Stability of Beta over Market Phases

transnational research diary of pay and economic science ISSN 1450-2887 set off 50 (2010) Eurojournals Publishing, Inc. 2010 http//www. eurojournals. com/finance. htm constancy of important oer trade mannequins An verifiable Study on Indian none mart Koustubh Kanti Ray Assistant Professor, Financial Management at Indian Institute of Fo stand-in Management (IIFM), Bhopal, India. E-mail emailprotected ac. in Abstract The pregnant role played by genus of import in diverse aspects of financial ending making has forced people from sm exclusively investors to investment bankers to consider on important in the era of globalization.In the point changing food mart condition, it is imperative to understand the s tableness of genus genus Beta which augments an efficient investment decisions with superfluous information on genus Beta. This reputation adjudicated the perceptual constancy of of import for India merchandise place for a ten year stop ein truthwhere from 1999 to 2009. The monthly proceeds information of 30 selected pipelines be considered for examining the stability of important in unalike securities sedulousness shapes. This stability of genus Beta is tried and true use three econometric forges i. e. victimisation eon as a inconstant, utilise dummy variables and the cream puff riddle. The roots obtained from the three posers ar mixed and false.However thither atomic ingathering 18 9 inventoryings where whole the three simulations describe resembling signal of important unbalance all everyplace the food merchandise place classs. Keywords Stability of Beta, Phase reinvigorated of import, Indian Market Beta, Dummy Variable, chow probe 1. Introduction The groovy Asset Pricing gravel (CAPM) developed by Sharpe (1964), Lintner (1965) and Mossin (1966) has been the dominating capital securities industry equilibrium stick since its initiation. It continues to be extensively use in pract ical portfolio management and in academic research. Its inseparable implication is that the contribution of an impartmation to the variance of the commercialize portfolio he assets positive risk, or of import risk is the proper sum of m angiotensin-converting enzymey of the assets risk and the only organized determinant of the assets return. Risk is the assessable uncertainty (Knight, 1921) in predicting the future instances that be affected by orthogonal and internal factors. Sharpe (1963) had classified risks as dogmatic risk and unsystematic risk. The elements of systematic risk argon external to the firm. The external factors be changes in economic environment, elicit rate changes, inflation, etc. On the other hand, internal factors be the sources of unsystematic risk.Unsystematic risks atomic number 18 categorized as business risk or financial risk specific to the firm. The systematic risk related with the general securities industry movement cannot be who le eradicated through diversification. The unsystematic risk, which is confine to a firm, can be eliminated or reduced to a considerable extent by choosing an appropriate portfolio of securities. more than or less of the sources of unsystematic risk ar consumer preferences, worker strikes and management competitiveness. These factors be nonsymbiotic of the factors topicing melody merchandise.Hence, systematic risk go forth influence all the securities in the foodstuff, whereas unsystematic risk is protection specific. International research Journal of pay and economics exhaust 50 (2010) 175 Theoretically defined, beta is the systematic family among the return on the portfolio and the return on the commercialise (Rosenberg and Marathe, 1979). It refers to the slope in a linear kindred jeerted to data on the rate of return on an investment and the rate of return of the trade (or food foodstuff ability). Beta is a technique of telling how volatile a stock is c omp bed with the rest of the marketplace.When the return on the portfolio is more than the return on the market, beta is wideer than star and those portfolios be referred to as aggressive portfolios. That means, in a booming market condition, aggressive portfolio will achieve a good deal better than the market movement. While in a nominateish market environment the fall of aggressive portfolios will besides be some(prenominal) prominent. On the other hand, when the return on portfolio is less than the market return, beta measure is less than iodin and those portfolios atomic number 18 treated as defensive.In causal agency of defensive portfolios, when the market is rising, the performances associated with it will be less than the market portfolio. However, when the market moves down, the fall in the defensive portfolios would likewise be less than the market portfolio. In those situations where, the return of the portfolio accurately matches the return of the market, b eta is equal to bingle that rargonly happens in real life situations. Beta esteem is important to many financial decisions such as those relating to stock selection, capital budgeting, and performance evaluation. It is noteworthy for both practitioners and academics.Practitioners use beta in financial decision making to estimate cost of capital. Beta is likewise a samara variable in the academic research for example it is used for examen asset set models and market energy. Given the importance of this variable a pertinent question for both practitioners and academics is how to obtain an efficient mind. This study is aimed at testing the beta stability for India. Further the stability of beta is of great concern as it is a vital tool for almost all investment decisions and plays a solid role in the modern portfolio theory.The estimation of beta for individual securities employ a simple market model has been widely evaluated as well as criticized in the finance literature. peerless important aspect of this simple market model is the assumption of balance that propounds the estimated beta is valid for all the market conditions. Many studies questioned this assumption and examined the relationship amid beta and market return in distinguishable market conditions, but the results are mixed and inconclusive. In this paper, an attempt is made to look into the stability of beta in the Indian stock market during the conclusion 10 years i. . from awful 1999 to shocking, 2009. With this objective, the paper is dissever into fin sections including the amaze section. Section 2 reviews the existing literature and discusses the findings of major empirical researches conducted in India and other countries. Section 3 describes the data sources and methodology. Section 4 asidelines the results of tests for probe the stability of beta and its findings. Section 5 is dedicated to summary, conclusion and mountain range for further research in the area. 2. L iterature reviewSeveral studies are carried kayoed(p) to study the nature and the behavior of beta. Baesel (1974) studied the wedge of the length of the estimation sentence detachment on beta stability. Using monthly data, betas were estimated using estimation intervals of one year, dickens years, four years, six years and nine years. He conclude that the stability of beta increments significantly as the length of the estimation interval increases. Levy (1971) and Levitz (1974) suck shown that portfolio betas are very invariable whereas individual security betas are passing un invariable.Like oerbold Blume (1971) used monthly prices data and successive seven-year dividing lines and shown that the portfolio betas are very stable where as individual security betas are highly unstable in nature. He shows that, the stability of individual beta increases with increase in the clipping of estimation period. Similar results were also obtained by Altman et al (1974). In both the themes, initial and succeeding estimation periods are of the similar length. Allen et al. (1994) have considered the subject of comparative stability of beta coefficients for individual securities and portfolios.The common perception is that the portfolio betas are more stable than those for individual securities. They argue that if the portfolio betas are more stable than those for individual securities, the 176 International seek Journal of pay and Economics add 50 (2010) large confidence can be placed in portfolio beta estimates over longer periods of time. notwithstanding, their study concludes that larger confidence in portfolio betas is not justified. Alexander and Chervany (1980) show empirically that uttermost(a) betas are less stable compared to interior beta.They proved it by using mean absolute deviation as a measure of stability. tally to them, best estimation interval is generally four to six years. They also showed that ir observeive of the manner portf olios are formed, magnitudes of inter-temporal changes in beta decreases as the number of securities in the portfolios rise contradicting the work of Porter and Ezzell (1975). Chawla (2001) investigated the stability of beta using monthly data on returns for the period April 1996 to evidence 2000. The tability of beta was tested using dickens alternative econometric methods, including time variable in the retrogression and dummy variables for the slope coefficient. Both the methods do away with the stability of beta in majority of cases. Many studies focused on the time vary beta using conditional CAPM (Jagannathan and Wang (1996) Lewellen and Nagel (2003)). These studies concluded that the fluctuations and events that influence the market force change the leverage of the firm and the variance of the stock return which eventually will change the beta.Haddad (2007) examine the degree of return capriciousness sedulousness and time-varying nature of systematic risk of two Egypt ian stock portfolios. He used the Schwert and spangle (1990) market model to study the relationship between market capitalization and time varying beta for a exemplar of investable Egyptian portfolios during the period January, 2001 to June, 2004. According to Haddad, the small stocks portfolio exhibits difference in capriciousness persistence and time variableness. The study also suggests that the volatility persistence of severally portfolio and its systematic risk are significantly positively related.Because of that, the systematic risks of unalike portfolios tend to move in a contrary counseling during the periods of increase market volatility. The stability of beta is also examined with reference to security market conditions. For example, Fabozzi and Francis (1977) in their seminal paper considered the differential effect of strapper and bear market conditions for 700 individual securities listed in NYSE. Using a Dual Beta Market Model (DBM), they established that est imated betas of most of the securities are stable in both the market conditions.They experienced it with three different set of bull and bear market definitions and concluded with the same results for all these definitions. Fama and French (1992, 1996), Jegadeesh (1992) and others revealed that betas are not statistically related to returns. McNulty et al (2002) highlight the problems with historical beta when computing the cost of capital, and suggest as an alternative- the forward-looking market-derived capital pricing model (MCPM), which uses filling data to evaluate paleness risk. In the similar line, French et al. (1983) merge forward-looking volatility with istorical correlation to improve the amount of betas. Siegel (1995) notes the improvement of a beta based on forward-looking option data, and proceeds to propose the creation of a new derivative, called an exchange option, which would let in for the calculation of what he refers to as implicit betas. Unfortunately the e xchange options discussed by Siegel (1995) are not yet traded, and in that locationfore his method cannot be use in practice to compute forward-looking betas. A few studies are carried out to explore the reason for imbalance of beta.For example, Scott & Brown (1980) show that when returns of the market are subjected to measurement misapprehensions, the concurrent autocorrelated equalisers and inter-temporal correlation between market returns and equaliser results in biased and unstable estimates of betas. This is so even when true set of betas are stable over time. They also derived an expression for the instability in the estimated beta between two periods. Chen (1981) investigates the connection between variability of beta coefficient and portfolio equalizer risk. If beta coefficient changes over time, OLS method is not adapted to estimate portfolio residual risk.It will lead to inaccurate conclusion that larger portfolio residual risk is associated with higher variability in beta. A Bayesian approach is proposed to estimate the time varying beta so as to provide a precise estimate of portfolio residual risk. Bildersee and Roberts (1981) show that during the periods interest rates fluctuate, betas would fluctuate systematically. The change would be in tune with their appreciate relative to the market and the pattern of changes in interest rate. International look Journal of finance and Economics Issue 50 (2010) 177Few research studies are available in the Indian context to examine the factors influencing systematic risk. For example, Vipul (1999) examines the effect of confede balancen size, industry group and liquidity of the scrip on beta. He considered equity shares of 114 companies listed at Bombay ocellus Exchange from July 1986 to June 1993 for his study. He found that size of the company affects the nurse of betas and the beta of medium sized companies is the lowest which increases with increase or decrease in the size of the company. Th e study also concluded that industry group and liquidity of the scrip do not affect beta.In another study, Gupta & Sehgal (1999) examine the relationship between systematic risk and accounting variables for the period April 1984 to bump into 1993. There is a confirmation of relationship in the expected direction between systematic risk and variables such as debt-equity ratio, current ratio and net sales. The association between systematic risk and variables like profitability, payout ratio, earning offshoot and earnings volatility measures is not in accordance with expected sign. The relationship was investigated using correlation analysis in the study. 3. Data Type and interrogation MethodologyThe data related to the study is taken for 30 stocks from BSE-100 baron. The top 30 stocks are chosen on the basis of their market capitalization in BSE-100 index. These 30 stocks are selected from BSE100 stocks in such a itinerary that the nonstop price data is available for the study period. The adjusted closing prices of these 30 stocks were collected for the last 10 years period i. e. from princely 1999 to August 2009. The stock and market (BSE-100) data has been collected from prowess (CMIE) for the supra period. BSE-100 index is a broad-based index and descends globally accepted free-float methodology.Scrip selection in the index is generally taken into account a balanced sectoral representation of the listed companies in the universe of Bombay Stock Exchange (BSE). As per the stock market guideline, the stocks inducted in the index are on the basis of their final grossing. Where the final rank is arrived at by assigning 75 share weightage to the rank on the basis of three-month average full market capitalization and 25 percent weightage to the liquidity rank based on three-month average daily swage & three-month average impact cost.The average closing price for to severally one month of 30 socks is computed for the period August 1999 to August 2009. Therefore we have one hundred twenty average monthly prices for individually(prenominal) of the 30 stocks included in the research. The next method has been used to compute the monthly return on each of the stock. P i,t P i,t-1 ri,t = P i, t-1 Where P i,t = Average price of stock i in the month t Pi,t-1 = Average price of stock i in the month t-1 r i,t= Return of ith stock in the month t. The monthly market return is computed in the following way Bt Bt-1 mt = B t-1Where Bt = BSE-100 exponent at time period t Bt-1 = BSE-100 Index at time period t-1 mt = Market return at time period t. After the monthly stock and market returns are calculated as per the to a higher place formula, we identified the different market chassiss to compute beta separately. The market phases are identified, by creating a cumulative wealth index from the market returns. The cumulative wealth index data is presented in annexure-1. As per the cumulative wealth index, we identified five different mark et 178 International Research Journal of pay and Economics Issue 50 (2010) hases in BSE-100 index. We recognized that on that point are three bullish phases (Jan-1999 to Feb-2000, Oct-2001 to Dec-2007 and Dec-2008 to August 2009) and two bearish phases (Mar-2000 to Sept2001, Jan-2008 to no-2008). The summary of different market phases is envisioned in Table -1& figure-1 below. Table-1 distinguishable Market Phases Market Phases Phase I Phase II Phase collar Phase IV Phase V Market Phase Timing Start End Jan-1999 Feb-2000 Mar-2000 Sep-2001 Oct-2001 Dec-07 Jan-2008 no(prenominal)-08 Dec-2008 Aug-09 Market Type Bullish Bearish Bullish Bearish Bullish Figure-1 Different Market PhasesAfter these five market phases are identified, the beta apprize has been computed for each stock for each market phases following the below mentioned fixing equality. ri,t = ? + ? mt + e (1) ri,t = Return on scrip i at time period t mt = Market rate of return at time period t e = Random error ? & = Parameters to be estimated The higher up fixation equation is applied to calculate beta coefficient of each stocks for each market phases separately and taking the entire ten years period. As the objective of the paper is to test the stability of beta in different market phases, the hypothesis has been set accordingly.The nonentity hypothesis (H0) being the beta is stable over the market phases, whereas the alternative hypothesis (H1) is that the beta set are not stable and varies according to phases in the market. The hypothesis has been tested with the help of three econometric models- using time as a variable, using dummy variables to measure the change of slope over the period and through Chow test. International Research Journal of Finance and Economics Issue 50 (2010) 179 3. 1. testing the Stability of Beta using time as a variableIn case of measuring stability of beta using time as a variable, in the above regression model (1) another variable i. e. t mt is used a s a separate explanatory variable. Where the time variable t takes a honour of t=1 for the first market phase, t=2 for the encourage market phase and so on for all other market phases identified. In this method the objective is to see whether the beta determine are stable over time or not. After including the tmt variable, the above regression model (1) can be written as ri,t = ? + ? 1mt + ? 2( t*mt) + e (2) The above regression equation can be re-framed as below ri,t = ? + (? + ? 2*t )*mt + e (2) To test the stability of beta, we essentially have to see whether the expression ? 2 is significant or not. If it is significant, we contain to reject the null hypothesis and accept alternative hypothesis. It is implied that the sensitivity of stock return to market return i. e. (? 1 + ? 2*t)* mt changes with time, and hence, beta is not stable. If ? 2 is not significant, (? 1 + ? 2*t)* mt will get reduced to ? 1*mt , implying that ? 1, or the beta of stock, does not vary with time an d is thus stable over time. The statistical logical systemal implication of ? 2 is tested using the respective p- determine. . 2. Testing the Stability of Beta using dummy variable In case of the second method of testing the beta stability, dummy variables are used in above mentioned regression equation (1) for the slope coefficients. As five market phases discovered, at that place are 4 dummy variables used in the new equation (Levine et al. 2006). The new regression equation is reframed as follows ri,t = ? 0 + ? 1* mt + ? 2*D1* mt + ? 3*D2* mt + ? 4*D3* mt + ? 5*D4*mt + e (3) Where D1 = 1 for phase 1 (Jan 1999 to Feb 2000) data = 0 otherwise. D2 = 1 for phase II ( may 2000 to Sept 2001) data = 0 otherwise D3 1 for phase III (Oct 2001 to Dec 2007) data = 0 otherwise D4 = 1 for phase IV (Jan 2008 to nary(prenominal) 2008) data = 0 otherwise = return on stock I in period t. r i,t mt = return on market in period t. e = error term and ? 0, ? 1, ? 2, ? 3, ? 4 & ? 5 = coefficients t o be estimated. As there are 5 market phases, we use 4 dummy variables in the above equation (3). The use of 5 dummy variable would lead to a dummy variable trap. We treat the 5th phase viz. Dec-08 to Aug-09 as the base period. The significance of ? 2, ? 3, ? 4 and ? 5 will tell us whether the beta is stable over the time periods or not.For the beta to be truly stable over the entire period, all coefficients like, ? 2, ? 3, ? 4 and ? 5 should be statistically insignificant and where we need to accept the null hypothesis. The logic is that if ? 2, ? 3, ? 4 and ? 5 are insignificant, the equation reduces to the following, thus implying that beta is stable over time. ri,t = ? 0 + ? 1*mt + e (4) th 3. 3. Testing for Structural or Parameter Stability of Regression Model The Chow Test In the third method, for structural or parameter stability of regression models, the Chow test has been conducted (Gujarati, 2004).When we use a regression model involving time series data, it may happen 180 International Research Journal of Finance and Economics Issue 50 (2010) that there is a structural change in the relationship between the regress and the regressors. By structural change, we mean that the determine of the parameters of the model do not breathe the same through the entire time period. We divide our sample data into five time periods according to the different market phases identified earlier.We have six thinkable regressions for each stock (five regressions for each market phases and one for the whole ten year period). The regression equations are mentioned below. ri,t = ? 1 + ? 2mt + ut (5) (6) r i, t = ? 1 + ? 2mt + ut Equation (5) is for each market phases and equation (6) is for the whole period. There are 128 observations (n=128) for the whole period and n1=14, n2=19, n3=75, n4=11 and n5=9 are the number of observations for phase-I to phase-V respectively. The us in the above regression equations represent the error terms.Regression (6) assumes that there is no difference over the five time periods and therefore estimates the relationship between stock prices and market for the entire time period consisting of 128 observations. In other words, this regression assumes that the tease as well as the slope coefficient remains the same over the entire period that is, there is no structural change. no(prenominal) the possible differences, that is, structural changes, may be caused by differences in the intercept or the slope coefficient or both. This is examined with a formal test called Chow test (Chow, 1960). The mechanics of the Chow test are as followsFirst the regression (6) is estimated, which is appropriate if there is no parameter instability, and obtained the restricted residual sum of squares (RSSR) with df = (n1+n2+n3+n4+n5) ? k, where k is the number of parameters estimated, 2 in the present case. This is called restricted residual sum of squares because it is obtained by imposing the restrictions that the sub-period regressions are not different. Secondly estimated the phase wise other regression equations and obtain its residual sum of squares, RSS1 to RSS8 with degrees of freedom, df = (no of observations in each phase ? ). Since the five sets of samples are deemed independent, in the third graduation we can add RSS1 to RSS8 to obtain what may be called the unrestricted residual sum of squares (RSSUR) with df = (n1+n2+n3+n4+n5)? 2k. Now the idea behind the Chow test is that if in fact there is no structural change (i. e. , all phases regressions are essentially the same), then the RSSR and RSSUR should not be statistically different. Therefore in the fourth step the following ratio is formed to get the F-value. F = (RSSR ? RSSUR)/k / (RSSUR)/ ((n1 + n2+n3+n4+n5) ? 2k) F k, ((n1+n2+n3+n4+n5) ? 2k) (7)We cannot reject the null hypothesis of parameter stability (i. e. , no structural change) if the computed F value is not statistically significant (F value does not exceed the critical F value obtained fr om the F table at the chosen level of significance or the p value). Contrarily, if the computed F value is statistically significant (F value exceeds the critical F value), we reject the null hypothesis of parameter stability and conclude that the phase wise regressions are different. 4. Test Results and Findings initially the beta coefficient is calculated using the mine run Least Square (OLS) technique as defined in equation (1).The estimation was carried out by using monthly return data for the 5 market phases for each of the 30 stocks. To compare the phase wise beta estimation with the entire 10 year period, the same estimation also carried out taking the whole 10 years for each stock separately. Stock wise beta values over 5 market phases and the entire period is reported in appendix-2. From annexure-2, it is revealed that there are 14 stocks beta value is greater than 1 in phase I. This figure (beta value greater than 1) has reduced to 6, 11, 12 and 10 for phase-2 to phase-5 respectively.It is also illustrated that, there are 8 stocks whose beta value is greater than 1 in respect to boilersuit between Jan-99 to Aug-09 and highest being for Wipro of 1. 47. The stocks having beta value International Research Journal of Finance and Economics Issue 50 (2010) 181 more than 1 are considered to be volatile securities. It is noticed that, as we increase the period of estimation to full ten years period, there are less number of stocks proved to be more volatile. place of the total 30 stocks considered in the study, only one company i. e.L&T has beta more than 1 in all phases including the boilersuit period. But none of the companys overall beta value is more than the phase wise betas. There are seven companies (RIL, NALCO, ITC, GAIL, Hindustan Lever, Hero Honda and Cipla) whose beta values are less than 1 all through the phases including overall period. These stocks are considered to be less volatile than the market. There are 3 companies (Cipla, ITC and Hind ustan Lever) recent beta value (Dec 2008 to August 2009) is negative, where Ciplas phase I beta value is also negative along with other two stocks like SAIL and NALCO.It is observed from annexure-2 that there are only two companies from the software sector (Infosys and Wipro) whose beta values are consistently declining over time. However there are 7 stocks viz. Cipla, insolatepharma, Wipro, Grasim, Hindustan Lever, Infosys and ITC whose beta values are masking a decreasing trend from phase 3 onwards, while Tata steel is the only stock whose beta values are showing an increasing trend during the same period. It is observed from the annexure-2 that, on an overall basis 29 out of 30 stocks have their beta values statistically significant at 5% level.This number has varied from 8 to 30 over the various phases, indicating that the beta values of the stocks have fluctuated significantly. This implies that the volatility of the stocks depend on the market phases i. e. bearish or bullish . Thus the result rejects the null hypothesis that the beta is stable over various market phases. The null hypothesis is jilted in 29 out of 30 cases in case of overall period, while 30 out of 30 cases in respect to phase-3. Since the period of estimation of beta is more in case of overall period and in phase-3, the obtained results are similar in both the cases.But the remaining phase wise results do not follow any pattern. In respect of period of estimating the value of beat the results are comparable to the finding of Baesel (1974) and Altman et al (1974). It is mentioned earlier that to examine the stability of beta over different market phases, three separate models have been used in paper. The results obtained from these models are interpreted in the following paragraphs. The estimated results for regression model-2 that includes t*mt as a separate variable are interpret in annexure-3.It is observed that the value of R2, a measure of goodness of fit varies from 0. 11 to 0. 6 1. It is only in 5 out of 30 regression results, the value is greater than 0. 50. The coefficient of mt (? 1) is found to be highly statistically significant at 5% level in 19 out of 30 cases. It is in 11 regressions, the coefficient is statistically insignificant. As discussed earlier, the significance of the coefficient of variable t*mt implies the rejection of the null hypothesis of stable beta over time. It is observed that the coefficient (? ) is significant in 14 cases out of 30. The regression results quest that in 50% cases the null hypothesis of stability of beta over the market phases is rejected. This means 50% stocks reported stability of beta over different phases. So model (2) cannot infer that beta is not stable over market phases. The estimated results for coefficients for regression model-3 that incorporates dummy variables are depicted in annexure-4. It is noticed from the results that the R2 value fluctuates from 0. 15 to 0. 62 and in case of 8 stocks this value is greater than 0. 0. It is mentioned earlier that the null hypothesis of stability of beta will be rejected if any of the coefficients (? 2, ? 3, ? 4 & ? 5) corresponding to D1*mt, D2*mt, D3*mt or D4*mt were found to be statistically significant. It is observed from the results presented in appendix-4, that there are 17 out of 30 stocks stand for statistically significant at 5% level at least one of the coefficient. There are only 2 cases where 3 coefficients are significant and none of the stocks reported significant for all the 4 coefficients.Further in 6 cases where 2 out of 4 coefficients are reported significant, where as in 9 cases depicted significant only for one coefficient. The outcome of this model in brief can be stated that, in case of 17 stocks out of 30 stocks, the stability of beta hypothesis is rejected meaning, in rest 13 cases there is a stability of beta over the market phases. 182 International Research Journal of Finance and Economics Issue 50 (2010) The est imated results of Chow test are depicted in annexure-5. The results show that, 12 out of 30 cases the F-value is statistically significant and rest 18 stocks are reported insignificant at 5% level.Based on the F- statistics and its corresponding p-values, the null hypothesis of beta stability over the market phases is rejected in 12 cases and accepted in 18 cases. The F-values are also supported by log likelihood ratio and it p-values, which also reported statistical significance in 12 cases. The outcome of Chow test confirms that the beta values are not stable or there is a structural change in 12 out of 30 stocks in different market phases. But the rest 18 stocks reported stability or no structural change in beta values over the market phases.From the above deliberations, it is observed that all the three models described above exhibit a mixed and inconclusive result. There are 14, 17 and 12 stocks are statistically significant as per model2, model-3 and model-7 respectively. This means as per model-2 the beta values of 14 stocks out of 30 stocks are instable over the period. But this number is 17 and 12 in case of model3 and 7 respectively. However, on the basis of results obtained from different models, it is not possible to conclude that the beta values of the stocks are stable or instable over the market phases.But if we closely glance at the results obtained from three models, it is very apparent that in case of 9 stocks where all the three models represented similar results and rejected the null hypothesis. These stocks include Sun pharmaceutical, Wipro, Tata motors, Tata brace, Hindalco, Hindustan Unilever, HDFC, Infosys and z Entertainment. This indicates that beta values are not stable over the market phases in these 9 stocks. Similarly there are 6 stocks where two models recommended instability of beta and 4 stocks where only one model reported a change in beta values over the period.There are 11 cases where none of the models rejected the null h ypothesis, which proved that the beta values are stable over the time in these stocks. 5. Conclusion The objective of the present study is to examine the stability of beta in different Indian market phases. For the purpose of the study monthly return data of 30 stocks for the period from 1999 to 2009 is considered. Considering the bullish and bearish condition in the Indian market, we divided the whole 10 years into 5 different market phases. Initially the beta has been estimated for different market phases and also taking the whole 10 years period.The results show that the beta values are not showing any particular pattern but in the overall phase almost all the stocks are statistically significant. Further the beta stability is examined using three different models. In the first method the beta coefficient is calculated considering the market phases as time variable. The results show that in 50% of cases the null hypothesis is rejected as the beta is stable over different market p hases. In the similar line the results obtained in respect to model two states that in 17 out of 30 cases the null hypothesis is rejected.This confirms that in 17 cases the stability of beta is not there over the market phases but in rest 13 cases it stable over the market phases. In the third method of investigating beta stability, the Chow test has been conducted. The F-statistics under Chow test reveals that, beta is instable in 12 out of 30 stocks considered in the study in different market phases. We can thus finally conclude that the results obtained from different models are mixed and inconclusive in nature, where it is less ground to conclude that the beta values are stable or instable over the market phases.But there are 9 stocks which gives a strong indication that their beta values are not stable over the market phases. In these 9 cases, all the three models reported similar signal of beta instability over the market phases. The instability of beta has its implications in taking gravid corporate financial decisions. Financial decisions should not be based on the overall beta of the company. Rather, the companys periodical beta should be relied upon for taking certain managerial decisions.Considering the inconclusive results obtained from present study, it is suggested that the future research on beta in Indian market may be investigated from (a) industry wise stability of beta in different market phases (b) stability of beta from portfolio point of view (c) optimal time limit for stability of beta (d) forward looking beta and its stability (e) impact of market and company specific factors and stability of beta and (f) market efficiency study using phase wise beta under the event study methodology. International Research Journal of Finance and Economics Issue 50 (2010) 83 References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Allen R G, Impson C M and Karafiath I (1994), An Empirical Investigation of Beta Stability Portfolios vs. Individual Securities, Journal of Business Finance & accounting, Vol. 21, No. 6. Alexander, Gordon. , J. Sharpe. , Chervany, Norman L. (1980) On the Estimation and Stability of Beta, Journal of Financial Quantitative compendium, Vol. XV, No. 1, environ, pp. 123-137. Altman, Edward I. , Bertrand Jacquillat and MichelLevasseur (1974) Comparative Analysis of Risk Measures France and the get together States Journal of Finance, December, pp. 1495-1511. Baesel J B (1974), On the Assessment of Risk nigh Further Considerations, The Journal of Finance, Vol. 29, No. 5, pp. 1491-1494. Bildersee, John S and Robert, Gorden S. (1981) Beta asymmetry when Interest Rate Level Changes, Journal of Financial Quantitative Analysis, September, Vol. XVI, No. 3. Blume Marshall E (1971), On the Assessment of Risk, Journal of Finance, Vol. 26, No. 1. pp. 1-10 Chawla D (2001), Testing Stability of Beta in the Indian Stock Market, Decision, Vol. 8, No 2, pp. 1-22. Chen, Son-Nan (1981) Beta Non-station arity, Portfolio Residual Risk and Diversification, Journal of Financial and Quantitative Analysis, defect, Vol. XVI, No. 1. Chow, Gregory, C. (1960) Tests of Equality Between Sets of Coefficients in two Linear Regressions, Econometrica, vol. 28, no. 3, pp. 591605. Fabozzi, F. J. and Francis, J. C. (1977) Stability tests for alphas and betas over bull and bear market conditions, Journal of Finance, 32, 10939. Fama E. F. , French K. R. , 1992, The cross-section of expected stock returns, Journal of Finance 47, 427-465. Fama E. F. , French K. R. 1996, The CAPM is wanted, dead or alive, Journal of Finance 51, 1947-1958. French, D. , J. Groth, and J. Kolari, 1983, Current Investor Expectations and burst Betas, Journal of Portfolio Management, 12-17. Gujarati, Damodar N. (2004) Basic Econometrics, Fourth Edition The McGraw? Hill Companies, pp-273-278. Gupta, O. p. AND Sehgal, Sanjay (1999) Relationship between Accounting Variables and taxonomic Risk The Indian Experience, Indian Accou nting Review, June, Vol. 3, No. 1. Haddad M M (2007), An Intertemporal Test of the Beta Stationarity The Case of Egypt, sum East Business and Economic Review, Vol. 9, No. 1, Egypt. Jegadeesh N, 1992, Does market risk really explain the size effect? , Journal of Financial and Quantitative Analysis 27, 337-351. Jagannathan, Ravi and Zhenyu Wang, The Conditional CAPM and the Cross-Section of Expected Returns. Journal of Finance 51, 3-53, (1996). Knight F H (1921), Risk, Uncertainty and Profit, Houghton Mifflin Company Chicago, Part 1, Chapter 1, Paragraph 26. Levitz Gerald D (1974), Market Risk and the Management of Institutional Equity Portfolios, Financial Analysts Journal, Vol. 30, No. 1, pp. 53-60. Levine, David, M. , David Stephen. , timothy C.Krehbiel and Mark L. Berenson (2006) Statistics for Managers, Printice-Hall India, 4th Edition, pp-599-600. Levy Robert A (1971), Stationarity of Beta Coefficients, Financial Analysts Journal, Vol. 27, No. 6, pp. 55-62. Lewellen, J. and Na gel, S. (2003) The conditional CAPM does not explain asset-pricing anomalies, MIT Sloan Working Paper No. 4427-03. Lintner, John. 1965. credential Prices, Risk, and Maximal Gains from Diversification. Journal of Finance, V. 20 December, pp 587-616. 184 International Research Journal of Finance and Economics Issue 50 (2010) 25 McNulty, J. , T. Yeh, W. Schulze, and M.Lubatin, (2002), Whats Your Real Cost of jacket crown? Harvard Business Review, 80, October, 114-121. Mossin, Jan. (1966) Equilibrium in a Capital Asset Market. Econometrica, V. 34, No. 2 pp 768-83. Porter, R. Burr and John R. Ezell (1975) A Note on the prognosticative ability of Beta Coefficients, Journal of Business Research, Vol. 3, No. 4, October, pp. 365-372. Rosenberg and Marathe V (1979), Tests of Capital Asset Pricing Hypotheses, Research in Finance, Vol. 1, pp. 115-223. Schwert G W and Sequin P J (1990), Heteroscedasticity in Stock Returns, Journal of Finance, Vol. 45, pp. 1129-1155.Scott, Elton and Brown, S tewart (1980) Biased Estimators and hazardous Betas, The Journal of Finance, March, Vol. XXV, No. 1. Sharpe W F (1963), A Simplified Model for Portfolio Analysis Management Science, Vol. 9, No. 2, pp. 277-293. Sharpe, William F. 1964. Capital Asset Prices A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, V. 19 September, pp 425-442. Siegel, A. , (1995) touchstone Systematic Risk Using Implicit Beta, Management Science, 41, 124-128. Vipul (1999) Systematic Risk Do Size, Industry and Liquidity Matter? , Prajanan, Vol. XXVII, No. 2, 1999. 26 27 28 29 30 31 32 33 34 185 International Research Journal of Finance and Economics Issue 50 (2010) Annexure-1 month December 1998 January 1999 February 1999 March 1999 April 1999 May 1999 June 1999 July 1999 August 1999 September 1999 October 1999 November 1999 December 1999 January 2000 February 2000 March 2000 April 2000 May 2000 June 2000 July 2000 August 2000 September 2000 October 2000 November 2000 December 20 00 January 2001 February 2001 March 2001 April 2001 May 2001 June 2001 July 2001 August 2001 September 2001 October 2001 November 2001 December 2001 January 2002 February 2002 March 2002 April 2002May 2002 June 2002 July 2002 August 2002 September 2002 October 2002 November 2002 December 2002 January 2003 February 2003 March 2003 April 2003 May 2003 June 2003 July 2003 August 2003 September 2003 October 2003 November 2003 December 2003 January 2004 February 2004 Identification of Market Phases mop up Price Return (R) 1+R Cumulative Wealth Index Market Phases 1359. 03 1461. 52 1506. 95 1651. 37 1449. 64 1714. 02 1790. 51 1988. 06 2192. 94 2213. 33 2071. 50 2253. 29 2624. 49 2875. 37 3293. 29 2902. 20 2396. 22 2156. 99 2397. 06 2153. 26 2306. 07 2075. 67 1916. 99 2061. 18 2032. 20 2209. 31 2139. 72 1691. 71 1682. 1 1763. 35 1630. 02 1564. 46 1534. 73 1312. 50 1389. 17 1557. 01 1557. 22 1592. 27 1707. 72 1716. 28 1671. 63 1596. 71 1650. 34 1506. 23 1580. 55 1473. 88 1458. 78 1594. 03 1664. 67 1600. 87 1628. 72 1500. 72 1470. 31 1641. 44 1819. 36 1893. 45 2229. 25 2314. 62 2485. 43 2594. 34 3074. 87 2946. 14 2923. 99 0. 08 0. 03 0. 10 -0. 12 0. 18 0. 04 0. 11 0. 10 0. 01 -0. 06 0. 09 0. 16 0. 10 0. 15 -0. 12 -0. 17 -0. 10 0. 11 -0. 10 0. 07 -0. 10 -0. 08 0. 08 -0. 01 0. 09 -0. 03 -0. 21 -0. 01 0. 05 -0. 08 -0. 04 -0. 02 -0. 14 0. 06 0. 12 0. 00 0. 02 0. 07 0. 01 -0. 03 -0. 04 0. 03 -0. 09 0. 05 -0. 07 -0. 01 0. 09 0. 04 -0. 04 0. 2 -0. 08 -0. 02 0. 12 0. 11 0. 04 0. 18 0. 04 0. 07 0. 04 0. 19 -0. 04 -0. 01 1. 08 1. 03 1. 10 0. 88 1. 18 1. 04 1. 11 1. 10 1. 01 0. 94 1. 09 1. 16 1. 10 1. 15 0. 88 0. 83 0. 90 1. 11 0. 90 1. 07 0. 90 0. 92 1. 08 0. 99 1. 09 0. 97 0. 79 0. 99 1. 05 0. 92 0. 96 0. 98 0. 86 1. 06 1. 12 1. 00 1. 02 1. 07 1. 01 0. 97 0. 96 1. 03 0. 91 1. 05 0. 93 0. 99 1. 09 1. 04 0. 96 1. 02 0. 92 0. 98 1. 12 1. 11 1. 04 1. 18 1. 04 1. 07 1. 04 1. 19 0. 96 0. 99 1. 08 1. 11 1. 22 1. 07 1. 26 1. 32 1. 46 1. 61 1. 63 1. 52 1. 66 1. 93 2. 12 2. 42 0. 88 0. 73 0. 65 0. 73 0. 65 0. 70 0. 63 0. 58 0. 63 0. 62 0. 67 0. 65 0. 51 0. 51 0. 54 0. 9 0. 48 0. 47 0. 40 1. 06 1. 19 1. 19 1. 21 1. 30 1. 31 1. 27 1. 22 1. 26 1. 15 1. 20 1. 12 1. 11 1. 21 1. 27 1. 22 1. 24 1. 14 1. 12 1. 25 1. 39 1. 44 1. 70 1. 76 1. 89 1. 98 2. 34 2. 24 2. 23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 186 March 2004 April 2004 May 2004 June 2004 July 2004 August 2004 September 2004 October 2004 November 2004 December 2004 January 2005 February 2005 March 2005 April 2005 May 2005 June 2005 July 2005 August 2005 September 2005 October 2005 November 2005 ecember 2005 January 2006 February 2006 March 2006April 2006 May 2006 June 2006 July 2006 August 2006 September 2006 October 2006 November 2006 ecember 2006 January 2007 February 2007 March 2007 April 2007 May 2007 June 2007 July 2007 August 2007 September 2007 October 2007 November 2007 December 2007 January 2008 February 2008 March 2008 April 2008 May 2008 June 2008 July 2008 August 2008 September 2008 October 2008 November 2008 December 2008 January 2009 February 2009 March 2009 April 2009 May 2009 June 2009 July 2009 August 2009 International Research Journal of Finance and Economics Issue 50 (2010) 2966. 31 3025. 14 2525. 35 2561. 16 2755. 22 2789. 07 2997. 97 027. 96 3339. 75 3580. 34 3521. 71 3611. 90 3481. 86 3313. 45 3601. 73 3800. 24 4072. 15 4184. 83 4566. 63 4159. 59 4649. 87 4953. 28 5224. 97 5422. 67 5904. 17 6251. 39 5385. 21 5382. 11 5422. 39 5933. 77 6328. 33 6603. 60 6931. 05 6982. 56 7145. 91 6527. 12 6587. 21 7032. 93 7468. 70 7605. 37 8004. 05 7857. 61 8967. 41 10391. 19 10384. 40 11154. 28 9440. 94 9404. 98 8232. 82 9199. 46 8683. 27 7029. 74 7488. 48 7621. 40 6691. 57 4953. 98 4600. 45 4988. 04 4790. 32 4516. 38 4942. 51 5803. 97 7620. 13 7571. 49 8176. 54 8225. 50 0. 01 0. 02 -0. 17 0. 01 0. 08 0. 01 0. 07 0. 01 0. 10 0. 07 -0. 02 0. 03 -0. 04 -0. 05 0. 9 0. 06 0. 07 0. 03 0. 09 -0. 09 0. 12 0. 07 0. 05 0. 04 0. 09 0. 06 -0. 14 0. 00 0. 01 0. 09 0. 07 0. 04 0. 05 0. 01 0. 02 -0. 09 0. 01 0. 07 0. 06 0. 02 0. 05 -0. 02 0. 14 0. 16 0. 00 0. 07 -0. 15 0. 00 -0. 12 0. 12 -0. 06 -0. 19 0. 07 0. 02 -0. 12 -0. 26 -0. 07 0. 08 -0. 04 -0. 06 0. 09 0. 17 0. 31 -0. 01 0. 08 0. 01 1. 01 1. 02 0. 83 1. 01 1. 08 1. 01 1. 07 1. 01 1. 10 1. 07 0. 98 1. 03 0. 96 0. 95 1. 09 1. 06 1. 07 1. 03 1. 09 0. 91 1. 12 1. 07 1. 05 1. 04 1. 09 1. 06 0. 86 1. 00 1. 01 1. 09 1. 07 1. 04 1. 05 1. 01 1. 02 0. 91 1. 01 1. 07 1. 06 1. 02 1. 05 0. 98 1. 14 1. 16 1. 00 1. 07 0. 85 1. 00 0. 88 1. 12 . 94 0. 81 1. 07 1. 02 0. 88 0. 74 0. 93 1. 08 0. 96 0. 94 1. 09 1. 17 1. 31 0. 99 1. 08 1. 01 2. 26 2. 30 1. 92 1. 95 2. 10 2. 13 2. 28 2. 31 2. 54 2. 73 2. 68 2. 75 2. 65 2. 52 2. 74 2. 90 3. 10 3. 19 3. 48 3. 17 3. 54 3. 77 3. 98 4. 13 4. 50 4. 76 4. 10 4. 10 4. 13 4. 52 4. 82 5. 03 5. 28 5. 32 5. 44 4. 97 5. 02 5. 36 5. 69 5. 79 6. 10 5. 99 6. 83 7. 92 7. 91 8. 50 0. 85 0. 84 0. 74 0. 82 0. 78 0. 63 0. 67 0. 68 0. 60 0. 44 0. 41 1. 08 1. 04 0. 98 1. 07 1. 26 1. 66 1. 65 1. 78 1. 79 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5International Research Journal of Finance and Economics Issue 50 (2010) Annexure-2 Beta values of individual securities over all the five phases Overall Phase I Phase II Phase III Phase IV ? p-val ? p-val ? p-val ? p-val ? p-val Bharat unfathomed Electricals Ltd. 0. 86 0. 00* 0. 67 0. 21 1. 18 0. 00* 1. 10 0. 00* 0. 80 0. 02* Bharat Petroleum Corpn. Ltd. 0. 80 0. 00* 1. 02 0. 15 0. 66 0. 06 1. 13 0. 00* 1. 30 0. 06 Cipla Ltd. 0. 51 0. 00* -0. 04 0. 95 0. 75 0. 02* 0. 80 0. 00* 0. 51 0. 07 Sun Pharmaceutical Inds. Ltd. 0. 69 0. 00* 1. 13 0. 15 0. 80 0. 08 0. 57 0. 00* 0. 74 0. 00* Ranbaxy Laboratories Ltd. 0. 94 0. 00* 1. 19 0. 3 0. 63 0. 03* 0. 78 0. 00* 1. 07 0. 10 Wipro Ltd. 1. 47 0. 00* 2. 79 0. 02* 2. 63 0. 00* 0. 88 0. 00* 0. 87 0. 00* Reliance Infrastructure Ltd. 1. 24 0. 00* 1. 38 0. 02* 0. 26 0. 39 1. 20 0. 00* 1. 50 0. 00* Larsen & Toubro Ltd. 1. 30 0. 00* 1. 12 0. 08 1. 70 0. 00* 1. 21 0. 00* 1. 07 0. 00* State argot Of India 1. 01 0. 00* 1. 22 0. 08 0. 86 0. 00* 1. 03 0. 00* 1. 08 0. 01* Tata Motors Ltd. 1. 20 0. 00* 1. 07 0. 08 -0. 13 0. 65 1. 11 0. 00* 1. 20 0. 00* Oil & Natural flatulency Corpn. Ltd. 0. 79 0. 00* 0. 43 0. 47 0. 59 0. 03* 1. 06 0. 00* 1. 03 0. 01* Steel Authority Of India Ltd. 1. 23 0. 00* -0. 31 0. 68 0. 99 0. 00* 1. 54 0. 0* 1. 12 0. 01* Tata Steel Ltd. 1. 22 0. 00* 0. 79 0. 17 0. 64 0. 05* 1. 25 0. 00* 1. 39 0. 00* Grasim Industries Ltd. 0. 94 0. 00* 1. 24 0. 13 0. 91 0. 01* 0. 95 0. 00* 0. 86 0. 00* H D F C Bank Ltd. 0. 79 0. 00* 1. 38 0. 03* 0. 36 0. 10 0. 68 0. 00* 0. 98 0. 00* Hero Honda Motors Ltd. 0. 47 0. 00* 0. 24 0. 64 0. 04 0. 85 0. 79 0. 00* 0. 93 0. 00* Hindalco Industries Ltd. 1. 00 0. 00* 0. 03 0. 95 0. 39 0. 06 1. 22 0. 00* 1. 44 0. 00* Hindustan Unilever Ltd. 0. 49 0. 00* 0. 78 0. 01* 0. 42 0. 06 0. 77 0. 00* 0. 67 0. 00* HDFC Ltd. 0. 74 0. 00* 0. 77 0. 01* 0. 50 0. 06 0. 85 0. 00* 1. 01 0. 00* Infosys Technologies Ltd. . 91 0. 00* 1. 33 0. 05* 1. 30 0. 00* 0. 73 0. 00* 0. 67 0. 06 G A I L (India) Ltd. 0. 49 0. 00* 0. 00 1. 00 0. 46 0. 11 0. 79 0. 00* 0. 34 0. 18 I C I C I Bank Ltd. 0. 84 0. 00* 1. 85 0. 05* 0. 06 0. 88 0. 50 0. 00* 0. 57 0. 14 I T C Ltd. 0. 37 0. 00* 0. 54 0. 13 0. 57 0. 01* 0. 42 0. 00* 0. 27 0. 24 National Aluminium Co. Ltd. 0. 49 0. 00* -0. 31 0. 75 0. 24 0. 37 0. 73 0. 00* 0. 21 0. 69 Indian Oil Corpn. Ltd. 0. 87 0. 10 0. 32 0. 56 0. 65 0. 00* 1. 24 0. 00* 0. 75 0. 01* Reliance Industries Ltd. 0. 51 0. 00* 0. 34 0. 47 0. 08 0. 81 0. 41 0. 00* 0. 74 0. 06 Sterlite Industries (India) Ltd. 1. 11 0. 00* 0. 99 0. 14 1. 3 0. 09 0. 87 0. 00* 0. 01 0. 96 Tata Communications Ltd. 0. 78 0. 00* 1. 10 0. 05* 1. 18 0. 00* 0. 87 0. 00* 0. 85 0. 09 Unitech Ltd. 0. 79 0. 00* 0. 47 0. 14 0. 48 0. 02* 0. 87 0. 00* 0. 21 0. 47 Zee Entertainment Ent. Ltd. 1. 00 0. 00* 1. 39 0. 0 8 0. 72 0. 07 0. 78 0. 00* 1. 13 0. 03* * indicates significance of coefficient at 5% level of significant Name of the Company Annexure-3 187 Phase V ? p-val 0. 74 0. 00* 0. 48 0. 03* -0. 13 0. 65 0. 16 0. 55 1. 96 0. 01* 0. 78 0. 10 2. 46 0. 00* 1. 77 0. 00* 1. 55 0. 00* 1. 33 0. 02* 0. 94 0. 01* 1. 66 0. 00* 2. 07 0. 00* 0. 41 0. 29 0. 96 0. 00* 0. 29 0. 21 1. 63 0. 01* -0. 1 0. 68 0. 95 0. 00* 0. 07 0. 83 0. 38 0. 03* 1. 35 0. 02* -0. 01 0. 95 0. 50 0. 19 0. 98 0. 02* 0. 57 0. 10 0. 85 0. 03* 0. 43 0. 15 1. 27 0. 11 0. 74 0. 07 Estimates of regression equation using Time as a Variable Name of the Company Bharat Heavy Electricals Ltd. Bharat Petroleum Corpn. Ltd. Cipla Ltd. Sun Pharmaceutical Inds. Ltd. Ranbaxy Laboratories Ltd. Wipro Ltd. Reliance Infrastructure Ltd. Larsen & Toubro Ltd. State Bank Of India Tata Motors Ltd. Oil & Natural Gas Corpn. Ltd. Steel Authority Of India Ltd. Tata Steel Ltd. Grasim Industries Ltd. H D F C Bank Ltd. Hero Honda Motors Ltd. Hindalco Industrie s Ltd.Hindustan Unilever Ltd. HDFC Ltd. Constant 0. 02 0. 01 0. 02 0. 03 0. 01 0. 01 0. 01 0. 01 0. 01 0. 00 0. 01 0. 02 0. 01 0. 01 0. 02 0. 02 0. 00 0. 00 0. 02 mt (? 1) 0. 56 (0. 03) 0. 79 (0. 02) 0. 94 (0. 00) 1. 69 (0. 00) 0. 63 (0. 05) 3. 35 (0. 00) 0. 25 (0. 44) 1. 10 (0. 00) 0. 71 (0. 00) 0. 61 (0. 02) 0. 25 (0. 38) 0. 26 (0. 51) 0. 01 (0. 99) 0. 97 (0. 00) 0. 92 (0. 00) 0. 19 (0. 42) -0. 12 (0. 60) 0. 91 (0. 00) 0. 37 (0. 04) t*mt (? 2) 0. 10 (0. 22) 0. 00 (0. 96) -0. 14 (0. 10) -0. 33 (0. 00)* 0. 10 (0. 29) -0. 62 (0. 00)* 0. 33 (0. 00)* 0. 07 (0. 37) 0. 10 (0. 17) 0. 20 (0. 02)* 0. 18 (0. 03)* 0. 32 (0. 01)*