The study investigates the relationship between accounting variables and systematic risk of firms listed in the official market of the Stock Exchange of Mauritius (SEM). In other words, to analyse the extent to which accounting variables significantly determines the market risk. Prior research has shown that financial ratios, profitability ratios and activity ratios are important determinants of the systematic risk of a common stock.
4.1 Objective of the study
The purpose of the research is to:
Examine the impact of accounting variables on systematic risk of listed companies in the SEM, that is to determine whether the accounting variables are positively, negatively or not correlated to the security beta.
Computing beta to see whether it is determined by the above variables.
Analysing the effects of the variables using panel data.
To prove the validity of the hypothesis concerning a firm's accounting variables in the estimation of the firm's systematic risk.
Since systematic risk is theoretically an important decision variable for investors, creditors and managers, the ability of accounting information to assess systematic risk is of particular importance. Finding out these determinants of systematic risk is useful for investors and management to the extent that some of these variables can be under management's control. For almost all investment decisions, beta or systematic risk plays a significant role in risk measurement and risk management. Hence, this study will help business managers to better assess the importance of their particular corporate decisions and also investors to predict any future variations in a firm's systematic risk.
4.2 Research Methodology
This section explains the procedure that will be used to achieve the objectives of the study. It includes the model of the determinants of systematic risk, the data sources and the empirical procedure.
4.2.1 Model
The main focus of the study is to use Capital Asset Pricing Model (CAPM), in order to estimate beta for each companies. The CAPM states that an investment contains two types of risk, systematic risk and unsystematic risk. Unsystematic risk is diversifiable. In other words, the risk can be eliminated by combining the assets with other assets in a diversified portfolio. Whereas systematic risk is non-diversifiable risk that reflects the future is unknowable and cannot be eliminated by diversification. According to CAPM, systematic risk or beta is the only relevant measure of a stock's risk. It therefore measures the volatility of a stock's return, that is, it shows how much the price of a particular stock changes compared with how much the stock market as a whole changes.
4.2.2 Assumptions of CAPM:
Some of the assumptions of CAPM are listed as follows:
Investors are rational and risk averse.
The market is perfect, that is there are no taxes on sales or purchases, no transaction costs and no short sales restrictions.
Investors maximise utility defined over expected return and return variance.
Unlimited amounts may be borrowed or loaned at the risk free rate.
Investors have homogenous expectations regarding future asset returns.
Capital market is in equilibrium, that is all the investment decisions have been made and all information is at the same time available to all investors.
4.2.3 Limitations of CAPM:
The CAPM is based on some unrealistic assumptions, for instance, it assumes that all investors can borrow and lend at the same rate or all the investors have the homogeneous expectations. But this assumption of homogeneous expectation is unrealistic even if all the investors are equally & fully informed.
In studies of the CAPM applied to common stocks, the CAPM does not explain the differences in returns for securities that differ over time, differ on the basis of dividend yield, and differ on the basis of the market value of equity.
A beta is an estimate of systematic risk. For stocks, the beta is typically estimated using historical returns. But the estimate for beta depends on the method and period in which it is measured. For assets other than stocks, beta estimation is more difficult.
Though it lacks reality and is difficult to apply, the CAPM makes some sense regarding the role of diversification and the type of risk that should be considered in investment decisions making.
However, the simple linear model will be used which is expressed in terms of expected returns and expected risk. This model has been developed by John Linter (1965), Jan Mossin (1966) & William Sharpe (1964). Moreover, Sharpe et al (1965) suggests that the expected rate of return of a security equals the risk free rate of return plus a risk premium, as shown below:
E(Ri) = Rf + [E(Rm) - Rf] * βi ----------- Equation 1
Where, Ri is the expected rate of return of security i, Rf is the risk free rate of return, Rm is the market portfolio rate of return and βi is the systematic risk of security i. βi measures the tendency of asset i to co-vary with the market portfolio. It represents that part of the asset's risk that cannot be diversified away and this is the risk that investors are compensated for bearing. CAPM shows that the relevant measure of an asset's risk is its beta (β) which implies that the expected returns increase linearly with risk. Thus, only the systematic or market risk affects the return.
According to Copeland and Weston (1992), this theoretical CAPM is in ex-ante form, which cannot be measured and needs to be transformed into a form that uses observed data. Therefore, it must be assumed that the rate of return on any asset is a fair game, that is, on average the realised rate of return on an asset equals the expected rate of return for period t.
Assuming that returns are normally distributed, then in the fair game model, βi, the systematic risk of security i is defined in the same way as βi in the CAPM.
The derivation of the equation is shown in the appendix.
Rit = Rft + [Rmt - Rft] * βi + eit ----------------- Eqn 2
Equation 2 represents an empirical model of the CAPM that is expressed in terms of ex post observations.
4.2.4 Calculation of returns
Returns on each security
The return on a security is equal to the change in value of the security. For simplicity purposes, dividend is omitted. The yearly return for each firm has been calculated as shown below:
Ri = (P1 - P0) / P0
Where, P1 is the price of the security at the end of a year, P0 is the price of the security at the beginning of a year.
Returns on the market
RM is the return on the market portfolio which should consist of an investment in all possible securities. However, as the market portfolio is not observable, the return indicated by the yearly movements in the SEMDEX has been used as a substitute to the market return. Thus, the return on the market has been calculated as follows:
Return for year t = SEMDEX at end of year t minus SEMDEX at beginning of year t
SEMDEX at beginning of year t
Risk free return
Rf is the return on the risk-free security, usually proxied by some government security such as the T-bill. The annual weighted rate of return on t-bills, obtained from the Bank of Mauritius has been used as the risk free rate.
4.3 Sample selection
For the purpose of this study, listed companies on the official market have been considered. The basic criterion used to select these stocks is based on the continuity of trading and information about listed companies is more readily available. Moreover, it represents a reliable source of information since the companies are subject to audit and are regulated by the listing rules of SEM.
There are 40 companies listed on the official market of SEM emerging from different sectors, some of which are investment sector, bank and insurance sector, commerce sector. This study is based on 36 out of 40 firms that are listed on the official market for the period 1999 to 2008. The firm Trinity Financial Group Limited under the foreign sector is dropped since it is not incorporated in Mauritius and hence its data is not readily available. Moreover, Mauritius Leasing Company Limited, Naiade Resort Ltd and Caudan Development Ltd are also dropped due to the fact that these companies have been listed after 2004, and their share prices prior to 2004 are not readily available.
4.4 The data sources
This study uses ratios which are commonly used in prior research on risk analysis. Ratios used are liquidity, profitability, leverage and activity ratios which are presented in Table 1 of the appendix. These variables or ratios reveal the results of policy decisions at company level that are most likely to be associated with the systematic risk of a firm. They are calculated by using accounting data which are secondary data that have already been collected for another purpose. They have been obtained from the annual reports of the firms as produced by the Registrar of Companies and the share prices have been collected from the SEM.
In addition to these accounting ratios, other non-accounting measures of risk like inflation, real gross domestic product (GDP), dividend payout, market value of equity, growth in earnings and asset size are included in the sample. Inclusion of these measures may help in the understanding of the impact of a corporate event on the firm's risk.
4.5 Static Panel Data Estimation
In this study, regression analysis will be used to formulate the relationship between systematic risk and its determinants. Regression analysis is concerned with the study of the dependence of one variable, the dependent variable, on one or more other variables, the explanatory variables. In this study, the dependent variable is systematic risk and the explanatory variables are the determinants of systematic risk, some of which are leverage, quick ratio, return on assets, dividend payout and asset size. The explanatory variables are obtained by calculating ratios using accounting data which are shown in the Table 2 of the appendix.
Furthermore, the analysis will focus on the use of panel data also called as cross-sectional time series data. It is a combination of time series and cross sectional analysis. Panel data are data where multiple cases are observed at two or more time periods. In cross-sectional analysis, the dependent variable is observed for several firms at one point in time. In contrast, for time series analysis a single firm's dependent variable is observed over different period of time. A combination of both implies that systematic risk (the dependent variable) will be studied for several firms over a number of years. This technique allows taking advantage of both cross-sectional and time series analysis.
There are two types of panel data regression, the FIXED effect model and the RANDOM effect models. Fixed effect regression is used when you want to control for omitted variables that differ between cases but are constant over time. It allows using the changes in the variables over time to estimate the effects of the independent variables on the dependent variable. In contrast, random effect models are used when some omitted variables may be constant over time but vary between cases, and others may be fixed between cases but vary over time. The fixed effects model produces Ordinary Least Squares (OLS) estimates while the random effects model produces Feasible Generalised Least Squares (FGLS) estimates.
To choose between fixed and random effects, the Hausman test can be run. Fixed effects are always a reasonable thing to do with panel data since they always give consistent results but they may not be the most efficient model to run. Random effects will give better P-values as they are a more efficient estimator.
The Hausman test tests the null hypothesis that the coefficients estimated by the efficient random effects estimator are the same as the ones estimated by the consistent fixed effects estimator. If χ2 is less than 5 %, the null hypothesis is rejected. If they are insignificant, that is, if Prob>chi2 is greater than 0.05, then it is safe to use random effects. However, if P-value is significant, then the fixed effects should be used.
A multiple regression analysis using one of the above methods, whichever is better under the Hausman test, will be used to study the dependence of a dependent variable on other explanatory variables.
The analysis will be split into seven models, whereby each model will include different variables. This will help to determine which variables will better explain systematic risk. The seven regression equations are as follows:
Model 1
LNBETAt = α + b1 LNCURAT + b2 LNASTN + b3 LNRTNAS+ b4 LNGEAR + ε
Model 2
LNBETAt = α + b1 LNCASHCL+ b2 LNWCAPTN + b3 LNRTNAS+ b4 LNGEAR + ε
Model 3
LNBETAt = α + b1 LNQUIRAT + b2 LNINCTN + b3 LNRTNEQT+ b4 LNTLEQT + ε
Model 4
LNBETAt = α + b1 LNWCAPTAS + b2 LNASTN + b3 LNRTNEQT+ b4 LNTLEQT + ε
Model 5
LNBETAt = α + b1 LNCURAT + b2 LNASTN + b3 LNRTNAS+ b4 LNGEAR + b5 LNMVE + b6 LNGR + b7 LNASIZE + b8 LNDP + b9 LNINF + b10 LNRGDP + ε
Model 6
LNBETAt = α + b1 LNLIQ + b2 LNPROF + b3 LNACT+ b4 LEV + ε
Model 7
LNBETAt = α + b1 LNLIQ + b2 LNPROF + b3 LNACT+ b4 LEV + b5 LNMVE + b6 LNGR + b7 LNASIZE + b8 LNDP + b9 LNINF + b10 LNRGDP + ε
4.6 Statistical tests
4.6.1 Descriptive statistics
The aim of the descriptive statistics is to summarise the dataset. For the descriptive statistics, the measure of central tendency (mean), measure of dispersion (variance and standard deviation), measure of skewness and kurtosis will be calculated.
4.6.2 Panel Unit root test
The panel unit root tests will be carried out on the levels and the first differences of the variables. This test will examine whether the variables are stationary or not. Thus, all the variables will have to be tested for stationarity and in cases of non-stationarity the series will have to be made stationary by differencing the variable. Stationarity is defined as "a quality of a process in which the mean and standard deviation of the process do not change with time". The most important property of a stationary process is that the auto-correlation function (acf) depends on lag alone and does not change with the time at which the function was calculated.
According to Levin, Lin and Chu (2002), Im, Persaran and Shin (2003), and Breitung (2000) panel-based unit root test have higher power than time series unit root test. In this study, the Levin, Lin and Chu (2002) panel unit root test will be used.
4.6.2.1 Levin, Lin and Chu (2002) test
Levin, Lin and Chu (2002) start panel unit root test by consider the following basic ADF specification: [1]
DYi t = αYi t-1 + ∑pi j=1 βit DYi t-j + X*i t δ+ ei t
Where, DYi t = difference term of Yi t
Yi t1 = Panel data
α = Ï-1
pi = the number of lag order for difference terms
X*i t = exogenous variable in model such as country fixed effects and individual time trend
ei t = the error term of equation 1I
Therefore, it is required to check whether the data contains unit roots. The hypotheses of Levin Lin Chu (2002) panel unit root test are as follows:
H0: data has unit root
H1: data is stationary
If the p-value is significant, that is, if P>t is less than 0.05, then the null hypothesis is rejected, implying that the panel data is stationary and has not unit root. While if the p-value is significant, subsequently the null hypothesis is accepted, this means that the data has unit root.
4.6.3 Diagnostics Test
According to Beck (2001) and Plumper et al (2005), there are estimation problems associated with panel data regression, namely, heteroscedasticity and autocorrelation. Heteroscedasticity can occur since cross-sectional data are considered, while autocorrelation can also occur since time series data are involved.
4.6.3.1 Test for heteroscedasticity
Heteroscedasticity occurs since the variance of the dependent variable varies across the data. Long and Ervin (2000) find that when heteroscedasticity is severe, ignoring it may bias the standard errors and p values.
4.7 Dynamic Panel Data Estimation
The systematic risk and its determinants have been estimated and tested using the static regression analysis. The variables in the seven models will now be tested using Generalised Method of Moments (GMM). Generally, GMM is a method for estimating models by exploiting moment conditions. The dynamics panel data is modeled by including a lagged dependent variable as an explanatory variable. In other words, it is a model whereby the lag of the dependent variable is used as independent variable. Moreover, the Arellano Bond estimator will be used as the GMM estimator. The dynamic regression equations for the seven models are as follows:
Model 1
LNBETAit = α + b1 LNBETAi t-1 + b2 LNCURAT + b3 LNASTN + b4 LNRTNAS+ b5 LNGEAR + ε
Where, LNBETAi t-1 is the lagged value of the log of beta
Model 2
LNBETAt = α + b1 LNBETAi t-1 + b2 LNCASHCL+ b3 LNWCAPTN + b4 LNRTNAS+ b5 LNGEAR + ε
Model 3
LNBETAt = α + b1 LNBETAi t-1 + b2 LNQUIRAT + b3 LNINCTN + b4 LNRTNEQT+ b5 LNTLEQT + ε
Model 4
LNBETAt = α + b1 LNBETAi t-1 + b2 LNWCAPTAS + b3 LNASTN + b4 LNRTNEQT+ b5 LNTLEQT + ε
Model 5
LNBETAt = α + b1 LNBETAi t-1 + b2 LNCURAT + b3 LNASTN + b4 LNRTNAS+ b5 LNGEAR + b6 LNMVE + b7 LNGR + b8 LNASIZE + b9 LNDP + b10 LNINF + b11 LNRGDP + ε
Model 6
LNBETAt = α + b1 LNBETAi t-1 + b2 LNLIQ + b2 LNPROF + b4 LNACT+ b5 LEV + ε
Model 7
LNBETAt = α + b1 LNBETAi t-1 + b2 LNLIQ + b3 LNPROF + b4 LNACT+ b5 LEV + b6 LNMVE + b7 LNGR + b8 LNASIZE + b9 LNDP + b10 LNINF + b11 LNRGDP + ε
