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However, Jegadeesh and Titman (2001) show that such hypothesis would imply that momentum returns should increase linearly with the length of the test period, which is unlikely the case. Jegadeesh and Titman (1993) assume that stocks can be priced by a single factor model, based on their decomposition that is similar to Equation (4), they conclude that autocorrelation in idiosyncratic returns drives the momentum effect. More recently, studies like Moskowitz and Grinblatt (1999), Lewellen (2002), Chan et al. (2000), Bhojraj and Swaminathan (2001) and Nijman et al. (2004) either assume multifactor models to explain the cross-section of stock returns, or relax the assumption for the return generating process to investigate the underlying driving forces that affect momentum returns.
In the behavioural model of Barberis and Shleifer (2003), style-based investors (switchers) are assumed to allocate their funds at style level, and the amount of fund they allocate to that style is determined by the underlying style’s relative performance to others. Barberis and Shleifer (2003) propose that, in the presence of switchers, Equation (4) is strictly positive (Proposition 6, p195), suggesting that stock-level momentum is profitable.
Now consider style-level momentum. Suppose that all 2N stocks can be grouped into 2 styles, X and Y, for a given firm characteristic. It should suffice to consider only 2 styles here because as Barberis and Shleifer (2003) argue many styles come in natural pairs. Stocks with high firm attributes constitute one style, while those with low values form the twin. Small size stocks versus large-cap stocks and value stocks versus growth stocks are typical examples of twin styles.
Assume further that each style has N stocks and each stock belongs to one and only one of the 2 styles. A style momentum strategy buys style with good performance and sells style that perform poorly.
Following Barberis and Shleifer (2003), the weights of stocks in the long-short hedge portfolio are
where RX,t and RY,t is the return of style X and Y in period t, respectively. The expected return of a style momentum strategy is therefore given by
This is equal to the expected return of the stock-level momentum.
4.3 Data descriptions and methodology The empirical test in this chapter uses all stocks in the U.K. stock market. Previous related studies such as Lewellen (2002), Chen (2003), and Chen and De Bondt (2004) mainly focus on the U.S. data in their analysis. However as at the time of writing there are so far no studies in the literature to investigate whether the general findings of prior studies also apply in developed markets like the U.K. based on all the stocks in the market19. Hence Chapter 5 provides useful insight in the understanding of the style-level strategy based on data set outside the U.S. in a different market and institutional environment.
In this study, monthly U.K. stock prices and equity characteristic information are collected from Thomson Financial Datastream over the sample period of January 1980 to December 2003. Similar to Chapter 3, the equity characteristic variables used to categorise stocks into
Aarts and Lehnert (2005) also test the style momentum strategy in the U.K.
market, but their sample is based on ftse 300 Index and therefore provides less insight as whether there is style momentum effect in the U.K. stock market given a small sample size. Clare et al. (2010) also test the U.K. style momentum, but they use ftse 350 Growth Index and the ftse 350 Value Index as proxies for the growth stocks and the values stocks, and ftse100 and ftse small-cap Index to proxy for the large-cap and the small-cap stocks, respectively.
different style portfolios are price-to-cashflow ratios (PC), book-tomarket ratios (BM), dividend-yields (DY) and market value (MV)20.The use of these firm attributes to identify styles is partly justified by Kothari and Shanken (1997), Chan et al. (1998), and Berk et al. (1999).
Kothari and Shanken (1997) find that both BM and DY track the timeseries of expected stock returns in 1926-1991. Chan et al. (1998) assert that MV, BM and DY are most important fundamental variables.
Berk et al. (1999) argue that firm-specific characteristics relate to the underlying state variables that determine firm’s systematic risk and expected returns. Hence firms with the same characteristics tend to have the same underlying pervasive forces affecting stock returns, implying that equity style portfolios based on such characteristics could price individual stock returns. This chapter forms value and growth portfolios based on research variable PC, BM and DY. The reason for the use of these variables for a broad value-growth style momentum is to test its robustness.
At the end of December each year, all U.K. stocks are divided into 2 parts based on one firm characteristic value X (X = PC, BM, DY, respectively). Stocks in Part 1 all have X 0 and stocks in Part 2 all have X = 0. Only stocks denominated by local currency (£) are included in the analysis and those denominated by foreign currencies are excluded from the sample. Following the literature, stocks that belong to financial sectors are also excluded because their firm attributes do not have the same meanings as non-financial stocks do (Fama and French (1996)). Since the style variables used in this study are price-related ratios that relate to cash flow news, stocks in Part 2 (named as P10) are NOT studied as these stocks either do not have The definition of these variables can be seen in Chapter 3.
meaningful firm attribute values, or simply do not have such data in data source at hand. Therefore only stocks in Part 1 are covered throughout the study in this Chapter. For each firm characteristic variable, all stocks in Part 1 are ranked independently by their end-ofyear MV and X in ascending order and are further allocated to 3 equal-sized MV and 3 equal-sized X groups, resulting 9 (intersection) style portfolios (P1-P9). Firms with share price = £1 at the time of portfolio formation are excluded to avoid the influence of extreme price movements in low price stocks.21 After style portfolio formation at the end of each year, the style category of a stock belongs to (i.e. P1-P9) is fixed for the next 12 months, regardless whether the firm’s characteristic value X changed in the following year. If a firm is delisted during a year, the proceeds from the sale of the stock are invested equally in other firms in the portfolio. Hence there is no survival-bias in the sample and in essence the style portfolios are rebalanced annually.
Figure 4-1 illustrates 9 style portfolios based on independent two-way Chen and De Bondt (2004) only test BM based style portfolios and their P10 group is for those do not have DY values. They also exclude stocks with price $1. It is noteworthy that by construction the number of stocks in each style portfolio P1-P9 is not identical.
sorting of the size and value-growth dimensions. These portfolios are small-cap growth (SG), small-cap blend (SB), small-cap value (SV), mid-cap growth (MG), mid-cap blend (MB), mid-cap value (MV), largecap growth (LG), large-cap blend (LB) and large-cap value (LV). These style portfolios are consistent with the investment style concept widely applied by practitioners in the market. For example, the Morningstar style classification system categorises investment funds into small, mid-cap, large size, or growth, blend and value. The interaction of these styles forms 9 cells in the style box. Morningstar style definition is widely followed as many funds name their products after the Morningstar style analogue. Some style benchmarks such as S&P/BARRA indexes, S&P 500, Mid-Cap 400, and Small-Cap 600 are also sorted by BM to create additional style indexes such as S&P 500 Growth, S&P 500 Value, Mid-Cap 400 Growth, Mid-Cap 400 Value, Small-Cap 600 Growth, and Small-Cap 600 Value. It is noteworthy that the style portfolio created here are also implemental in market practice22.
4.4 Characteristics of equity style portfolios Table 4-1 characterises the 9 style portfolios. For comparison purpose, statistics for stocks in Part 2 (named as P10) are also displayed. The sample size based on PC, BM and DY sorting is different because not all stocks have all available data for these variables.
One may be concerned with the availability of the company characteristic values at the end of each December since firms release their financial reports on a quarterly or semi-annually basis. Institutional investors generally do their investment research based on proprietary or outsourced database and information in such database is updated timely to reflect the firm’s latest financial status.
It is suggested that the firm characteristics of most style portfolios (P1-P9) vary dramatically over time. From 1980 to 2000, the average PC ratio of SG and MG style portfolios (based on PC, hereafter SG-PC, MG-PC and etc.) increases and peaks in year 2000. Coincidentally, the average BM ratios for stocks in BM-based portfolios and the average DY ratios for stocks in DY-based portfolios tend to demonstrate a decline trend before 2000. At the end of 2003, LG companies have an average PC ratio 29.76, BM ratios 0.21 and DY 1.65, while stocks in SV portfolios have average PC, BM and DY ratios of 4.39, 1.96 and 10.34, respectively. The statistics represents the cross-sectional average percentile rank of 85%, 36% and 18% based on PC, BM and DY respectively for LG portfolios, and 43%, 78% and 83% for SV portfolios in 2003. It is noted that the PC ratios are more influenced by the size of the stock than BM and DY ratios do. For example, the average PC ratios are much higher for stocks in SG than in LG from 1980 to 2003, while the ratios of BM and DY are less volatile for the two style portfolios. Thus suggests that PC portfolios may demonstrate more size effects.
At the end of 2003, LG-PC, LG-BM and LG-DY style portfolios have average market value around £3.16 billion, £2.50 billion and £ 4.19 billion, respectively. In contrast, the average market value of SV-PC, SV-BM and SV-DY portfolios are only £11.1 million, £6.3 million and £17.1 million, respectively. Table 4-1 also reports the statistics based on 5-year interval from 1980 to 2000 and the average percentile rank of stocks in each style portfolio. As of end of year 2003, the average stocks in LG-PC, LG-BM and LG-DY style portfolios are larger in size than 85%, 82% and 89% of all stocks respectively in the market; this is in contrast to the rank of 95%, 95% and 78% respectively in yearend 1980. Meanwhile, stocks in the SV-PC, SV-BM and SV-DY portfolios are larger in size than 22%, 15% and 29% other stocks in end of year 2003, while the statistics is 55%, 52% and 9% in 1980, respectively.
Table 4-1 also presents the time-series average market value of each style portfolio relative to the cumulated value of all stocks. It shows that the data vary dramatically over time. At the end of 2003, for company attribute PC, large-cap stocks tend to be sorted into large blend portfolio (LB, P8) followed by large growth styles (LG, P9). The average market value of LB-PC and LG-PC portfolios represent 47% and 24% of the market value of all stocks. On the other hand, stocks sorted on BM are biased to LG and LB portfolios. LG-BM and LB-BM style portfolios count for 37% and 29% of the market value, respectively. As for characteristic value DY, similar to PC sorting, stocks tend to be classified into LB and LG portfolios and they represent 40% and 28% of the market value of all stocks, respectively.
Interestingly, there seems to be a trend that over time more and more stocks become growth-oriented based on PC and BM sorting from 1980 to 2000. Large growth portfolios defined by PC, BM and DY all dominant in terms of the size as a fraction of the summed value of all stocks in the market, partly reflecting the peak of the bubble for growth stocks in year 1999-2000. This is also evidenced by the extreme variations in average PC ratios for stocks in SG-PC (564.28) and MG-PC (278.12) portfolios in year 2000.
Table 4-2 documents the average monthly performance of passive style portfolio (P1-P9) based on PC, BM and DY during January 1980 to December 2003. For comparison purpose, stocks in Part 2 are treated a portfolio named P10. All returns are calculated using value weighted schemes. It can be seen that the sample sizes are different since not all stocks have all firm characteristic data in the database.
Hence, the time-series average number of stocks in P1-P9 portfolios is 810, 926 and 1283 based on PC, BM and DY sorting, respectively.
Correspondingly, the average number of stocks assigned to P10 is 830, 715 and 356. Hence all style portfolios are fully diversified in general sense.
Consistent with previous studies such as Gregory et al. (2001) for U.K.
market data, equity style portfolios demonstrate strong divergent return patterns. In general, value style portfolios earn higher returns than growth portfolios regardless how value and growth style is defined, and returns are lower for large-cap stocks. But the magnitude of value premium varies depending on different style descriptors. It is also evident that stocks perform exceptionally better in January (except for LG portfolios). Moreover, amongst P1-P9 styles based on different firm characteristic variables, small value portfolios are found to have performed best and large growth portfolios done worst in 2 out of 3 outcomes. For example, SV-PC style earns average monthly returns of 2.5%, and that for SV-BM and SV-DY is 1.92% and 1.65% respectively. This is in sharp contrast to returns of 0.74% (LG-PC), 0.86% (LG-BM) and 0.68% (LG-DY). It is noted that along the size dimension for PC- and BM-based styles, the average spread between small and large size value portfolios are larger than that between growth portfolios of different size. But it is opposite for styles based on DY, which suggests that along the size dimension the return spread between growth portfolios is larger than that of value portfolios.
While SV portfolios generally earn highest returns, the reported timeseries standard deviations would suggest that such portfolios are not necessarily the most risky ones. On the other hand, although LG portfolios have lowest returns, they are not necessarily less volatile.
For example, the time-series volatility for SV-PC, SV-BM and SV-DY is 5.25%, 5.09% and 4.72%, respectively, as compared to that of 5.09% (LG-PC), 4.96% (LG-BM) and 5.06% (LG-DY).