'Stability of Beta over Market Phases\r'

' multinational query ledger of finance and economic science ISSN 1450-2887 disoblige 50 (2010) © Eurojournals Publishing, Inc. 2010 http://www. eurojournals. com/finance. htm Stability of of import everywhere commercialize placeplace chassiss: An Empirical Study on Indian spud commercialise Koustubh Kanti Ray Assistant Professor, monetary commission at Indian Institute of Forest heed (IIFM), Bhopal, India. E-mail: [email protected] ac. in Abstract The evidential role played by meaning(a) in diverse aspects of pecuniary decision making has coerce people from minor investors to enthronization bankers to rethink on of import in the era of globalization.In the perplex changing grocery condition, it is imperative to understand the persistentness of important which augments an efficient investment decisions with add upitional information on important. This field of honor take apartd the perceptual constancy of important for India securities sedu lousness for a ten year occlusive from 1999 to 2009. The calendar periodical bring back information of 30 selected gun gun personal line of credits be considered for examining the stillness of important in contrasting grocery signifiers. This constancy of of import is stressed victimisation third econometric nonpluss i. e. employ date as a shifting, using poop covariants and the grub test. The results obtained from the three samples atomic reckon 18 interracial and inconclusive.However on that point ar 9 carnations where exclusively in all the three models report similar designate of important imbalance all everyplace the commercialise place shapes. Keywords: Stability of genus of import, material body refreshed genus genus important, Indian grocery important, Dummy Variable, chow see 1. inception The Capital Asset Pricing stick (CAPM) create by Sharpe (1964), Lintner (1965) and Mossin (1966) has been the dominating capital grocery store counterweight model since its initiation. It continues to be extensively utilise in practical portfolio management and in academic inquiry. Its internal implication is that the contri unlession of an plus to the divergency of the food groceryplace portfolio †he asset’s organized endangerment, or genus of import essay †is the proper measuring of the asset’s risk and the only organized antigenic de borderinant of the asset’s decrease. jeopardize is the assessable doubt (Knight, 1921) in predicting the future events that be doctored by external and internal factors. Sharpe (1963) had classified risks as systematic risk and unsystematic risk. The elements of systematic risk be external to the firm. The external factors be diversenesss in scotch environment, interest rate swops, inflation, etc. On the opposite hand, internal factors argon the sources of unsystematic risk.Unsystematic risks be reason as business risk or m unmatchabletary risk specific to the firm. The systematic risk think with the general mart movement preempt non be all eradicated through diversification. The unsystematic risk, which is confine to a firm, stomach be eliminated or reduced to a extensive extent by choosing an appropriate portfolio of securities. Some of the sources of unsystematic risk atomic number 18 con nubbleer preferences, worker strikes and management competitiveness. These factors atomic number 18 independent of the factors effecting rakehell trade.Hence, systematic risk go forbidden influence all the securities in the trade, whereas unsystematic risk is earnest specific. foreign enquiry journal of finance and economics †bulge verboten 50 (2010) 175 theoretically defined, important is the systematic relationship between the occur on the portfolio and the leave on the grocery store (Rosenberg and Marathe, 1979). It refers to the hawk in a linear relationship fitted to d ata on the rate of cash in unrivaleds chips on an investment and the rate of ingathering of the commercialize (or trade index). Beta is a proficiency of telling how volatile a bear is comp ard with the rest of the foodstuff.When the retrograde on the portfolio is more(prenominal) than the return on the market, genus Beta is greater than ace and those portfolios ar referred to as aggressive portfolios. That fashion, in a booming market condition, aggressive portfolio will give oft better than the market performance. While in a concentrateish market environment the guide of aggressive portfolios will withal be much prominent. On the opposite hand, when the return on portfolio is less(prenominal)(prenominal) than the market return, genus Beta measure is less than unitary and those portfolios argon treated as vindicatory.In quality of defensive portfolios, when the market is rising, the performances associated with it will be less than the market portfolio. Howev er, when the market moves down, the fall in the defensive portfolios would in like manner be less than the market portfolio. In those situations where, the return of the portfolio accurately matches the return of the market, important is equal to genius that r atomic number 18ly happens in real life situations. Beta thought is central to m whatever financial decisions such as those relating to stock selection, capital bud liquidateing, and performance evaluation. It is satisfying for 2 practitioners and academics.Practitioners expenditure genus Beta in financial decision making to estimate equal of capital. Beta is to a fault a key variable in the academic research; for example it is used for examination asset determine models and market energy. Given the brilliance of this variable a pertinent question for both practitioners and academics is how to obtain an efficient mind. This study is aimed at examination the important constancy for India. only the stability of beta is of great concern as it is a full of life tool for almost all investment decisions and plays a significant role in the modern portfolio theory.The attachment of beta for un shared securities using a simplex market model has been widely evaluated as rise as criticized in the finance writings. One important aspect of this simple market model is the boldness of symmetry that propounds the estimated beta is valid for all the market conditions. umpteen studies questioned this as subject matterption and examined the relationship between beta and market return in antithetic market conditions, notwithstanding the results are mixed and inconclusive. In this composition, an drive is made to investigate the stability of beta in the Indian stock market during the last 10 historic period i. . from dreadful 1999 to prideful, 2009. With this objective, the paper is divided into cinque sections including the present section. subsection 2 reviews the existing literature an d discusses the findings of major empirical researches conducted in India and other countries. Section 3 describes the data sources and mannerology. Section 4 fall reveallines the results of tests for examine the stability of beta and its findings. Section 5 is consecrated to summary, conclusion and scope for further research in the area. 2. Literature reviewSeveral studies are carried show up to study the nature and the behavior of beta. Baesel (1974) studied the impact of the space of the tenderness interval on beta stability. apply monthly data, betas were estimated using estimation intervals of one year, dickens years, quadruplet years, six years and nine years. He think that the stability of beta add-ons significantly as the length of the estimation interval increases. Levy (1971) and Levitz (1974) give birth targetn that portfolio betas are very fixed whereas singleistic security betas are passing un steadfast.Like clean Blume (1971) used monthly determine s data and incidental seven-year goals and shown that the portfolio betas are very inactive where as individual security betas are highly un electrostatic in nature. He shows that, the stability of individual beta increases with increase in the eon of estimation goal. Similar results were also obtained by Altman et al (1974). In both the cases, sign and succeeding estimation expi dimensionns are of the same length. Allen et al. (1994) accommodate considered the subject of comparative stability of beta coefficients for individual securities and portfolios.The usual perception is that the portfolio betas are more unchanging than those for individual securities. They argue that if the portfolio betas are more stable than those for individual securities, the 176 International Research diary of pay and economic science †Issue 50 (2010) larger federal agency can be placed in portfolio beta estimates everyplace longer accomplishments of clock. But, their study dissolv es that larger impudence in portfolio betas is non justified. Alexander and Chervany (1980) show through empirical observation that extreme betas are less stable compared to inside(prenominal) beta.They proved it by using mean downright deviation as a measure of stability. gibe to them, best estimation interval is generally quadruple to six years. They also showed that irrespective of the manner portfolios 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 borderland 2000. The tability of beta was tested using deuce alternative econometric methods, including time variable in the retrogression and titty variables for the list coefficient. Both the methods eliminate the stability of beta in majority of cases. Many studies focused on the time varying be ta using conditional CAPM (Jagannathan and Wang (1996) Le come upen and Nagel (2003)). These studies concluded that the fluctuations and events that influence the market might change the leverage of the firm and the variance of the stock return which ultimately will change the beta.Haddad (2007) examine the degree of return volatility tenaciousness and time-varying nature of systematic risk of devil Egyptian stock portfolios. He used the Schwert and Sequin (1990) market model to study the relationship between market capitalization and time varying beta for a sample of investable Egyptian portfolios during the period January, 2001 to June, 2004. According to Haddad, the small stocks portfolio exhibits difference in volatility persistence and time variability. The study also suggests that the volatility persistence of apiece portfolio and its systematic risk are significantly positively related.Because of that, the systematic risks of disparate portfolios tend to move in a antith etic direction during the periods of change magnitude 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 derivative instrument effect of bull and bear market conditions for 700 individual securities listed in NYSE. Using a Dual Beta food market Model (DBM), they established that estimated betas of most of the securities are stable in both the market conditions.They hit it with three different set of bull and bear market definitions and concluded with the same results for all these definitions. Fama and cut (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 advanced market-derived capital pricing model (MCPM), which uses option data to evaluate virtue risk. In t he similar line, French et al. (1983) merge innovational volatility with istorical correlational statistics to improve the measurement of betas. Siegel (1995) notes the returns of a beta base on forward- flavour option data, and proceeds to propose the creation of a new derivative, called an exchange option, which would allow for the calculation of what he refers to as â€Å"implicit” betas. Unfortunately the exchange options discussed by Siegel (1995) are not yet traded, and thitherfore his method cannot be applied in practice to see forward-looking betas. A few studies are carried out to explore the reason for instability of beta.For example, Scott & Brown (1980) show that when returns of the market are subjected to measurement phantasms, the concurrent autocorrelated ends and inter-temporal correlation between market returns and residual results in aslope and unstable estimates of betas. This is so even when true set of betas are stable everyplace time. The y also derived an facial expression for the instability in the estimated beta between two periods. Chen (1981) investigates the connection between variability of beta coefficient and portfolio residual risk. If beta coefficient changes everyplace time, OLS method is not suitable to estimate portfolio residual risk.It will antedate 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 dead estimate of portfolio residual risk. Bildersee and Roberts (1981) show that during the periods interest order fluctuate, betas would fluctuate systematically. The change would be in line of descent with their esteem relative to the market and the pattern of changes in interest rate. International Research journal of finance and economic science †Issue 50 (2010) 177Few research studies are available in the Indian context to examine the factors influe ncing systematic risk. For example, Vipul (1999) examines the effect of caller-out surface, industry convocation and liquidity of the scrip on beta. He considered equity shares of 114 companies listed at Bombay Stock Exchange from July 1986 to June 1993 for his study. He found that size of the company affects the range of betas and the beta of medium surface companies is the lowest which increases with increase or decrease in the size of the company. The 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 attest 1993. on that point is a confirmation of relationship in the expect direction between systematic risk and variables such as debt-equity ratio, current ratio and net sales. The draw between systematic risk and variables like profitability, payout ratio, earning harvest-festival and earn ings volatility measures is not in conformation with expected sign. The relationship was investigated using correlation depth psychology in the study. 3. Data Type and Research MethodologyThe data related to the study is taken for 30 stocks from BSE-100 index. The take in 30 stocks are chosen on the solid ground of their market capitalization in BSE-100 index. These 30 stocks are selected from BSE100 stocks in such a way that the consecutive price data is available for the study period. The familiarized closing prices of these 30 stocks were collected for the last 10 years period i. e. from August 1999 to August 2009. The stock and market (BSE-100) data has been collected from prowess (CMIE) for the to a higher place period. BSE-100 index is a broad-based index and notes globally accredited 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 (B SE). As per the stock market guideline, the stocks inducted in the index are on the basis of their final associationing. Where the final rate is arrived at by assigning 75 percent weightage to the rank on the basis of three-month honest full market capitalization and 25 percent weightage to the liquidity rank based on three-month average daily employee turn everywhere & three-month average impact cost.The average closing price for to separately one month of 30 socks is encryptd for the period August 1999 to August 2009. because we clear 120 average monthly prices for each of the 30 stocks included in the research. The adjacent method has been used to compute the monthly return on each of the stock. P i,t †P i,t-1 ri,t = â€â€â€â€â€â€â€â€â€â€ P i, t-1 Where: P i,t = mean(a) price of stock â€Å"i” in the month t Pi,t-1 = Average price of stock â€Å"i” in the month t-1 r i,t= father of ith stock in the month t. The mont hly market return is computed in the next way: Bt †Bt-1 mt = â€â€â€â€â€â€â€â€â€â€ B t-1Where: Bt = BSE-100 Index 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 work out as per the above formula, we identified the different market classs to compute beta separately. The market casts are identified, by creating a additive wealth index from the market returns. The cumulative wealth index data is presented in annexure-1. As per the cumulative wealth index, we identified quin different market 178 International Research Journal of finance and Economics †Issue 50 (2010) hases in BSE-100 index. We acknowledge that on that point are three optimistic phases (Jan-1999 to Feb-2000, Oct-2001 to declension-2007 and Dec-2008 to August 2009) and two pessimistic phases (Mar-2000 to Sept2001, Jan-2008 to zero(prenominal)-2008). The summary of different marke t phases is represent in Table -1& figure-1 below. Table-1: Different Market Phases Market Phases Phase I Phase II Phase III Phase IV Phase V Market Phase Timing croak End Jan-1999 Feb-2000 Mar-2000 Sep-2001 Oct-2001 Dec-07 Jan-2008 nary(prenominal)-08 Dec-2008 Aug-09 Market Type Bullish pessimistic Bullish Bearish Bullish Figure-1: Different Market PhasesAfter these five market phases are identified, the beta rank has been computed for each stock for each market phases following the below mentioned atavism par. 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 above atavism equation is applied to calculate beta coefficient of each stocks for each market phases separately and taking the wide-cut ten years period. As the objective of the paper is to test the stability of beta in different market phases, the guess has been set accordingly.The zilch venture (H0) being the beta is stable over the market phases, whereas the alternative dead reckoning (H1) is that the beta comforts are not stable and varies according to phases in the market. The guessing has been tested with the help of three econometric models- using time as a variable, using pot variables to measure the change of slope over the period and through cabbage test. International Research Journal of finance and Economics †Issue 50 (2010) 179 3. 1. examination the Stability of Beta using time as a variableIn case of measuring stability of beta using time as a variable, in the above reasoning backward model (1) another variable i. e. ” t mt” is used as a separate explanatory variable. Where the time variable t takes a cheer of t=1 for the commencement exercise market phase, t=2 for the second market phase and so on for all other market phases identified. In this method the objective is to see whether the beta entertains are stable over time or not. After including the tmt variable, the above relapsingion 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 basically go through to see whether the expression ? 2 is significant or not. If it is significant, we need to get rid of the idle accomplishableness 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 and is on that pointfore stable over time. The statistical implication of ? 2 is tested using the respective p-value. . 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 abo ve mentioned regression equation (1) for the slope coefficients. As five market phases discovered, there 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 other unfermented. D2 = 1 for phase II (whitethorn 2000 to Sept 2001) data = 0 other intelligent D3 1 for phase III (Oct 2001 to Dec 2007) data = 0 otherwise D4 = 1 for phase IV (Jan 2008 to zero(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 to 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 entailment 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 unblemished period, all coefficients like, ? 2, ? 3, ? 4 and ? 5 should be statistically insignificant and where we need to accept the zippo 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 geomorphologic or Parameter Stability of Regression Model: The chow Test In the third method, for morphological 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 clxxx 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 p arameters of the model do not remain 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 possible regressions for each stock (five regressions for each market phases and one for the unharmed 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 total period. in that location 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 u’s 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 regressio n assumes that the intercept as well as the slope coefficient remains the same over the entire period; that is, there is no structural change. zero(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 follows:First 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 shocking 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 p hase ? ). Since the five sets of samples are deemed independent, in the third step 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 basically 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 comminuted F value obtained from 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 nu ll 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 Ordinary 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 inform 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 boilers suit 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. Out 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 boilers suit period. But none of the company’s general 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 general period. These stocks are considered to be less volatile than the market. There are 3 companies (Cipla, ITC and Hindustan Lever) youthful beta value (Dec 2008 to August 2009) is damaging, where Cipla’s phase I beta value is also negative along with other two stocks like can vass 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, solarizepharma, Wipro, Grasim, Hindustan Lever, Infosys and ITC whose beta values are showing 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 rejected in 29 out of 3 0 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 be 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 depicted in annexure-3.It is observed that the value of R2, a measure of goodness of fit varies from 0. 11 to 0. 61. 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 signi ficant 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 indicate 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 in bodilys 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 correspond 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 estimated results of Chow test are depicted in annexure-5. The results show that, 12 out of 30 cases the F-value is statistically significant a nd 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 likeliness 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 m odel3 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 regard 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 stigma, Hindalco, Hindustan Unilever, HDFC, Infosys and Zee merriment. 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 hypothesis, 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 low gear 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 phases. In the similar line the results obtained in respect to model two states that in 17 out of 30 cases the null hypothesis is reject ed.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 analyze 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 material 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 sound corporate financial decisions. pecuniary decisions should not be based on the overall beta of the company. Rather, the com pany’s periodical beta should be relied upon for taking plastered 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. 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[26] [27] [28] [29] 30] [31] [32] [33] [34] 185 International Research Journal of Finance and Economic s †Issue 50 (2010) Annexure-1: Month December 1998 January 1999 February 1999 work on 1999 April 1999 May 1999 June 1999 July 1999 August 1999 September 1999 October 1999 November 1999 December 1999 January 2000 February 2000 attest 2000 April 2000 May 2000 June 2000 July 2000 August 2000 September 2000 October 2000 November 2000 December 2000 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 Closing 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 Nove mber 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 78 57. 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 boilers suit Phase I Phase II Phase III Phase IV ? p-val ? p-val ? p-val ? p-val ? p-val Bharat Heavy 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* rock oil & Natural Gas Corpn. Ltd. 0. 79 0. 00* 0. 43 0. 47 0. 59 0. 03* 1. 06 0. 00* 1. 03 0. 01* Steel warrant 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 cant 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 atomic number 13 Co. Ltd. 0. 49 0. 00* -0. 31 0. 75 0. 24 0. 37 0. 73 0. 00* 0. 21 0. 69 Indian vegetable 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. 08 0. 72 0. 07 0. 78 0. 00* 1. 13 0. 03* * indicates significance of coefficient at 5% level of significant delineate 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 chanc e upon 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 Industries 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)*\r\n'