UK Industry Beta Risk

UK Industry Beta Risk Ross Davies and John Thompson CIBEF (www.cibef.com) Liverpool Business School Liverpool John Moores University John Foster Building Mount Pleasant Liverpool Corresponding Author Email Address: busjthom@totalise.co.uk October 2003

Abstract This paper reports investigations into monthly industry betas within the UK throughout the period 1/1/86 to 1/4/99. The simple market model was used to obtain estimates of industry betas. Initial estimation was carried out using OLS but, where the diagnostic statistics indicated the presence of ARCH effects, GARCH methodology was employed. After a satisfactory basic equation was obtained, the equations were re-estimated with dummy variables representing different stages of the trade cycle to ascertain whether the estimated betas were constant over the trade cycle. Some additional explanatory power was obtained. Finally additional dummy variables were added to the equations to see if the effects of the stock exchange crash in 1987 and/or the LIFFE/Euronext merger influenced the beta values. These were found to have little impact. 1 Introduction The empirical literature has shown that beta has shown a tendency to vary over time. In this paper we look at average betas for industry groups to examine whether betas have varied over the trade cycle and also whether there is further change in response to specific and identifiable shocks. We think it is important to identify the shocks a priori rather than to use the data to search for breaks by statistical methods. Data rarely speaks for itself. Consequently we have identified two potential breaks in the series. The first is the stock exchange crash in 1987 and the second the LIFFE/Euronext merger in 1999. The first break point was selected because the crash had a resounding effect in the markets. The second merger was purely domestic but it did suggest a closer integration of European derivatives markets, which may have affected stock trading. In section 2 we briefly survey the current literature before moving on, in section 3, to describe the data. In section 4 we start the empirical work by estimating betas and in section 5 discuss whether these are stable over time. Our conclusions are presented in section 6. 2 Literature Survey The relevant literature is voluminous so we have perforce to restrict our analysis to a few salient papers. As is well known the Capital Asset Pricing Model (CAPM) restricts the determinants of the price of a security to: 1 The risk-free rate of interest 2 The security s beta 3 The rate of return on the market model So that CAPM can be specified as 1 : 1 Strictly speaking equation (1) should be specified in terms of expectations but we have omitted the expectations operator for the sake of convenience. 2

R i,t = R f = β(r m R f ) + ε t (1) Critique of the CAPM has been directed to a number of these areas. First, and perhaps the most important, Roll [1977] argues that the market model should include all risky assets, i.e. both real and financial and that, therefore, CAPM is virtually untestable. Other critiques have been directed towards the methodology of estimation, the incorporation of other variables such as size effect, price to earnings ratio, leverage, book to market equity, macroeconomic variables (such as the industrial production index and inflation) and the stability of beta over the trade cycle. In this paper we concentrate on the last issue; i.e. whether beta is constant over the trade cycle though, of course, the state of the trade cycle would be expected to encompass a wide range of macroeconomic variables. As noted earlier, we shall also look at the behaviour of the estimated betas before and after the 1987 stock exchange crash and also a purely UK event namely the merger of LIFFE and Euronext in 1992. In fact studies concerning the role of macroeconomic variables in CAPM models are quite limited in number. Studies by Fama and French [1989], Chen [1991] and Ferson and Harvey [1991] have found a relationship between returns and macroeconomic variables representing the state of the economy. Jaganathan and Wang [1996] used the interest rate spread between low and high rated bonds to capture trade cycle effects. In a similar study using Australian data over the period January 1974 to December 1992, Ragunathan, Faff and Brooks [2000] used dummy variables to represent the trade cycle and found the betas for a five out of 23 industry groups were significantly different during the expansion and contractionary phases. They also examined the effect of other countries trade cycles (US and Japan) and found 9 of the industrial groups these to have a significant impact on estimated betas. Our study will follow similar methodology to that adopted by Ragunathan et al but will concentrate on UK data and will utilise alternative estimation methods to accommodate estimation problems thrown up by the estimating equations diagnostic statistics. 3 Data The return was defined as log(p t /P t-1 ) where P refers to the share price and t to the current period and t-1 to the previous period (months in the case of this study as is noted below). The basic data used in this study is index data classified according to category of industry. The precise classifications used were those utilised in the DataStream data bank 2 with 38 value-weighted industry indices consisting of all shares quoted on the London Stock exchange. The market proxy was the return on the FTSE all share index and we recognise that this market return does not satisfy the Roll critique since it certainly does not include all risky assets. Decisions on the frequency of observation require a trade-off between the number of observations and the incorporation of noise in the series. We decided on monthly data because it gave a reasonable number of observations (160) whilst eliminating much of the noise present in say daily observations. This decision also impinges on the choice 2 We used DataStream rather than the FTSE indices to avoid shares moving in and out of the index. 3

of the time period. A problem exists because DataStream revised their industrial classifications in April 1999. This left us with the choice of utilising the earlier period (i.e. prior to April 1999) giving the 160 observations noted above or the later period (i.e. up to 1/08/03) which only provided 53 monthly observations. We chose the earlier period running from 1/1/86 to 1/4/99 whilst recognising the potential problem of the data being outdated. Determining cycle dates is quite difficult because whilst important macroeconomic series tend to move together the degree of synchronisation is not exact. However this task is undertaken for a number of countries by a section previously under the scope of Columbia University, but now recognised in its own right as the Economic Cycle Research Institute (ECRI) 3. The calculation of cycle turning points and the thought process of their derivation is best summed up by the following derived from the institutional website: Business cycles are pronounced, pervasive and persistent advances and declines in aggregate economic activity, which cannot be defined by any single variable, but by the consensus of key measures of output, income, employment and sales. These indicators define "the economy" and constitute ECRI's coincident indexes for each country. ECRI provides the following information for the UK for the period of our study: Trough March 1981 Peak May 1990 Trough March 1992 Consequently the dummy variables take the value 1, for the periods 1/1/86 to May 1990 and March 1992 to April 1999 (i.e. the expansionary stages) and 0 for the period June to March 1992 (i.e. the contractionary stage). The second set of dummy variables apply to the specific events mentioned earlier, i.e. the 1987 crash and the LIFFE merger. The dummy variable values pre October 1987 were assigned the value of 0 and the value of zero and the values after that date 1. For the LIFFE/Euronext merger the values prior to 1/4/99 assumed 0 and those after 1. As we are proposing to use OLS estimation it is necessary to examine the degree of integration of the returns for the individual industry categories and the market proxy. The basic regression estimated to determine the degree of integration is: Y t = α + βy t-1 + δtime + ε t (2) where Y refers to the return for the series in question. The test involves testing whether β = 0 or is significantly less than zero in which case we are able to reject the hypothesis that the series is I(1) and therefore conclude it is stationary. The resulting Dickey-Fuller test is sensitive to autocorrelated error terms and there are two ways of dealing with this problem The first approach consists of 3 The website address for this data source is www.businesscycle.com 4

adding lagged values of the dependent variable as additional explanatory variables in equation (2) above; i.e. the Augmented Dickey-Fuller (ADF) test and the second due to Phillips and Perron [1988] amends the test statistic. Both approaches are adopted by us though in effect the introduction of lags was unnecessary as the LM test in all cases failed to reject the hypothesis of zero autocorrelation. The first step in the analysis is to test the significance of the time trend. This was done with reference to the critical values contained in Dickey and Fuller [1981]. In no case was the coefficient on time significant so that equation (2) was estimated without the time trend and produced estimates of β for all 38 industrial category returns, which were significantly less than 0 at the 1% level. These results were also confirmed through calculation of the Phillips-Perron statistics, which were again significantly negative at the 1% level. Consequently we were able to reject the null hypothesis that the variables are I(1) and conclude that in fact the returns were stationary. 4 This permits us to use OLS regression to estimate the relevant betas and we discuss this in the following section. 4 Estimation of the Basic Equation We first of all proceeded to estimate the following equation for all the industrial categories: R i,t = α + βr m,t + ε t (3) Where R refers to return and the subscripts i & m refer to the individual industry category and market return respectively. The diagnostic statistics were then examined to see if the residuals were free of autocorrelation and/or any ARCH effects. In the former case lagged values of the dependent variable were added until the autocorrelation was eliminated. In the case where ARCH effects were detected a GARCH model was estimated. A summary of the estimation methods are shown in table 1. In the cases of autocorrelated error terms, equation 3 was amended by adding lagged dependent variables until such time as the relevant LM test enabled the rejection at the 5% level of the hypothesis that the error terms were autocorrelated. Hence equation (3) was transformed to: R i,t = α + βr m,t + Σπ j Ret i,t-j + ε t (3a) Turning now to the equations displaying Arch effects, these were re-estimated using a GARCH (1,1) 5 model; i.e. Mean equation: R i,t = α + βr m,t + ε t (4) Variance Equation: σ 2 t = α + γε² t-1 + δσ 2 t-1 4 For the sake of brevity the detailed results have been omitted from the paper. These and all other omitted detailed statistics are available from the authors on request. 5 There is a large number of GARCH models in existence but the most commonly used model is the GARCH(1,1). On grounds of parsimony, this model is to be preferred if the resulting estimated equation provides satisfactory diagnostic statistics. 5

The estimated coefficients were quite well estimated. The GARCH parameter (δ) was significantly different from zero at the 1% level in 11 out of the 12 equations estimated with the remaining coefficient being significantly different from zero at the 5% level. The significance of the ARCH parameter was weaker; 2 out of the 12 estimates being significant at the 1% level, 2 at the 5% level and 6 at the 10% level. No remaining ARCH effects were detected after the estimation of the GARCH model. The estimates of equations (2) and (4) are shown in table 2. Generally the estimated equations have a satisfactory level of explanation as evidenced by the adjusted R² values. The constants are rarely significantly different from zero. However the values of the betas appear to be too closely grouped around 1. 5 Stability of Betas 5.1.1 Behaviour over the Trade Cycle As discussed in section 3, we introduce dummy variables to account for the upswing and downswing phases of the trade cycle. An alternative approach would have to use the Chow test but this requires normality of the residuals, which is absent in some 11 of the estimated equations. Consequently it would be sensible to preserve consistency by using dummy variables in each of the equations. In the OLS estimated equations we tried a dummy variable to capture a possible change in value of beta during the trade cycle. In the GARCH equations the same approach was taken with respect to the mean equation. The resulting equation took the general form: R i,t = α + βr m,t + Σπ j Ret i,t-j + θd c.r m,t + ε t (5) where D c represents the cycle dummy variable Table 3 shows the estimated coefficient of the dummy variable where the coefficient was significant at the 10% level. Consequently only 7 of the slope dummies were significant at this level out of a potential of 38 coefficients (i.e. 18%). The industries recorded in table 3 are mainly domestic industries though this is not true of two of the categories, i.e. Oil, Exploration & Production and pharmaceuticals. Also it is noticeable that the coefficients for Diversified Industrials, Services and Transport are negative implying that beta decreases for those industries as the economy expands. The size of these changes seem to be quite large. In the case of the GARCH estimates we also examined whether the variance of the estimating equation had changed over time. This was done by incorporating a dummy slope variable in the GARCH variance equation so that it became: σ 2 t = α + γε² t-1 + δσ 2 t-1 + θd c. R m,t (6) Applying the same criteria to the significance of θ in equation (6) we find that 7 of the estimates were significant at the 10% level (64%) and 5 at the 5% level (45%). These are shown in table 4. Most of the coefficients are positive suggesting that the variance increases as the economy expands, but two are negative (construction, utilities) are 6

negative suggesting that the variance decreases as the economy expands. In all cases however the magnitude of the estimated dummy variables is quite small. 5.1.2 Breaks in the Series We pursued the same methodology to test for the effects of breaks in the series. The two potential breaks we considered were the 1987 stock exchange crash and the LIFFE/Euronext merger. In each case where dummy variables were significant in the case of trade cycles, the respective dummy variable was retained in the estimating equation so that the break dummy became an extra variable. Thus the estimating equation became: R i,t = α + βr m,t + Σπ j Ret i,t-j + θd c.r m,t + γd 87.R m,t + ε t (7) where D 87 represents the stock exchange crash dummy variable As far as the first break was concerned, the results for the above equations show that the dummy variable in (7) was significant at the 10% level for only 5 out of a potential 37 6 equations (13.5%). These were Banks-Retail, Engineering, Financials, Health Care and Telecommunications. In four out of the five cases the dummy variable was signed positively. In the remaining case (health care) it was negatively signed. When the level of significance is reduced to 5%, four remained with financials dropping out. These results are detailed in table 5 As far as the LIFFE/Euronext merger is concerned, the estimating equation took the general form: R i,t = α + βr m,t + Σπ j Ret i,t-j + θd c.r m,t + λm.r m,t + ε t (8) where M represents the merger dummy variable The results for equations (7) detailed in table 6 show that the dummy variable was significant at the 10% level in only 11 out of a potential 38 equations. These are: Alcoholic Beverages, Banks-Retail*, Consumer Goods, Chemicals, Diversified Industrials, Financials*, Food Producers, General Industrials, Household Good & Textiles, Other Financial*, Paper and Packaging & Printing. Out of these industries, the dummy variables are positively signed in the case of the industries indicated by * and negative in all other cases. When viewing at the 5% level of significance the only following are significant: Alcoholic Beverages, Chemicals, General Industrials, Household Good & Textiles, Other Financial and Paper, Packaging & Printing (all these dummy variables except for other financial are negatively signed). This translates into 6 out of a potential 38 industries (16%) at the 5% level. Again the magnitude of the coefficients is quite small. 6 The category retailers general was omitted from these tests because of the severe autocorrelation problems involved in its estimation. 7

6 Conclusions We obtained OLS and GARCH estimates of our basic equation, i.e. equation (3). After having obtained satisfactory estimates of this equation we then examined the stability of the estimated betas i) over the trade cycle and ii) in response to external shocks. Our results show that: 1. About 20% of Betas seem to vary over the trade cycle. The magnitude of the changes seems quite large. 2. The variance of the Beta estimating equation varies in about 45% of the GARCH estimates but with small magnitude 3. The stock exchange crash seems to have had minimal effects on betas but with a small size 4. The LIFFE/Euronext merger also seems to have had an effect again but with a small size We propose to extend our work in two directions. First, we will try alternative series representing the market return to see if it is possible to obtain a greater degree of variability in the estimated betas and second, we will investigate whether other country cycles have an effect on UK betas. This second facet was examined by Ragunathan et al [2000] for Australia and trade cycles US and Japan did materially affect the Australian betas. We would not expect the same effect in the UK given the larger size of its economy. 8

Table 1: Summary of Estimation Results of Basic Equation (3.1) No Autocorrelation or ARCH effects Banks, Retail Breweries Pubs & Restaurants. Distributors Electronic & Electrical Engineering Vehicles Extractive Industries Financials Insurance Investment Trusts Life Assurance Leisure & Hotels Oil Integrated Paper, Packing & Print. Property Resources Retailers, Food Services Support Services Telecommunications Tobacco Transport Autocorrelation Diversified Industrials Household Good & Textiles Media Oil, Exploration & Production Retailers General ARCH Alcoholic Beverages Building Materials & Merchandise Consumer Goods Chemicals Engineering Health Care Other Financial Pharmaceuticals Utilities Autocorrelation and ARCH Construction Food Producers General Industrials 9

Table 2 Final Estimates Industrial Category Estimation Method α β R ² Alcohol Beverages GARCH 0.002 (0.1) Building Materials & GARCH -0.005 Merchants (0.01) Banks Retail OLS 0.003 (0.9) Breweries Pubs OLS 0.001 & Restaurants ().01) Consumer Goods GARCH 0.004 (2.0) Chemicals GARCH -0.005 (1.8) Construction GARCH -0.006 (1.5) Diversified Industrials OLS -0.010 (3.6) Distributors OLS -0.006 (1.9) Electronic & Electrical OLS -0.001 (0.5) Engineering GARCH -0.003 (1.1) Engineering, Vehicles OLS -0.002 (0.6) Extractive Industries OLS -0.003 (0.6) Financials OLS 0.001 (0.3) Food Producers GARCH 0.001 (0.5) General Industrials GARCH 0.002 (1.2) Health Care GARCH -0.003 (0.9) Household Good & Textiles OLS -0.005 (1.4) Insurance OLS -0.005 (1.7) Investment Trusts OLS -0.001 (0.5) Life Assurance OLS 0.003 (0.9) Leisure & Hotels OLS -0.001 (0.5) 1.013 (15.4) 1.144 (33.3) 1.197 (20.3) 0.837 (15.6) 0.966 (28.9) 1.041 (28.9) 1.200 (16.6) 1.098 (19.4) 1.110 (20.0) 0.923 (17.2) 1.100 (22.8) 1.289 (17.0) 1.117 (12.4) 1.138 (31.0) 0.853 (21.0) 1.067 (35.1) 0.898 (18.1) 0.973 (15.1) 1.151 (20.1) 1.019 (34.0) 0.971 (15.1) 1.090 (21.5) 0.672 0.668 0.723 0.607 0.802 0.713 0.654 0.737 0.718 0.654 0.730 0.648 0.494 0.859 0.725 0.777 0.651 0.616 0.719 0.880 0.589 0.744 10

Media OLS -0.001 (0.3) Oil, Exploration OLS -0.009 & Production (1.3) Other Financial GARCH 0.001 (1.8) Oil Integrated OLS 0.003 (1.0) Pharmaceuticals GARCH 0.008 (1.8) Paper, Packaging OLS -0.006 & Printing (1.7) Property OLS -0.004 (1.3) Resources OLS 0.002 (0.6) Retailers, Food OLS -0.001 (0.2) Retailers General OLS -0.001 (0.3) Services OLS -0.001 (0.3) Support Services OLS 0.001 (0.4) Telecommunications OLS 0.003 (0.9) Tobacco OLS 0.003 (0.7) Transport OLS -0.001 (0.5) Utilities GARCH 0.002 (0.5) 1.157 (21.4) 1.210 (9.3) 1.058 (18.8) 0.810 (12.6) 0.983 (18.2) 1.049 (15.7) 0.942 (14.6) 0.884 (14.6) 0.691 (11.5) 0.846 (14.1) 0.978 36.7 0.997 (18.5) 0.946 (14.3) 0.940 (10.9) 1.009 (23.3) 0.824 (16.9) 0.763 0.409 0.698 0.500 0.485 0.608 0.572 0.455 0.455 0.607 0.895 0.683 0.565 0.425 0.775 0.512 11

Table 3 Industries where the Slope Dummy is Significant at the 10% Level Industry Estimation Method θ t statistic Consumer Goods GARCH 0.177 2.4 Diversified Industrials OLS -0.328 2.1 Health Care GARCH 0.320 3.3 Oil, Exploration & Production OLS 0.793 2.2 Pharmaceuticals GARCH 0.004 2.2 Services OLS -0.133 1.7 Transport OLS -0.221 1.7 Table 4: Garch Estimates of Variance where the Slope Dummy is significant at the 10% Level or above Industry Θ t statistic Alcoholic Beverages 0.002 1.8 Consumer Goods 0.001 2.6 Construction -0.008 2.3 Engineering 0.002 2.2 Health Care 0.004 2.8 Pharmaceuticals 0.005 2.2 Utilities -0.003 1.7 Table 5 Industries where the 1987 Crash Dummy is significant at the 10% Level or above Industry Estimation method γ t statistic Banks OLS 0.018 2.0 Engineering GARCH 0.008 2.2 Financials OLS 0.010 1.9 Health Care GARCH -0.014 2.2 Telecommunications OLS 0.022 2.2 12

Table 6 Industries where the LIFFE/Euronext Dummy is significant at the 10% Level or above Industry Estimation Method λ t statistic Alcoholic Beverages GARCH -0.014 2.3 Banks, Retail OLS 0.011 1.9 Consumer Goods GARCH -0.008 1.9 Chemicals GARCH -0.014 2.8 Diversified Industrials OLS -0.010 1.7 Financials OLS 0.007 1.8 Food Producers GARCH -0.006 1.7 General Industrials GARCH -0.007 2.8 Household Good & Textiles OLS -0.015 2.1 Other Financial GARCH 0.016 2.8 Paper, Packaging & Printing OLS -0.014 2.1 13

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