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Table 4-2 also reports the time-series average cross-sectional standard deviation of returns for stocks within each style portfolio. Chen and De Bondt (2004) argue that this statistics represents a measure of “stock-picker’s risk”. The results in Table 4-2 for P1-P9 suggests that on average the returns offered by individual stocks in SG-PC, SG-BM and SV-DY are much wider than those in LB-PC, LB-BM and LB-DY portfolios. Moreover, the statistics is larger for SV portfolios than LG portfolios regardless which style variables used, indicating that stocks in SV portfolios have higher cross-sectional volatility than stocks in LG styles. Besides, P10 stocks have shown to have the widest crosssectional variation in returns.
Figure 4-2 illustrates the time-series variations in the annual returns for SV and LG style portfolios based on PC, BM and DY. The returns are calculated in the same way as in Table 4-2 but are annualised.
Figure 4-2 shows both the qualitative and quantitative similarity for the return patterns of value and growth styles based on different style variables. Figure 4-3 presents the dynamics of annual value and growth style returns and the value premium. The value (growth) style returns are calculated as the average of SV (SG), MV (MG) and LV (LG) portfolio returns, and the value premium is the spread between value and growth returns. Similarly, the small-cap premiums are calculated as the return spread between small size portfolios and the large size portfolios, which are the average of SG (LG), SB (LB) and SV (LV), respectively. Figure 4-3 suggests that indeed in the long-term value stocks beats growth stocks although there are short periods that the two style returns reversal. This also applies to small-cap stocks that exhibit long-term better performance relative to large-caps. It is evident that a combination of the two style effects seems to be able to yield an even larger style premium, namely, the return spread between SV and LG styles seems to have larger upper side spread but not necessarily larger downside reversals. These results are consistent with the empirical studies regarding the size effect in the literature.
For example, Hoeowitz et al. (2000a) document that the observed size premium is not linear across all stocks but is concentrated only in smaller firms. Likewise, Fama and French (2008) observe that the size premium is the strongest among U.S. tiny firms based on data from 1963-2005. Fama and French (2012) also find that value premiums differ across size dimension, specifically, value premiums decrease with size.
Overall, the empirical findings in Table 4-2 and Figure 4-2, 4-3 are consistent with recent study of Berk et al. (1999). Berk et al. (1999) argue that the same firm characteristics tend to have the same state variables affecting the systematic risks and expected returns. If styles capture the underlying driving forces that determine the asset returns, style portfolio should have explanatory ability in predicting individual returns, and the cross-sectional dispersion of systematic risks across all stocks within a style is lower. The results in this section suggests that firm attributes PC, BM and DY capture the basic economic driving forces that describe the asset return dynamics.
Table 4-2 the performance of simple equity style investing Style portfolios (P1-P9) are formed at the end of each year based on firm characteristics PC, BM and DY between 1980 and 2003. P10 stocks are those that do not have meaningful characteristic values. This table reports the average monthly returns (%) earned by these portfolios during January 1982 to December 2003. The time-series averages of (1) monthly valueweighted average portfolio returns; (2) portfolio returns for January only; (3) portfolio returns for February through December; and (4) the monthly crosssectional standard deviations of stock returns within each style portfolio are presented. Finally, the corresponding time-series standard deviations and the time-series average number of stocks in each portfolio are also reported.
Compound annual performance of style portfolios based on PC (1982-2004) 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Compound annual performance of style portfolios based on BM (1982-2004) 1.0 0.8 0.6 0.4 0.2 0.0
Compound annual performance of style portfolios based on DY (1982-2004) 1.0 0.8 0.6 0.4 0.2 0.0
Figure 4-3 Size and value premiums dynamics This figure shows the annual small-cap spreads and value premiums between 1982 and 2004, as well as the annual return differential between the small-cap value and large-cap growth portfolios.
4.5 The profitability of style momentum strategies If there are equity style cycles in the U.K. stock market and it is of long duration, then smart investors can engage in the style rotation strategy to capitalise on the divergence of style returns. This section explores the profitability of such tactical trading strategies that incorporates the information of investment style evolution.
A style momentum strategy is to buy stocks in styles that perform well in the past and to sell stocks in styles that do poorly recently. The fundamental idea for such strategy can be justified by investors’ behavioural trading as in Barberis and Shleifer (2003) and the rational framework such as Berk et al. (1999). In essence, style momentum is a positive feedback adaptive trading model based on equity style cycles.
Starting from January 1982, 9 style portfolios (P1-P9) based on firm characteristics X (X = PC, BM and DY) are ranked every month by their performance in the past j months (j = 3, 6, 12). The formation of these style portfolios are described in section 3. Hedge portfolios are formed to buy the top one (or top two) winner style portfolio(s) and to sell the corresponding bottom one (or bottom two) loser portfolio(s).
The hedge portfolios are held for k test periods (k = 3, 6, 9, 12, 24, or 36 months). The test for the style momentum strategy builds on the “overlapping method” proposed by Jegadeesh and Titman (1993).
At every month end t, rank all style portfolios (P1-P9) according to their value weighted compound returns over the previous j months, t-j+1 to t and identify the winner and loser styles.
Form hedge portfolios based on top and bottom one or two styles (i.e. winner and loser) using equally weighted scheme.
Measure the return to each of the hedge portfolios in every month for the next k months after formation, t+1 to t+k or t+2 to t+k+1 if there is one month skipped after hedge portfolio formation to avoid short term price reversals.
The return to the winner (loser) styles in period t+1 is the average of the returns to the winner (loser) style portfolios identified at time point t, t-1,…, t-k+1 in period t+1. If a month’s gap is left, the return at period t+1 is the average of the returns to the winner (loser) style portfolios at t-1, t-2,…, t-k. Hence, the return to the winner (loser) style portfolios is the average return to the k winner (loser) styles identified consecutively over the previous k months.
The returns to the style momentum strategy (j,k,0) or (j,k,1) if a month’s gap is allowed is the mean return to the self-financing portfolios of winner-minus-loser styles over the entire sample.
Table 4-3 reports the equally weighted average monthly returns for winner and loser styles as well as the style momentum payoffs over the sample period 1982:01-2004:12. Panel A and B use 2 extreme style portfolios to construct hedge portfolios, while Panel C and D use 4 style portfolios to form hedge portfolios. Panels A and C report the k test period returns when there is no time gap between the rank and test periods, while Panels B and D report the test result when skipping one month after hedge portfolio formation.
The results suggest that the PC- and DY-based style momentum strategy is profitable at least up to 12 months and possibly longer according to the 3-, 6- and 12-month sorting. Style momentum effect is a bit shorter based on a 12-month ranking period and two extreme BM-based style portfolios in the test. When using two extreme styles, a style momentum based on characteristics variable PC and the 3month ranking period and the 3-month test period without skipping a month (hereafter SM-PC (3,3,0)) yields the average monthly return of 48 basis point (abbreviated as ‘BPS’ hereafter), while the SM-PC (3,12,0), SM-PC (12,3,0) and SM-PC (12,12,0) strategies generate monthly average performance of 34 BPS, 98 BPS and 33 BPS, respectively. In comparison to PC-based results, the SM-BM (3,3,0), SM-BM (3,12,0), SM-BM (12,12,0) and SM-BM (12,12,0) strategies yield 57 BPS, 29 BPS, 63 BPS and 19 BPS monthly returns, respectively, and the SM-DY(3,3,0), SM-DY (3,12,0), SM-DY (12,3,0) and SM-DY (12,12,0) strategies have respective monthly performance of 74 BPS, 47 BPS, 77 BPS and 45 BPS. These returns are significant at conventional level (except for SM-BM (12,12,0)).
For a robust check, results are also presented when skipping one month between ranking period and test period. Lo and MacKinlay (1990) and Jagadeesh and Titman (1995) show that portfolios can exhibit positive serial correlation due to lead-lag effect. Jagadeesh (1990) also show the effect of bid-ask spread in the return calculations.
To mitigate such effects on the style portfolios, Panel B and D report the style momentum returns when skipping one month.
It can be seen that except for SM-BM strategy, the style momentum profits are still significant in short and intermediate term up to 9 months. Using four extreme styles instead of two slightly improve the style momentum performance but such change is not material (Panel C). It is noteworthy that the returns for hedge portfolios are always positive because the holding periods are overlapping. The style momentum payoffs are strong over intermediate horizons and they generally increase for longer rank periods and decrease when the test periods become longer. The long-term reversal of style momentum returns is consistent with the story of Barberis and Shleifer (2003).
While style momentum based on firm characteristic variable PC, BM and DY are all profitable, their return magnitude varies. It is evident that the returns and the duration of style momentum are weaker and shorter for BM-based strategy as compared to PC- and DY-based styles, suggesting that the mispricing of styles based on BM factor are less severe relative to styles base on PC and DY. This may imply that the information content contained in characteristics BM is much efficient. Fama and French (1992) argue that BM is a risk factor relating to the variations in cross-sectional expected stock returns. It is plausible that because investors understand the widely accepted three-factor model and use it to pricing asset values, the misspricing occurs less severe on style level based on BM sorting.
It is interesting further to examine how different style portfolios (P1-P9) perform on the quarterly and annually basis. One may ask if winner and loser styles cluster in a few stocks with certain characteristics, and/or what the cumulative quarterly or annual profit would be if an investor follows the different investment styles represented by P1-P9 portfolios.
Table 4 displays the best and the worst styles and the corresponding cumulative returns based on 3-month and 12-month rank periods starting from 1982 to 2004. It is evident that value styles tend to be the winner style and growth style tend to be the loser style, in particularly when the ranking period is longer, which is consistent with general findings that value strategy works at long-term. For example, for styles based on PC, SV portfolio has been the winner in 20 out of 92 ranks, and LG portfolio been the loser style in 19 out of 92 ranks according to quarterly sorting. If sorting is based on past 12 months, SV is the winner in 49 out of 92 and LG being the loser in 26 out of 92 ranks. Similar findings apply to BM and DY based style portfolios. This findings that momentum profits differ across stocks with certain characteristics are consistent with the literature. Previous studies show that momentum returns are higher for small stocks (Hong et al. (2000)), and stocks with high market-to-book ratios (Daniel and Titman (1999)). More recently, Fama and French (2012) also document that momentum returns differ across size groups.
Specifically, momentum returns decrease from smaller to large stocks.
Table 4-3 The profitability of style momentum strategies Starting in January 1982, 9 style portfolios (P1-P9) are ranked every month by their performance in the past J months (J = 3, 6, 12). Hedge portfolios are formed to buy the top (or the top two) winner style portfolio(s) and to sell the corresponding loser portfolio(s). The hedge portfolios are held for K test periods (K=3, 6, 9, 12, 24, or 36 months). This table reports the equally weighted average returns per month. Panel A and B use two style portfolios to form the long-short hedge portfolios, while Panel C and D use 4 style portfolios to construct hedge portfolios. Panels A and C report the K test period returns when there is no time gap between the rank and test periods, while Panels B and D report the test result when skipping one month.
J = 12 Winner 0.0166 0.0159 0.0156 0.0152 0.0138 0.0142 0.0153 0.0145 0.0143 0.0141 0.0139 0.0141 0.0153 0.0157 0.0153 0.0151 0.0146 0.0144 Loser 0.0096 0.0116 0.0124 0.0128 0.0136 0.0134 0.0121 0.0137 0.0134 0.0131 0.0134 0.0132 0.0092 0.0103 0.0108 0.0111 0.0116 0.012 Hedge portfolio 0.0069 0.0043 0.0032 0.0024 0.0002 0.0008 0.0032 0.0008 0.0009 0.001 0.0005 0.0009 0.0061 0.0054 0.0045 0.004 0.003 0.0024 t - ratios 3.3131 2.1881 1.6953 1.2943 0.1499 0.5975 1.3012 0.3513 0.4043 0.5464 0.3243 0.6288 2.9669 2.8687 2.5309 2.3265 2.2166 2.1303
Table 4-4 Style momentum portfolios by quarter and year 1982-2004 At the beginning of each quarter (year), based on firm characteristic variable PC, BM and DY respectively, 9 style portfolios (P1P9) are ranked by their returns over the previous quarter (year), and the most extreme winner or loser portfolios are identified.