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These variables represent a firm’s fundamental characteristics and are generally found to be associated with the variations on average stock returns. In market practice, many investors also use these variables to classify stocks into different size and value-growth styles to simplify their asset allocation process. The definition of these variables in
Datastream is as follows:
This study was conducted in 2005-2006, thus the most recent available sample data for the research was up to December 2004.
DY: the dividend yield. It is the dividend per share as a percentage of the share price. In Datastream the underlying dividend is calculated as the anticipated payment over the following 12 months and maybe calculated on a rolling 12month basis. Special or one-off dividends are generally excluded.
Figure 3-1 depicts the time-series number of stocks that have positive values for a given firm characteristic value in the sample period. It is suggested that for a given month not every stock has all the 4 characteristic information available in Datastream. Most stocks have market value information but roughly only half of the stocks have readily available dividend yield data. Hence style investing based on different characteristic variables would have different sample size.
Figure 3-1 Number of stocks based on the available firm characteristics in the sample The time-series number of stocks with positive firm characteristic values is plotted over the period 1979:12 to 2004:12. It is shown that for a given month, not every stock has all the 4 variable information used in the study.
As mentioned in previous section, the 4 macroeconomic variables used in this study are default risk premium (def), dividend yield (div), the term spread (term) and short-term interest rate (yld). def is the yield spread between the lower- to higher- bond and is measured as the yield on corporate bonds less the yield on long-term U.K.
government bonds. div is the dividend yield on the overall market index as proxied by the Datastream U.K. market index. term is the difference between the 20-year gilt and 3-month Treasury bill yields and the short-term interest rate yld is proxied by the 3-month Treasury bill yield. Table 3.1 presents the correlation matrix of these variables.
Table 3-1 Correlation Matrix of the Macro Variables This table shows the correlation matrix between the macro variables used in the study. Panel A reports the raw correlations. In Panel B the variable yld1 is the innovations of the raw yld regressed on variables def, div and term, representing the raw yld’s explanatory part orthogonal to variable def, div and term in regression (7).
Panel A shows that the variable yld is highly correlated with div and term, while correlations among other variables are relatively low. The correlation between variables yld and div is 0.7746 and the correlation of yld with term and def is -0.5908 and 0.1628, respectively. The observed high correlations between yld and other variables suggest that Equation (7) may suffer from multicollinearity problem. To eliminate this problem, the variable yld is regressed on other three variables (def, div, term) and the innovation of the regression, yld1, is used to replace the original variable yld in Equation (7), representing its explanatory power that is orthogonal to def, div and term. This process is mainly econometrically motivated. For notation purpose, the variable yld1 will still be noted yld later. After this procedure, as reported in Panel B the correlations between the 4 variables become reasonably low.9
3.3.2 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 It is worth noting, however, that the empirical results are qualitatively the same in this study should this procedure is not applied.
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.
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) schemes.
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).
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 1 to t where t is the current month. Portfolios Q1-Q5 for different characteristic variables are formed based on equally-weighted and value weighted schemes.
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.
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 C1 Ck j k tests will be j 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.
3.4 Empirical results 3.4.1 The returns of simple style investing strategies Table 3-3 documents the average monthly returns during the K-month holding periods spanning from January 1982 to December 2004 for simple style investing strategies that buy and sell different stock groups based on past J-month firm characteristics and subsequently hold for K months.12 For brevity, only formation and testing periods of (6, 12) and (12, 6) months are reported (for other formation and holding periods the results are qualitatively similar). Since style portfolios are built using the overlapping method, there may be autocorrelations in the time-series average returns. Hence the t ratios in brackets are calculated using Newey-West (1987) heteroscedasticity and autocorrelation consistent variance with lags equal to K, the testing periods.13 Table 3-3 suggests that, consistent with the literature, there is strong evidence of divergent style return patterns in the U.K. stock market.
For example, during January 1982 to December 2004, on average U.K.
value stocks outperform growth stocks at 1.66% (PC), 0.80% (DY) and 1.24% (MTBV) per month in the subsequent 12 months if stocks are classified using past 6-month characterises and returns are calculated using equally-weighted scheme. This is in contrast to value-weighted premiums of 1.28% (PC), 0.83% (DY) and 0.97% (MTBV). Moreover, if instead the stocks are categorised according to the past 12-month characteristics, equally-weighted average monthly value premiums in the subsequent 6 months after portfolio formation would be 1.82% To match the return prediction that requires at least 24 months observations, the tests are based on data starts from January 1982 rather than January 1980.
Using Fama-MacBeth (1973) approach will overstate the test statistics because of the autocorrelations of the returns series. It is reasonable to assume the lags equals to the number of the holding periods K because there are K portfolios involved in the calculation of monthly holding returns.
(PC), 0.88% (DY) and 1.36% (MTBV) as compared to 1.30% (PC), 0.82% (DY) and 1.00% (MTBV) of value weighted scheme. It is noted that in the same period the equally-weighted size premiums based on (6, 12) and (12, 6) are 0.90% and 0.97% respectively as compared to value weighted size premiums of 0.90% and 1.06% respectively. The value and size premiums are economically significant, and in most scenarios the style premiums within the subperiods are also significant.
Table 3.3 also reveals some evidence of seasonality in style return patterns.
Since the January effect is the most important calendar anomaly observed in the stock market, to better understand the style return properties, Table 3-3 also reports the January-only and nonJanuary-only average returns. It can be seen that the size premium and value premiums based on PC and MTBV are more pronounced in January than those in non-January months, while the value premium based on DY is less evident to show such January effect.
The interaction of styles is also evident in table 3.3. It is shown that equally-weighted value premiums are generally higher than value weighted premiums, suggesting that in this U.K. data set value stocks generally have much smaller market values than growth stocks, which is consistent with results showed in Table 3-2.
3.4.2 Style returns and the business cycles
While Table 3-3 offers some evidence for the style return differentials classified by different equity characteristics in the U.K. stock market, a question to ask is whether there are variations in style returns within the different stages in the business cycles. To pursue this question, the dynamics of U.K. economy are first analysed in the sample period. Given the lack of official data to define and identify the business cycle turning points for the U.K. economy, this section follows the traditional definition to define economic recession as two consecutive quarters of decline in real GDP growth. Graph 3.2 depicts the times-series of U.K. quarterly GDP growth over the period of January 1980 to December 2004.
Figure 3-2 U.K. GDP quarterly growth rate (1980:01-2004:12)
This graph depicts the time-series of U.K. real GDP growth rate over the period from January 1980 to December 2004. Data are obtained from the Datastream. According to the traditional definition of economic recession, 4 U.K. recession periods are identified, i.e. 1984:01-1984:06, 1986:01-1986:06, 2000:01-2000:06 and 2001:01-2001:06. The rest periods can be regarded as expansions.
0.08 0.06 0.04 0.02
-0.06 During the sample period, the U.K. economy has arguably experienced 4 economic recessions and 5 expansions. Specifically, during 1984:01and 2001:01-2001:06 the U.K. economy has seen two consecutive declines in real GDP growth rate, hence these periods are identified as recessions, and the rest are regarded as expansionary periods. It is also noted that as similar to the U.S., the recessionary periods have short durations than expansionary periods.
Table 3-4 reports the style investing returns in different economic states. For brevity only results based on formation and testing periods (12, 6) are reported. Style returns during recessionary periods are much volatile as compared to returns in expansionary periods. Style investing returns in recessionary periods are larger than those in expansionary periods, suggesting that on average return U.K. value premiums are larger when the economy is in bad regimes. The average equally-weighted value premiums during recessions are 2.81% (PC), 2.44% (DY) and 3.09% (MTBV) as compared to 1.72% (PC), 0.73% (DY) and 0.87% (MTBV) in expansions based on sorting of different firm characteristics. The returns based on value weighted scheme are also supportive of this finding. Coincidentally, the size premium is also found to be more pronounced during recessions. These results are consistent with recent empirical findings such as Kwag and Lee (2006) who suggest that the benefit of value investing is even greater during periods of contraction than expansion.