Stability of Beta over Market Phases

International Research Journal of Finance and Economics ISSN 1450-2887 Issue 50 (2010) © EuroJournals Publishing, Inc. 2010 http://www. eurojournals. com/finance. htm Stability of Beta over Market Phases: An Empirical Study on Indian Stock Market Koustubh Kanti Ray Assistant Professor, Financial Management at Indian Institute of Forest Management (IIFM), Bhopal, India. E-mail: [email protected] ac. in Abstract The significant role played by beta in diverse aspects of financial decision making has forced people from small investors to investment bankers to rethink on beta in the era of globalization.
In the present changing market condition, it is imperative to understand the stability of beta which augments an efficient investment decisions with additional information on beta. This study examined the stability of beta for India market for a ten year period from 1999 to 2009. The monthly return data of 30 selected stocks are considered for examining the stability of beta in different market phases. This stability of beta is tested using three econometric models i. e. using time as a variable, using dummy variables and the Chow test. The results obtained from the three models are mixed and inconclusive.
However there are 9 stocks where all the three models reported similar signal of beta instability over the market phases. Keywords: Stability of Beta, Phase wise beta, Indian Market Beta, Dummy Variable, Chow Test 1. Introduction The Capital Asset Pricing Model (CAPM) developed by Sharpe (1964), Lintner (1965) and Mossin (1966) has been the dominating capital market equilibrium model since its initiation. It continues to be extensively used in practical portfolio management and in academic research. Its essential implication is that the contribution of an asset to the variance of the market portfolio – he asset’s systematic risk, or beta risk – is the proper measure of the asset’s risk and the only systematic determinant of the asset’s return. Risk is the assessable uncertainty (Knight, 1921) in predicting the future events that are affected by external and internal factors. Sharpe (1963) had classified risks as systematic risk and unsystematic risk. The elements of systematic risk are external to the firm. The external factors are changes in economic environment, interest rate changes, inflation, etc. On the other hand, internal factors are the sources of unsystematic risk.

Unsystematic risks are categorized as business risk or financial risk specific to the firm. The systematic risk related with the general market movement cannot be totally 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. Some of the sources of unsystematic risk are consumer preferences, worker strikes and management competitiveness. These factors are independent of the factors effecting stock market.
Hence, systematic risk will influence all the securities in the market, whereas unsystematic risk is security specific. International Research Journal of Finance and Economics – Issue 50 (2010) 175 Theoretically defined, beta is the systematic relationship between the return on the portfolio and the return on the market (Rosenberg and Marathe, 1979). It refers to the slope in a linear relationship fitted to data on the rate of return on an investment and the rate of return of the market (or market index). Beta is a technique of telling how volatile a stock is compared with the rest of the market.
When the return on the portfolio is more than the return on the market, beta is greater than one and those portfolios are referred to as aggressive portfolios. That means, in a booming market condition, aggressive portfolio will achieve much better than the market performance. While in a bearish market environment the fall of aggressive portfolios will also be much prominent. On the other hand, when the return on portfolio is less than the market return, beta measure is less than one and those portfolios are treated as defensive.
In case 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 also be less than the market portfolio. In those situations where, the return of the portfolio accurately matches the return of the market, beta is equal to one that rarely happens in real life situations. Beta estimation is central to many financial decisions such as those relating to stock selection, capital budgeting, and performance evaluation. It is significant for both practitioners and academics.
Practitioners use beta in financial decision making to estimate cost of capital. Beta is also a key variable in the academic research; for example it is used for testing asset pricing models and market efficiency. Given the importance of this variable a pertinent question for both practitioners and academics is how to obtain an efficient estimation. 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 significant role in the modern portfolio theory.
The estimation of beta for individual securities using a simple market model has been widely evaluated as well as criticized in the finance literature. One important aspect of this simple market model is the assumption of symmetry that propounds the estimated beta is valid for all the market conditions. Many studies questioned this assumption and examined the relationship between beta and market return in different market conditions, but the results are mixed and inconclusive. In this paper, an attempt is made to investigate the stability of beta in the Indian stock market during the last 10 years i. . from August 1999 to August, 2009. With this objective, the paper is divided into five sections including the present 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 outlines the results of tests for investigating the stability of beta and its findings. Section 5 is dedicated to summary, conclusion and scope for further research in the area. 2. Literature review
Several studies are carried out to study the nature and the behavior of beta. Baesel (1974) studied the impact of the length of the estimation interval on beta stability. Using monthly data, betas were estimated using estimation intervals of one year, two years, four years, six years and nine years. He concluded that the stability of beta increases significantly as the length of the estimation interval increases. Levy (1971) and Levitz (1974) have shown that portfolio betas are very stable whereas individual security betas are highly unstable.
Likewise Blume (1971) used monthly prices data and successive seven-year periods 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 time of estimation period. Similar results were also obtained by Altman et al (1974). In both the cases, initial and succeeding estimation periods are of the same length. Allen et al. (1994) have considered the subject of comparative stability of beta coefficients for individual securities and portfolios.
The usual 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 Research Journal of Finance and Economics – Issue 50 (2010) larger confidence can be placed in portfolio beta estimates over longer periods of time. But, their study concludes that larger confidence in portfolio betas is not justified. Alexander and Chervany (1980) show empirically that extreme betas are less stable compared to interior beta.
They proved it by using mean absolute deviation as a measure of stability. According to them, best estimation interval is generally four 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 March 2000. The tability of beta was tested using two alternative econometric methods, including time variable in the regression and dummy variables for the slope coefficient. Both the methods reject the stability of beta in majority of cases. Many studies focused on the time varying beta using conditional CAPM (Jagannathan and Wang (1996) Lewellen 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 persistence and time-varying nature of systematic risk of two 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 each portfolio and its systematic risk are significantly positively related.
Because of that, the systematic risks of different portfolios tend to move in a different direction during the periods of increasing 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 bull and bear market conditions for 700 individual securities listed in NYSE. Using a Dual Beta Market Model (DBM), they established that estimated 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 option data to evaluate equity risk. In the similar line, French et al. (1983) merge forward-looking volatility with istorical correlation to improve the measurement 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 allow for the calculation of what he refers to as “implicit” betas. Unfortunately the exchange options discussed by Siegel (1995) are not yet traded, and therefore his method cannot be applied in practice to compute 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 errors, the concurrent autocorrelated residuals and inter-temporal correlation between market returns and residual results in biased and unstable estimates of betas. This is so even when true values 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 residual risk. If beta coefficient changes over time, OLS method is not suitable 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 value relative to the market and the pattern of changes in interest rate. International Research Journal of Finance and Economics – Issue 50 (2010) 177
Few research studies are available in the Indian context to examine the factors influencing systematic risk. For example, Vipul (1999) examines the effect of company size, industry group 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 value of betas and the beta of medium sized 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 March 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 growth 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 Research Methodology
The data related to the study is taken for 30 stocks from BSE-100 index. 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 way that the continuous 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 August 1999 to August 2009. The stock and market (BSE-100) data has been collected from prowess (CMIE) for the above period. BSE-100 index is a broad-based index and follows 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 ranking. Where the final rank is arrived at by assigning 75 percent 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 turnover & three-month average impact cost.
The average closing price for each month of 30 socks is computed for the period August 1999 to August 2009. Therefore we have 120 average monthly prices for each of the 30 stocks included in the research. The following 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-1
Where: 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 calculated as per the above formula, we identified the different market phases 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 market 178 International Research Journal of Finance and Economics – Issue 50 (2010) hases in BSE-100 index. We recognized that there 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 Nov-2008). The summary of different market phases is depicted 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 Start End Jan-1999 Feb-2000 Mar-2000 Sep-2001 Oct-2001 Dec-07 Jan-2008 Nov-08 Dec-2008 Aug-09 Market Type Bullish Bearish Bullish Bearish Bullish Figure-1: Different Market Phases
After these five market phases are identified, the beta value has been computed for each stock for each market phases following the below mentioned regression equation. 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 regression 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 null hypothesis (H0) being the beta is stable over the market phases, whereas the alternative hypothesis (H1) is that the beta values 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 variable
In 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 as a separate explanatory variable. Where the time variable t takes a value of t=1 for the first 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 values 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 basically have to see whether the expression ? 2 is significant or not. If it is significant, we need 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 and is thus stable over time. The statistical significance of ? 2 is tested using the respective p-values. . 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, 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 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 Nov 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 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 values of the parameters 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 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 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 regression assumes that the intercept as well as the slope coefficient remains the same over the entire period; that is, there is no structural change. Now 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 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 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 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 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 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 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 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 overall 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 overall period. But none of the company’s 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 Hindustan Lever) recent beta value (Dec 2008 to August 2009) is negative, where Cipla’s 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, Sunpharma, 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 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 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 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 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 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 represented 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 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 Steel, Hindalco, Hindustan Unilever, HDFC, Infosys and Zee 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 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 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 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 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 sound corporate financial decisions. Financial decisions should not be based on the overall beta of the company. Rather, the company’s 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 Analysis, Vol. XV, No. 1, March, pp. 123-137. Altman, Edward I. , Bertrand Jacquillat and Michel
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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 Nagel, S. (2003) The conditional CAPM does not explain asset-pricing anomalies, MIT Sloan Working Paper No. 4427-03. Lintner, John. 1965. “Security 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), What’s Your Real Cost of Capital? 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 Predictive 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, Stewart (1980) “Biased Estimators and Unstable 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) “Measuring 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 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 2002
May 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 November 2005 ecember 2005 January 2006 February 2006 March 2006
April 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 5
International 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 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 Bank 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 Gas 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. 08 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 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)*

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