Data description

While U.S. markets data are widely used to develop ground theory, test asset pricing models and investigate the cross-sectional and time- series returns across different asset classes, this chapter will focus on the U.K. stock market only. The study of U.K. market is less covered

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in the extant style investing literature, and this chapter will be able to provide additional evidence to compare with other studies in different economic and institutional environments. The source of stock prices and firm characteristic information are obtained from the Datastream. The sample in this study spans from December 1979 to December 20048 _{. Stocks that are denominated by foreign currencies are} excluded because their returns are also affected by foreign exchange rate fluctuations. All delisted (dead or suspended) stocks are retrieved and added back to the sample when they were “alive” in a specific time period. The firm characteristics used to classify stocks into size or value-growth groups are market capitalisations (MV), price to cash flow ratios (PC), market to book ratios (MTBV) and dividend yield (DY). 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:

 MV: market capitalisation. It is equal to the share price

multiplied by the number of ordinary shares in issue displayed in millions of units of British pounds (£).

 PC: price to cash flow ratios. It is the price divided by the

adjusted price cash earnings per share for the appropriate financial year end, which is adjusted for any exception and extraordinary profits or losses.

 MTBV: market value to book value ratios. This is the ratio of

the market value divided by the net book value. Essentially it is the inverse of book-to-market ratio (BM).

8 _{This study was conducted in 2005-2006, thus the most recent available sample}

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 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 12- month 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),

0 200 400 600 800 1000 1200 1400 1600 1800 2000 PC DY MTBV MV

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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).

def yld div term

def 1 0.1628 0.0907 -0.2311

yld 0.1628 1 0.7746 -0.5908

div 0.0907 0.7746 1 -0.0859

term -0.2311 -0.5908 -0.0859 1

def yld1 div term

def 1 0.0000 0.0907 -0.2311

yld1 0.0000 1 0.0000 0.0000

div 0.0907 0.0000 1 -0.0859

term -0.2311 0.0000 -0.0859 1

Panel A Raw Correlation Matrix

Panel B New Correlation Matrix

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

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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