted returns from

Given the evidence on the profitability of simple style investing strategies, this section examines how the predicted and unpredicted returns from Equation (7) are related to the U.K. size and value premiums in more detail.

If business cycle risk is the only exogenous driving force to determine such divergent style return patterns, arguably controlling for business cycle effects could substantially reduce the return differentials across styles. Hence the hedge portfolio returns would not be significant if the predicted ability of Equation (7) is already accounted for. For this investigation, the same simple style investing strategies as described in Section 3.3.2 are implemented. However, to control for the business cycle effect impounded in stock returns, when calculating the hedge portfolio returns in the K-month testing period, the observed (realised) stock returns are replaced with the unpredicted returns (i.e. intercept plus residual) from the business cycle model. As mentioned in Section 3.4.3, the intercept of Equation (7) is not included in the predicted return part because this time-varying component may capture the cross-sectional information that is not related to the business cycle. Table 3-5 presents the hedge portfolio returns using the predicted and unpredicted stock returns in the K-month testing period, representing style premiums after controlling for the firm-specific information and business cycle effects, respectively.

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

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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. Controlling for the unpredicted returns from Equation (7) decreases the value premium and leads to the opposite sign.

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

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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

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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.

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Table 3-5 Style Investing Returns Adjusted for Macro Variables and Firm-specific Component from Model

Stock returns are predicted by , def is the default spread, yld is the three-month T-

bill yield, div is the overall market dividend yield and term is the term spread. The parameters of the model are estimated by a 60-month rolling window containing stocks with minimum 24 months return observations. The one-month-ahead predicted and unpredicted portion of this equation is used to replace the observed stock returns in the K-testing period to calculate the firm-specific-controlled and business-cycle- controlled value and size premiums. The t ratios in brackets are calculated using Newey-West (1987) heteroscedasticity and autocorrelation consistent variance with lags equal to K, the testing periods. *, ** and *** denote significance at the 10%, 5% and 1% levels, respectively.

Periods Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 01/1982-12/1993 -1.26 49.2 -0.53 54.5 -1.20 49.6 2.66 60.3 4.61 54.5 2.82 59.9 1.39 77.0 4.14 100.0 1.61 78.8 t-value (-0.62) (-0.18) (-0.59) (1.28) (1.53) (1.34) (5.96)*** (4.79)*** (7.30)*** 01/1994-12/2004 3.71 43.0 1.18 36.4 3.50 42.4 -2.03 57.9 0.43 63.6 -1.83 58.3 1.69 80.0 1.38 60.0 1.66 78.4 t-value (0.72) (0.24) (0.71) (-0.41) (0.10) (-0.39) (4.06)*** (1.16) (3.76)*** 01/1982-12/2004 1.18 46.2 0.33 45.5 1.11 46.1 0.36 59.1 2.52 59.1 0.54 59.1 1.56 78.9 2.88 81.8 1.66 79.2 t-value (0.42) (0.11) (0.41) (0.13) (0.95) (0.21) (6.72) (3.62) (6.96) 01/1982-12/1993 -1.42 47.1 -2.09 40.0 -1.47 46.6 3.01 61.2 6.04 60.0 3.24 61.1 1.60 79.3 4.01 100.0 1.78 80.9 t-value (-0.73) (-0.86) (-0.78) (1.49) (1.51) (1.64) (6.58)*** (5.77)*** (7.86)*** 01/1994-12/2004 3.92 41.3 0.70 27.3 3.65 40.2 -2.06 59.5 1.12 72.7 -1.80 60.6 1.82 76.4 1.56 55.6 1.80 74.8 t-value (0.83) (0.14) (0.82) (-0.46) (0.27) (-0.43) (4.05)*** (1.06) (3.96)*** 01/1982-12/2004 1.25 44.2 -0.63 33.3 1.10 43.3 0.47 60.3 3.46 66.7 0.71 60.8 1.73 78.9 2.87 81.0 1.82 79.1 t-value (0.48) (-0.20) (0.45) (0.19) (1.16) (0.30) (7.23)*** (3.62)*** (7.72)*** 01/1982-12/1993 1.83 61.9 2.29 63.6 1.87 62.0 -0.92 51.6 -1.19 63.6 -0.94 52.6 0.95 70.6 1.12 72.7 0.96 70.8 t-value (0.92) (0.87) (0.96) (-0.45) (-0.39) (-0.47) (4.38)*** (1.80)* (4.14)*** 01/1994-12/2004 7.17 70.2 5.59 72.7 7.04 70.5 -6.48 30.6 -5.16 36.4 -6.37 31.1 0.67 56.5 0.21 60.0 0.63 56.8 t-value (2.14)** (1.67)* (2.17)** (-2.14)** (-1.79)* (-2.19)** (1.35) (0.22) (1.33) 01/1982-12/2004 4.45 66.0 3.94 68.2 4.41 66.2 -3.64 41.3 -3.18 50.0 -3.61 42.0 0.80 63.2 0.78 68.2 0.80 63.6 t-value (2.20)** (1.79)* (2.26)** (-1.90)* (-1.43) (-1.95)* (3.18)*** (1.38) (3.21)*** 01/1982-12/1993 1.69 57.0 2.24 70.0 1.73 58.0 -0.67 52.9 -0.96 60.0 -0.69 53.4 1.03 71.9 1.28 70.0 1.05 71.8 t-value (0.93) (0.74) (0.99) (-0.36) (-0.27) (-0.38) (4.30)*** (1.59) (4.17)*** 01/1994-12/2004 7.72 66.1 5.65 72.7 7.55 66.7 -6.97 35.5 -5.04 27.3 -6.81 34.8 0.77 58.2 0.28 55.6 0.73 58.0 t-value (2.41) (1.45) (2.47) (-2.35) (-1.48) (-2.42) (1.55) (0.27) (1.55) 01/1982-12/2004 4.71 61.6 4.03 71.4 4.65 62.4 -3.82 44.2 -3.10 42.9 -3.76 44.1 0.88 65.3 0.92 66.7 0.88 65.4 t-value (2.47)** (1.56) (2.56)** (-2.10)** (-1.19) (-2.16)* (3.43)*** (1.44) (3.55)***

Jan only All periods

PC (6,12)

Equally-weighted Hedge Portfolio Returns (%)

Style premium based on predicted returns Style premium based on unpredicted returns Raw style premium Non-Jan Jan only All periods

PC (12,6)

DY★ (6,12)

DY1 (12,6)

Non-Jan Non-Jan Jan only All periods

101 Table 3-5 (continued) Periods Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 Q1-Q5 %>0 01/1982-12/1993 -3.86 27.8 -4.55 27.3 -3.92 27.7 5.09 77.0 7.89 81.8 5.31 77.4 1.21 67.5 3.36 72.7 1.38 67.9 t-value (-2.28)** (-2.33)** (-2.38)** (2.88)*** (2.38)** (2.99)*** (5.09)*** (2.14)** (5.68)*** 01/1994-12/2004 -0.76 41.3 -2.13 27.3 -0.87 40.2 1.86 59.5 3.16 81.8 1.97 61.4 1.08 65.2 0.50 70.0 1.03 65.6 t-value (-0.13) (-0.31) (-0.15) (0.34) (0.51) (0.37) (1.85)* (0.36) (1.73)* 01/1982-12/2004 -2.34 34.4 -3.34 27.3 -2.42 33.8 3.51 68.4 5.52 81.8 3.67 69.5 1.16 67.2 2.16 72.7 1.24 67.7 t-value (-0.77) (-0.94) (-0.82) (1.21) (1.53) (1.31) (3.88)*** (1.98)** (4.03)*** 01/1982-12/1993 -3.64 28.1 -3.51 30.0 -3.63 28.2 5.07 76.9 6.25 70.0 5.16 76.3 1.42 74.4 2.75 70.0 1.52 74.0 t-value (-2.45)** (-1.58) (-2.52)** (3.30)*** (1.94)* (3.41)*** (6.08)*** (2.17)** (6.27)*** 01/1994-12/2004 0.80 42.1 -2.69 18.2 0.51 40.2 0.43 58.7 3.56 81.8 0.69 60.6 1.19 64.5 0.18 66.7 1.12 64.7 t-value (0.15) (-0.35) (0.10) (0.09) (0.50) (0.14) (1.90)* (0.10) (1.76)* 01/1982-12/2004 -1.42 35.1 -3.08 23.8 -1.55 34.2 2.75 67.8 4.84 76.2 2.91 68.4 1.32 71.1 1.75 71.4 1.36 71.1 t-value (-0.51) (-0.73) (-0.58) (1.05) (1.19) (1.15) (4.27)*** (1.66)* (4.33)*** 01/1982-12/1993 -14.12 21.4 -13.46 27.3 -14.07 21.9 15.18 80.2 14.37 81.8 15.11 80.3 1.02 61.9 0.86 54.5 1.01 61.3 t-value (-4.08)*** (-2.62)** (-4.16)*** (4.55)*** (2.86)*** (4.62)*** (1.74)* (0.77) (1.82)* 01/1994-12/2004 -17.43 6.6 -13.63 9.1 -17.11 6.8 17.86 91.7 18.80 90.9 17.94 91.7 0.39 49.6 4.72 70.0 0.74 51.2 t-value (-3.53)*** (-3.03)*** (-3.64)*** (3.59)*** (3.66)*** (3.77)*** (1.07) (3.43)*** (1.74)* 01/1982-12/2004 -15.74 14.2 -13.55 18.2 -15.56 14.5 16.49 85.8 16.58 86.4 16.50 85.9 0.71 56.3 3.05 63.6 0.90 56.9 t-value (-5.24)*** (-4.03)*** (-5.40)*** (5.56)*** (4.59)*** (5.75)*** (2.01)** (2.63)*** (2.59)*** 01/1982-12/1993 -15.63 18.2 -16.36 20.0 -15.69 18.3 16.79 82.6 17.13 80.0 16.82 82.4 1.15 61.2 0.76 50.0 1.12 60.3 t-value (-5.82)*** (-3.22)*** (-5.99)*** (6.48)*** (3.32)*** (6.61)*** (2.05)** (0.67) (2.13)** 01/1994-12/2004 -19.13 5.8 -14.96 9.1 -18.78 6.1 19.55 92.6 20.38 90.9 19.62 92.4 0.43 53.6 5.10 66.7 0.78 54.6 t-value (-4.19)*** (-2.99)*** (-4.36)*** (4.27)*** (3.55)*** (4.51)*** (0.99) (3.30)*** (1.61) 01/1982-12/2004 -17.38 12.0 -15.63 14.3 -17.24 12.2 18.17 87.6 18.83 85.7 18.23 87.5 0.77 57.0 3.22 61.9 0.97 57.4 t-value (-6.54)*** (-4.42)*** (-6.81)*** (6.90)*** (4.86)*** (7.21)*** (2.19)** (2.62)*** (2.78)*** Jan only All periods

MTBV (6,12)

Equally-weighted Hedge Portfolio Returns (%)

Style premium based on predicted returns Style premium based on unpredicted returns Raw style premium Non-Jan Jan only All periods

MTBV (12,6)

MV (6,12)

MV (12,6)

Non-Jan Non-Jan Jan only All periods

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