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Specifically, each month all stocks in P1-P9 style portfolios are first assigned into 9 deciles in ascending order according to their returns over the previous 3, 6, and 12 months. Hence loser stocks are in decile 1 and winner stocks are in decile 9. The price momentum indicator (PM) is simply the decile number to which P1-P9 stocks belong (i.e. 1, 2,…, 9). Further, 14 industry portfolios defined by Datastream INDC3 are ranked based on the prior 3-, 6-, and 12month industry returns. The industry with the lowest rank receives a score of 1 and that with the highest rank receives a score of 14. Thus every P1-P9 stock receives the score of the industry (IM) ranking to which it belongs. Finally, style momentum indicator (SM) is computed by ranking all 9 style portfolios based on their 3-, 6-, and 12-month returns. Again the loser style has a score of 1 and the winner style is assigned a score of 9. Thus every P1-P9 stock receives the score of the style portfolio to which it belongs. Under this procedure, every single stock in the style portfolios will have 3 parameters containing the price, industry and momentum ranking information. Cross-sectional regressions of raw buy-and-hold test period returns for individual stocks with 3-, 6- 12-, and 24-months holding periods on the SM, PM and IM indicators are fitted. Table 4-9 reports the time-series average estimated regression coefficients for styles based on different firm characteristics and test periods.
The results in Table 4-9 would suggest that, together with PM and IM, SM is a determinant that affects the equity return dynamics. The explanatory power of SM extends to at least 12 months and possibly longer. Similar to SM, the IM factor also has the ability in explaining stock returns. This is not the case for IM factor which shows the short-term explanatory ability only. It is estimated that the annual return differential between a stock that is from in-favour style and another from the out-of-favour style based on 3-month ranking would be 1.28%*(8) = 10.5% for PC-based style classification, and the spreads would be 7.9% and 5.8% for BM- and DY-based styles, respectively. The return spreads are equivalent in magnitude for stocks based on PM ranking but not for IM ranking. The explanatory power of SM generally increases for future stock returns longer than 12 months, and decrease for PM. Hence SM tends to have longerlasting effects than PM does, which is consistent with Chen (2003).
However, the tests based on U.K. sample suggest that the explanatory power of IM to individual stock returns is less significant, in particular when sorting is based on relatively long period and for longer stock return predictions.
As a summary, the empirical findings in this session suggest that style momentum is distinct from the price and industry momentum documented in the literature. The test results above confirm the stylebased positive feedback trading story of Barberis and Shleifer (2003) that style effects should persist even after controlling for stock-level continuations. Further, since information of style cycles is useful in predicting future individual stock returns, the results are also consistent with Berk et al. (1999) that firms of similar characteristics will have similar systematic risks and tend to be at the similar stage of investment style, and hence characteristic-based style portfolios could price stock returns. Overall, it is evident that equity style cycles do exist in the U.K stock market, and the evolution of equity style cycles conveys useful information and therefore plays an important role in the return generating process.
Table 4-9 Momentum effects and the cross-sectional stock returns Every month, all stocks in P1-P9 portfolios are assigned into 9 deciles in ascending order based on their previous 3-, 6-, and 12-month returns. Loser stocks are in decile 1 and winner stocks are in decile 9. A stock’s price momentum indicator (PM) is simply the decile number to which the stock belongs (i.e. 1, 2,…, 9). Further, 14 industry portfolios defined by Datastream INDC3 are ranked based on the prior 3-, 6-, and 12-month industry returns. The industry with the lowest rank receives a score of 1 and that with the highest rank receives a score of 14. Thus every stock receives the score of the industry (IM) ranking value to which it belongs. Finally, style momentum indicator (SM) is computed by ranking 9 style portfolios based on their 3-, 6-, and 12-month returns. Again the loser style has a score of 1 and the winner style is assigned a score of 9, and every stock receives the SM score of the style portfolio to which it belongs. Under this procedure, every stock in the style portfolios P1-P9 will have 3 parameters containing the price, industry and momentum ranking information. Cross-sectional regressions of raw buy-and-hold test period returns for individual stocks with 3-, 6- and 12-months holding periods on the SM, PM and IM indicators are tested. Following Fama-MacBeth (1973), this table reports the time-series average estimated regression coefficients for styles based on different firm characteristics and test periods. The t ratios in brackets are calculated based on the Newey-West (1987) heteroscedasticity and autocorrelation consistent standard errors with lags equal to K, the testing periods. *, ** and *** denote significance at the 10%, 5% and 1% levels, respectively.
4.7 The risk exposures of style momentum strategies Previous sections in this Chapter finds that style momentum is a phenomenon that is different from price and industry momentum, and the information of style cycles has predictive ability in future stock returns. It is noteworthy however that the predictive power of prior infavour or out-of-favour investment styles may be confounded with the well recognised book-to-market and size effect in the context of Fama and French (1996) three-factor model. For this reason, it is necessary to investigate whether style momentum portfolios contain additional information to predict future stock returns once the size and BM factors are controlled. To verify whether style momentum effect is due to covariation with such common risk factors, this section employs the Fama and French (1993) three-factor model to evaluate the payoffs of style momentum investing. The use of Fama and French three-factor model as a risk-based tool for performance evaluation is justified by its superiority over single factor models such as CAPM. In addition, studies such as Liew and Vassalou (2000) argue that SMB and HML contain the business cycle information like future GDP growth.
For each firm characteristics PC, MV and DY, the already familiar 9 style portfolios are ranked by their prior 3- or 12-month returns and hedge portfolios are formed to buy the past winner style and to sell the past loser style. The winner, loser and the hedge portfolio are held for 3 or 12 months when the strategy is repeated. Thus the test periods and the rank periods are non-overlapping. Starting from 1982:01the equally weighted average hedge portfolio returns during the test periods in excess of the 1-month Treasury bill rate are regressed on the contemporaneous monthly returns of Fama and French three factors. The Datastream UK index return is used as a proxy for market return.
Table 4-10 summarises the results. The three-factor model explains some of the variations in equity style momentum returns defined by characteristics variables BM and DY, but not for styles classified by PC. The Fama-French alphas of PC-based style momentum is 0.0084 and 0.0072 for ranking periods of 3- and 12-month respectively, both are significant at 1% level. However, when measured against the Fama-French three-factor model, the style-level mispricing for portfolios based on characteristics BM and DY is not significant. It is shown that the Fama-French alphas are 0.0025, 0.0017 for BM portfolios and 0.0015 and -0.0012 for DY portfolios based on 3- and 12-month ranking, respectively. Thus BM- and DY-based style momentum strategies do not generate abnormal returns at all.
There are also strong size-effects found in momentum returns because all loadings for the SMB factors are significantly positive, while the HML loadings vary. Specifically, the HML loading for PC-based hedge portfolio is positive and statistically significant, indicating that the loser style contains more value stocks than the winner style in short term. This is also evidenced by the positive but insignificant (significant) HML loading for winner (loser) style. In contrast, when the style ranking period is based on 12-month, both winner and loser styles as well as the momentum hedge portfolios contain positive and significant HML loadings, suggesting that over longer periods, value stocks outperform growth stocks defined PC. Similar results for HML factors can be found for DY-based style momentum returns but BMbased results seem to be slightly different. Even based on longer ranking period of 12-month, the HML loading for BM-based hedge portfolio is significantly negative (at 10% level), implying that growth stocks tend to outperform value stocks based on BM sorting. The negative sign of HML loadings suggests that controlling for the value and growth exposures can actually improve style momentum returns.
It is also noted that the alphas of winner styles are positive and those of loser styles are negative. This may suggest that style investors are more apt to move money in a style that has shown persistent good
performance than moving out money from a style that is found toperform poorly.
While PC-based momentum seems to be able to generate abnormal returns, such risk-adjusted returns are less likely caused by the differences in market risk of winner and loser styles. This is because regardless which style variables are tested, in most cases winner styles tend to have smaller betas than the losers. Jegadeesh and Titman (1993) also show that differences in market risk of long short side of the hedge portfolios do not cause price momentum profits. The style momentum portfolios are generally market neutral, only DYbased portfolio of 3-month ranking has significant negative beta.
As a final step, Table 4-11 examines the risk-return characteristics of style momentum strategies based on different subsamples. Because of the time-varying nature of style performance, a number of prior studies have related the momentum returns with the stage of business cycles. For example, Chordia and Shivakumar (2003) find that during economic recessions there is no price momentum effect.
Table 4-11 subdivides the whole sample period into 4 sub-periods, i.e.
1982-1986, 1987-1993, 1994-1999 and 2000-2004. It is shown that style momentum strategies perform better after year 1999 when the technology-media-telecoms (TMT) bubbles collapsed. This result is consistent with the empirical findings regarding the value and growth stock performance during 1990s and after 2000. Given that SV style generally beat LG style as suggested in Table 4-2, it is not surprisingly to find that the average raw monthly style momentum payoffs are much higher during year 2000-2004 than those in other periods.
However, characteristics PC-based style momentum strategy for 3month ranking periods seems does not work for periods 1982-1993, while BM-based strategy does not work in period 1994-1999, so it is with DY-based style momentum performance.
Table 4-11 also compares the performance of style continuation during different market conditions. Prior studies such as Cooper et al.
(2004) argue that momentum profits depend on the state of the market. Price momentum is much stronger in the up-market than that in down markets. The return decomposition introduced in section 2 suggests that momentum returns can be potentially driven by the dispersion in unconditional expected returns as Conrad and Kaul (1998) argue. Pesaran and Timmermann (1995) also suggest that the predictability of stock returns is low during calm market conditions.
For this reason, the profitability of style momentum strategy may depend on the relative force of past momentum. It can also be hypothesised that if winner style is risky than loser style, it should perform poorly (better) in bad (good) market states. Hence, the whole sample period is now subdivided into different periods with low, medium and high cross-sectional style volatilities. A high crosssectional dispersion in style return is defined by the top 20% of the style spreads, with medium dispersion being the middle 60% and low dispersion being the bottom 20%. The style momentum performance under bull, normal and bear market conditions is defined by the volatility on the Datastream UK country index in the ranking period.
Namely, the bull market is defined as the 20% of the best market performance; the normal market condition is the middle 60% and the bear market is the 20% with the worst performance periods. Table 4would suggest that style momentum strategies tend to perform very well shortly after the portfolio formation in bull market. However, for longer holding periods the evidence is mixed.
4.8 Summary and conclusions