Style portfolio construction

To match the minimum 24 months observation of stock returns, the empirical tests in this chapter are based on data after January 1982. Starting from January 1982 to December 2004, at the end of each month, all U.K. non-financial stocks are categorised into quintiles in ascending order according to their firm characteristics as measured by the previous J-month average values of the style variables10_{. Stocks} that are newly listed during the previous J months or those with negative characteristic values will be excluded in the study. Following the literature all financial stocks are also excluded because Fama and French (1996) argue that the financial ratios of such stocks may not have the usual meanings as non-financial stocks do. Besides, all the dead or suspended stocks are added back to the sample when they are still “alive” in each point of time. Each month stocks are sorted into 5 quintiles, quintile 1 (Q1) has the lowest value of characteristic values and quintile 5 (Q5) has the highest values of average characteristics. The number of stocks in Q1 and Q5 is identical and

9 _{It is worth noting, however, that the empirical results are qualitatively the same}

in this study should this procedure is not applied.

10 _{One may well be concerned that whether the strategies discussed here are}

practically applicable given the fact that companies only disclose the financial reports on a quarterly or semi-annually basis. Arguably, this sort of ‘information lag’ should not be a problem for institutional investors. Institutional investors do their investment research based on proprietary or outsourced database and arguably information in that database will be updated timely. The use of the average value of past J-month information also smooths the possible data error or outliers, making the ranking more reliable.

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hedge portfolios are constructed by longing Q1 stocks and shorting Q5 stocks (for research variable DY, the hedge portfolio is to long Q5 and to short Q1). The hedge portfolios are built in two ways, i.e. the equally-weighted (EW) and the value weighted (VW) schemes11_. Correspondingly, the returns of the two schemes are reported for different quintiles to provide useful insight of constituent stocks’ return patterns. The hedge portfolios are rebalanced in K months after formation and monthly hedge portfolio returns are calculated following the ‘overlapping’ principle proposed by Jegadeesh and Titman (1993). Specifically:

1. At every month end, all stocks are ranked into 5 quintiles according to their average firm characteristic values over the previous J months, time t J 1to t where t is the current month. Portfolios Q1-Q5 for different characteristic variables are formed based on equally-weighted and value weighted schemes.

2. Style portfolio returns are measured in every month for the next K months after formation, t1 to tK. The return of Q1 (Q5) portfolio in period t1 is the average of the returns to the

top (bottom) quintile portfolios formed at t t, 1, ,t K 1 in period t1. Thus the return to the Q1 (Q5) asset class is the

average return to the K Q1 (Q5) portfolios formed consecutively over the previous K months.

3. The returns of hedge portfolios ( ,J K) are the average return to the self-financing portfolio Q1-Q5 over the entire sample periods.

11 _{The two weighting schemes help identify the basic interaction between size and}

value-growth styles because value weighted returns are biased to large-cap stocks and the equally-weighted returns are biased to small-caps.

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For every style variable, the average performance of hedge portfolios based on a combination of formation and testing period ( ,J K) = 6, 12, 24 and 36 months in the entire sample periods are reported. Thus for a combination of ( ,J K) strategy, a total of 1 1

j k

C C  j k tests will be

considered. The longer formation and testing period helps to investigate the return patterns in a long-term perspective.

Table 3-2 summarises the characteristics of quintile portfolios based on formation periods of 6, 12, 24 and 36 months. On the value-growth dimension, value stocks can be generally defined as stocks with low price to cash flow ratios (Q1 of PC), low market-to-book value ratios (Q1 of MTBV) or high dividend yields (Q5 of DY). The opposite is for growth stocks. It is shown that these firm characteristics provide consistent style definitions, i.e. stocks with low PC generally have higher DY and lower MTBV. On the size dimension, it seems that the size differential between large and small stocks is very large. Q1 stocks are mainly genuine small companies, while Q5 stocks are all blue chips. It is also recognised that small size stocks have higher PC ratios than those in other quintiles, and DY in both small and large quintiles are much higher than those in other quintiles. Besides, it is suggested that value stocks tend to have small firm size as compared to growth stocks.

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Table 3-2 Time-series average equity characteristics of quintile portfolios

This table shows the time-series average characteristics of style portfolios classified by equity characteristics PC, DY, MTBV and MV based on formation period J = 6, 12, 24 and 36 months. The sample period is from January 1982 to December 2004. The sample size for different characteristic variable is different.

PC DY MTBV MV (m) PC DY MTBV MV (m) PC DY MTBV MV (m) PC DY MTBV MV (m) Q1(L)(Value) 4.18 5.43 1.72 342.7 4.48 5.30 1.69 389.6 4.87 5.19 1.73 473.0 5.22 5.11 1.80 582.8 Q2 6.30 5.08 1.96 515.7 6.59 5.05 2.04 528.9 7.01 5.06 2.17 579.5 7.18 5.05 2.22 580.1 Q3 8.22 4.51 2.58 618.8 8.36 4.53 2.54 662.8 8.61 4.54 2.63 726.0 8.88 4.57 2.64 836.2 Q4 13.08 3.84 3.44 883.4 12.38 3.88 3.50 922.0 11.14 3.95 3.32 1037.4 11.11 4.03 3.40 1168.3 Q5 (H)(Growth) 25.93 3.55 4.63 832.2 25.35 3.58 4.53 916.4 23.48 3.62 4.15 1053.7 22.17 3.62 4.03 1173.6 Q1(L)(Growth) 30.91 1.64 4.88 1016.1 24.70 1.75 4.93 1101.9 22.03 1.92 4.88 1225.5 25.54 2.07 4.56 1313.5 Q2 18.64 3.07 3.12 989.8 23.09 3.17 2.99 1040.5 25.27 3.34 2.82 1152.8 20.60 3.47 2.73 1323.6 Q3 14.87 4.26 2.39 751.4 15.11 4.32 2.34 770.7 14.05 4.41 2.42 822.8 11.09 4.48 2.54 843.0 Q4 15.15 5.68 2.25 567.1 11.62 5.67 2.24 562.0 9.25 5.66 2.15 595.2 9.36 5.55 2.06 660.0 Q5 (H)(Value) 13.60 8.29 1.70 346.1 13.75 8.04 1.80 355.2 10.67 7.67 2.02 360.0 10.84 7.48 2.17 367.8 Q1(L)(Value) 11.53 5.76 0.75 228.6 11.24 5.53 0.78 243.7 10.51 5.28 0.83 251.8 10.30 5.10 0.87 287.3 Q2 18.62 5.42 1.20 382.3 18.05 5.34 1.23 398.6 16.59 5.21 1.28 454.6 12.12 5.15 1.33 479.6 Q3 35.05 4.85 1.70 500.4 31.12 4.86 1.72 516.7 22.67 4.87 1.75 559.6 14.89 4.87 1.80 640.8 Q4 25.30 4.00 2.54 760.4 23.40 4.07 2.53 835.5 17.34 4.19 2.53 933.6 18.60 4.27 2.54 1029.2 Q5 (H)(Growth) 25.90 3.05 6.11 806.5 27.73 3.14 5.84 847.7 30.65 3.30 5.50 970.1 23.55 3.41 5.26 1081.1 Q1(L)(Small) 28.39 9.97 3.69 5.2 25.98 9.71 3.14 5.7 22.88 8.46 2.81 6.6 19.16 7.17 2.52 7.6 Q2 33.14 5.26 2.49 15.4 36.69 5.05 2.42 16.7 25.96 4.99 2.35 19.4 13.34 4.98 2.40 22.2 Q3 25.51 4.70 2.92 39.5 25.33 4.68 2.95 43.2 25.10 4.68 3.14 50.5 25.34 4.70 3.20 58.4 Q4 23.32 4.24 3.52 129.6 22.57 4.26 3.43 140.8 21.34 4.32 3.37 163.7 18.51 4.39 3.32 187.5 Q5 (H)(Large) 12.98 7.53 3.98 1664.0 12.75 7.77 4.00 1769.3 12.59 8.25 3.86 1957.9 12.44 8.69 3.91 2147.2 PC DY MTBV MV Research Variable Quintiles Formation period (J) J = 6 J = 12 J = 24 J = 36

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