Stability of Equity Systematic Securities Risk
Stability of Equity Systematic Securities Risk
S. Sathyanarayana, Sudhindra Gargesha /Volume 13/Issue 2/(April-September 2020)
Security returns are the primary motive of the investment in the equity shares. The returns vary based on the volatility or risk in the market. This volatility and risk can be technically measured by Beta of the Capital Asset Pricing Model (CAPM). Further, Beta also varies due to various factors. The variations in the beta helps measure the variations in the security returns of the equity shares. In this study, we compute the beta and studied the beta stability in the context of subprime crisis and currency demonetization. The portfolios also constructed to evaluate the beta stability based in the market capitalization. We use daily closing price of 30 composites stocks of Sensex index from April 2000 to March 2019. We use chow breakpoint test and multiple breakpoint tests to estimate the breaks in the computed BETA series. The Chow breakpoint test results find the break in Axis bank, HUL and ICICI banks where subprime crisis used as the event. However, remaining sample of stocks does not have breaks in the return series. In the period of currency demonetization, Bharti Airtel, Reliance Industries, Tata Motors, and Tata Steel socks beta affected significantly and therefore beta is not stable. However, remaining stocks betas are stable. The constructed portfolios do not have breaks in the subprime crisis beta series. However, the multiple breakpoint tests find breaks for the majority of the stocks. This shows that inconsistency in the Beta series of stocks and consequently there is need to analyze Beta behavior.
Key words: BETA; CAPM; Chow Breakpoint Test; Multiple Breakpoint test.
Capital asset Pricing Model (CAPM) theory establishes the relationship between risk and returns of the security. It also emphasis on the investor’s preferences and choice while investing in the stock market based on the risk level. Generally, the investors will have two types of risk viz. systematic risk and unsystematic risk. The CAPM assumes that unsystematic risk can be controllable and systematic risk cannot be controllable in nature. Consequently, CAPM establishes the relationship between systematic risk and stock returns. This relationship is positive and every additional risk needs to be compensated by the additional stock returns. Therefore, the analysis of the systematic risk helps to analyze the stock returns movements. In CAPM, systematic risk modeled and technically called as Beta co-efficient. This Beta denotes the ‘sensitivity of the stock returns towards market returns’. It also signals the variation of the stock returns, fluctuations in the market and liquidity concerns. Therefore, there is need to analyze the beta stability in the series. The CAPM theory states the value and sign of the beta signal the level of volatility in the returns series with respect to market returns. There is a possibility to predict and compare the level of risk and returns
between stock and market returns. Hence, this
study computes and estimates the beta stability in a company level by using historical daily dataset.
Indian economy is experiencing several economic reforms to boost the economy. In which, the demonetization is one of the significant major reforms implemented on 8th November 2016 to monitor the parallel economy in the country. Due to this, the general public and corporations faced lot of issues to get liquid cash for their daily affairs. Further, it has both positive and negative impact on the common people, corporations, companies and government. This also impacted the stock market significantly in terms of volatility. Therefore, this study examines Beta stability in the context of demonetization. This helps to examine the impact of demonetization on the beta series and also to know the significant structural change in the beta series. The significant change in the beta series proves that the impact of demonetization on the volatility and also on the investors behavior. In addition, we also test the unknown breaks in the beta series for the sample period used in the study. This process guides to study the beta flow over a period and number of breaks signals the frequency of the breaks in the individual company beta series.
2.0 REVIEW OF LITERATURE
Sharpe (1963) designed up a disentangled one-index standard to anticipate security returns. The significant components, and the important imperfection, of the solitary list model is that the main viewpoint directing a security's arrival is its affectability to modifications in the market portfolio return Ruler promoted the principal significant review verifying that costs of the stock for firms in a similar industry display a typical progress that goes past the market crunch. Utilizing month to month costs of shutting stock for 63 firms in six enterprises amid the June 1927 to Dec 1960 period, his review reports that while half of stock value progresses could be clarified by developments in the market list, 20% of the surplus deviation was represented the combination of ventures.
Mayers (1973) and Livengston (1977) in comparable reviews affirmed King's discoveries. The Meyers study included 60 of similar organizations utilized by King and 60 extra organizations, utilizing information through December 1967. Mayers reasoned that in spite of the fact that there were solid enterprises impacts, King maybe underscored the percent of surplus deviation deciphered by the business affiliation. Livengston utilized 10 industry gatherings and 50 organizations and furthermore contemplated restores every month from January 1966 through June 1970. He additionally discovered solid duty among a similar industry in stocks, and presumed that 18% of surplus deviation was considered for by industry impacts.
Aman (2012) analyzed the risk factor fluctuations of various Indian stock indices by using 10 years data. He concluded that the beta and R square values are stable for FMCG, healthcare and IT whereas reality, metal and IT are not stable sectors. It shows that beta and R square are changes based on the indices and time period. Levy (1971) and Levitz (1974) analyzed the fluctuations in the stock and portfolio beta series. They concluded that the portfolio betas are more stable compared to individual stock betas. These results are consistent with the results of Blume (1971) and Altman (1974). Further, Baesel (1974) argued that the beta estimation period interval positively impacts the stability of the beta. He also pointed out market conditions significantly impacts the beta stability of the stocks. Vipul (1999) analyzed the beta fluctuations by considering size and liquidity factor of the stocks. He pointed out that based on the size of the firm and liquidity factor level of beta stability changes. This motivates to study the stability of beta on the individual stocks. Haddad (2007) studied the variations and stability of systematic risk (beta) in Egyptian equity markets. He found that the beta stability changes over a period of time due to changes in the market conditions. Brooks et al. (1994) estimated the beta and also compared the beta stability between individual stocks and portfolios. He constructed the numerous portfolios based on various factor. He observed that the beta stability varies for individual stocks and constructed portfolios. This is due to individual stocks beta features and macro economic factors. Fabozzi and Francis (1978) studied the beta stability by using six years data and found that the 92% of stocks had stable betas and remaining stocks betas are unstable betas. Sunder (1980) classified the study period into various sub stages and analyse the beta stability. He found that increase in the time length of data set influence the beta fluctuations.
Chaturvedi and Jauhari (2012) analyzed the time varying nature of the beta by using monthly data of 15 selected stocks. They found time varying nature of the beta based on market conditions. Vasanth and Mallikarjunappa used Nifty index composite stocks data set to test the stability of the beta. They found the time varying beta based on a few stocks. Moonis and Shah (2003) studied the beta stability by using Indian financial market data and adopting Generalised Auto Regressive Conditional Hetero-scedasticity (GARCH) errors model. The results suggest that more than 50% stocks shown the inconsistency in the beta stability. Singh, R. (2008) also found the non-stationary of beta in the Indian stock market. Therefore, he suggests that beta is not suitable for practice use for the investors. Choudhary and Choudhary (2010) analysed the relationship between return and betas of 278 companies. They found that the beta is not sufficient to estimate the returns on securities. Blume (1975), Vasicek (1973) and Shalit and Yitzhaki (2002) found the instability in the beta series. Fabozzi and Francis (1978) studied the stock beta randomness by using 700 stocks on the New York stock exchange. They concluded that the
majority of the stocks have random betas. It is implied that there is instability in the beta factor. Sathyanarayana and Harish (2017) studied the beta stability by using 15 years of daily data of CNX Nifty 50 from 2000 to 2015. They found the stability of the beta in subprime crisis period. However, they found the multiple breaks in the beta series in the study period.
The above review of literature documents that beta is time varying, and beta stability also depends on the size and liquidity of the company. Studies also suggest that an inconsistency in the beta series due to company related factors. Further, there is an evidence that the beta fluctuations due to macroeconomic factors of the country or world. Therefore, we undertake the investigation of the beta stability in Indian stock market by using Sensex index stocks as sample stocks. We selected two major macroeconomic events are subprime crisis and demonetization. Our main objective is to test the beta stability changes due to subprime crisis and demonetization implemented in India. We framed the hypothesis - that there is stability in the beta series over a period of time for all the stocks.
3.0 RESEARCH METHODOLOGY
The study selects 30 stocks which are part of BSE Sensex index. This is well diversified index and it represents more than 15 major industries of Indian economy. These 30 stocks are classified as highly liquid stocks, therefore it easily represents the overall market sensitivity.
For the purpose of analysis, we collected the daily data from April 2000 to March 2019 from capital line data base. On the basis of market capitalization, three portfolios of ten companies each has been constructed. The portfolio 1 comprises top ten market capitalization stocks and portfolio 2 compose the next top market capitalized stocks, portfolio 3 involves the least
ten contains market capitalized stocks out of BSE Sensex index.
The daily continuously compounded returns of each stock and index returns were computed by using adjusted closing price.
Rt = ln( )
Where: Rt = return on day ‘t’
Ct = Closing Price on day ‘t’
C t-1 = Closing Price on day‘t-1’
And ln = natural log of underlying market series.
The Sharpe’s model which is in the form of regression equation used to compute beta values for each stock:
Rit = αi + βiRmt + eit
Ritis the individual security return for time period ‘t’.
Rmt indicates the market return (Sensex returns) for time period ‘t’.
αiand βi are the estimated regression coefficient, αi is the intercept of the equation and βi beta value of the security or market sensitivity of the stock.
eitis the error term
Chow Breakpoint test
The structure of time series data needs to be followed normality. However, this property is not always same. Therefore, in order to investigate for the structural break in the time series, we use the Chow test. In this study we test the beta structural changes in two major economic events viz. Subprime crisis of 2008 and demonetization which has been adopted on 2016. The following is the formula to compute the structural break points by using Chow test
F = (SC – (S1 + S2))/ (k)____ (S1 + S2) / (N1 + N2 -2k)
Where, SC is the sum of squared residuals from the entire data. S1 is the sum of squared residuals of the first interval (before 2008 crisis and before demonetization 2016) and S2 is the sum of squared residuals from the second interval i.e. after subprime crisis. However, N1 + N2 stand for the number of observations from first interval and second interval respectively. k is the total number of assigned parameters for the purpose of the study. The equation is an application of F-test, and it needed the sum of squared errors from three regressions one for the pooled data and one for each sample period
The following two hypotheses have been framed:
The null hypothesis of the test is that, there are no structural break points in the data.
H0: a1 = a2
H1: a1 ≠ a2
a1 = beta series before 2008 and beta series after 2016
a2= beta series after 2008 and beta series after 2016
Multiple breakpoint tests
Bai (1997) showed a new methodology to identify the breaks and further, the study conducted by Bai and Perron (1998, 2003a) created the methodology to identify the multiple breaks in the series. In this study, we estimate the structural breaks in the context of Global Maximize Test (GMT) created by Bai and Perron (1998). Further, we use U Dmax and W Dmax to estimate the multiple breaks in the series. These two factors help to estimate the breaks by maximizing the breakpoints and incorporating the weights to the individual company betas.
CUSUM test (Cumulative Sum test)
The CUSUM test is a sequential analysis used to investigate the sequential flow of residuals. This test works based on the unique graphical representation by plotting the series and this test also constructs the two critical lines at 5% probability. From this we can assess the stability of the series. The test statistic is;
Where, e represents the residual series, and denotes the dependent variable. signs , It is the vector of V*1 exogenous variables. In the model, is predicted to show zero mean. shows the regressor matrix based on all observations up to i. The is the coefficient of OLS regression based on the series of variables
4.0 RESULTS AND ANALYSIS
For the purpose of the study the researchers have taken US Subprime crisis is the event. In order to investigate the structural break point in the computed beta series the researchers have conducted a Chow Breakpoint test (Gregory Chow in 1960). For the purpose of the study the researchers have used annual beta series and they have used break date as 2008 for the chow test. For the study purpose the following hypothesis has been framed a1=a2, b1=b2 and c1=c2. One of the major assumptions of Chow test is that the error term ε is independent and identically distributed.
|COMPANIES||F-STATISTICS||PROB S.F.||LOG LIKELYHOOD||PROB S.F.|
The chow test results show that there is no break in the year 2008 for Asian Paints, Bharti Airtel, Cipla, Dr. Reddy’s Lab, GAIL, HDFC, HDFC Bank, Hero Motocorp, Infosys, L&T, ITC, Lupin, M&M, Maruti Suzuki, NTPC, ONGC, Reliance Industries, SBI, SunPharma, Tata Motors, Tata steel, TCS and Wipro do not have structural break in the computed beta series. However, Axis Bank, HUL and ICICI Bank have structural break in the computed beta series. It is evident from the above analysis that the subprime crisis has affected the private sector banks.
|Portfolios||F-STATISTICS||PROB S.F.||LOG LIKELYHOOD||PROB S.F.|
The chow test results show for the constructed three portfolios was found to be stable. The chow test results show that there is no break in the year 2008. We have: used annual beta series. The crisis was at mid-year of 2007. This might be the reason for the results. The annual beta series of the portfolios have no structural break in the year 2008.
The second event took for the purpose of the study was the policy announcement of Currency demonetization in India during the year 2016. In the following table the Chow results have been presented.
|COMPANIES||F-STATISTICS||PROB S.F.||LOG LIKELYHOOD||PROB S.F.|
The chow test results show that there is no break in the year 2016 (year of currency demonetization) for Adani Ports, Asian Paints, Axis Bank, Bajaj Auto, Cipla , Coal India , Dr.Reddys Labs, GAIL, HDFC, HDFC Ban, Hero Motocorp, HUL, ICICI Bank, Infosys, L&T, ITC, Lupin, M&M, Maruti Suzuki, NTPC, ONGC, Powergrid Reliance Industries, SBI, Sun Pharma, TCS and Wipro do not have structural break in the computed beta series. However, Bharti Airtel, Reliance Industries, Tata Motors and Tata Steel beta series have structural breaks in the computed beta series.
|COMPANIES||F-STATISTICS||PROB S.F.||LOG LIKELYHOOD||PROB S.F.|
The chow test results show for the constructed three portfolios was found to be stable. The chow test results show that there is no break in the year 2016. We have used annual beta series. The policy announcement year was 2016. This might be the reason for the results. The annual beta series of the portfolios have no structural break in the year 2016.
Multiple Break Point Test Results
According to Gujarati, Damodar (2007) in a time series data, a structural break, or structural change, is an unexpected shift can lead to colossal predicting errors and unreliability of the constructed model. Therefore, David Hendry (2012) argued that lack of stability of coefficients frequently caused forecast failure, and therefore the decision makers must regularly test for structural stability of the time series data taken for the purpose of the modelling. When there is more than one structural break in the time series data, the Chow test cannot by applied. Recently, Bai and Perron (2003) suggested a latest method for identification of unknown break points in the time series data. This test is aimed at detection of multiple structural breaks can be automatically detected in the time series data. Therefore, in the current study to investigate the multiple breaks (unknown) in the computed beta series we have conducted Bai and Perron (2003) test. This Bai and Perron test is a procedure of identification of unknown breakpoints in multiple levels of the time series. To assess the multiple breaks in the series in the current study we consider the UDmax determined breaks and WDmax determined breaks based on the Schwarz criterion and Liu, Wu, and Zidek (1997) proposed (LWZ) criterion. The following table no 4.5 presents the both with breaks and without break betas series of companies listed in BSE Sensex for the study period between 2000 to 2017 based on the UDmax determined breaks and WDmax determined breaks.
It is evident from the above table that there are one UDmax determined break and one WDmax determined breaks in the computed beta series of Asian Paints, followed by Axis Bank with one UDmax determined break and five WDmax determined breaks in the computed beta series, Bharti Airtel with no UDmax determined break and five WDmax determined breaks in the computed beta series, Cipla with three UDmax determined break and three WDmax determined breaks in the computed beta series, DrReddys Labs, with five UDmax determined break and five WDmax determined breaks in the computed beta series, GAIL, with five UDmax determined break and five WDmax determined breaks in the computed beta series, HDFC with one UDmax determined break and one WDmax determined breaks in the computed beta series, HDFC Bank, with one UDmax determined break and one WDmax determined breaks in the computed beta series, Hero Motocorp with three UDmax determined break and three WDmax determined breaks in the computed beta series, HUL with one UDmax determined break and one WDmax determined breaks in the computed beta series, ICICI Bank, with one UDmax determined break and one WDmax determined breaks in the computed beta series, Infosys, with one UDmax determined break and five WDmax determined breaks in the computed beta series, L&T with one UDmax determined break and five WDmax determined breaks in the computed beta series, ITC with one UDmax determined break and four WDmax determined breaks in the computed beta series, Lupin with two UDmax determined break and five WDmax determined breaks in the computed beta series, M&M with two UDmax determined break and five WDmax determined breaks in the computed beta series, Maruti Suzuki with two UDmax determined break and two WDmax determined breaks in the computed beta series, NTPC with two UDmax determined break and two WDmax determined breaks in the computed beta series, ONGC with one UDmax determined break and five WDmax determined breaks in the computed beta series, Reliance Industries with five UDmax determined break and five WDmax determined breaks in the computed beta series, SBI with two UDmax determined break and four WDmax determined breaks in the computed beta series, Tata Motors with five UDmax determined break and five WDmax determined breaks in the computed beta series, Tata Steel with two UDmax determined break and five WDmax determined breaks in the computed beta series, TCS with one UDmax determined break and five WDmax determined breaks in the computed beta series and Wipro with five UDmax determined break and five WDmax determined breaks in the computed beta series.
It is evident from the above table that there are one UDmax determined break and one WDmax determined breaks in the computed beta series of portfolio one, followed by four UDmax determined break and four WDmax determined breaks in the computed beta series for portfolio two and for portfolio five UDmax determined break and five WDmax determined breaks in the computed beta series.
In the last phase, CUSUM test has been conducted to find the sequential changes in the computed beta series of the 30 Sensex listed stocks and the constructed three portfolios. This technique is developed by Brown, Durbin, and Evans (1975) in their seminal work. They suggested to apply this important technique of recursive residuals while testing for structural change over time. In this context we have two important tests namely (i) cumulative sum (CUSUM) test and (ii) cumulative sum of squares (CUSUMSQ) test. These two tests are conducted with the following set of hypothesis that is the coefficient vector β is the same in every period (Null) with the alternative is not. This test does not require any prior specification of when the structural change takes place. On the basis of cumulative sum of the equations is errors in regression. This option plots the sum cumulation together graphically with the five percent critical lines. For a series that remains within stability, the cumulative sum will vary randomly around a mean of zero. The method finds instability in the distribution if the sum of cumulation goes outside the area between the two critical lines that is the parameters will not be treated stable if the error of recursive sum gets outside the two critical lines. CUSUM test result series nearer to zero mean value. However, this test is less robust compared to Chow test.
It is evident from the above table that the computed beta series is stable for Adani Ports, followed by unstable for Asian Paints and Axis Bank. For Bajaj Auto, Bharti Airtel, Cipla, Coal India, Dr Reddys Labs and GAIL computed beta series were stable for the period 2000-2017. L&T, ITC, Lupin, M&M, Maruti Suzuki, NTPC, ONGC, Powergrid Corporation, Reliance Industries, Sun Pharma and Tata Motors have reported stable beta for the study period. However, HDFC, HDFC Bank, Hero Motocorp, HUL, ICICI Bank, Infosys, SBI Tata Steel, TCS and Wipro betas were unstable for the study period.
In order to investigate the sequential changes in the beta series of the constructed portfolios the CUSUM test has been conducted. The above graph shows that all the three constructed portfolios have reported a sequential change in the computed beta series.
5.0 DISCUSSION AND CONCLUSION
The current empirical study entitled “Stability of beta in Indian stock market”, has been undertaken with an intention to investigate whether the betas are stable across the time or not. In order to realise the stated objectives the researchers have collected data for seventeen financial years from 2000 to 2019. The selected stocks which are components of BSE Sensex were taken into consideration. The current study has been conducted in two phases namely; computation of CAPM beta on first phase for 30 stocks by using OLS Regression and the known, unknown and sequential breaks tests have been conducted by using Chow breakpoint test to investigate impact of subprime crisis of 2008 and currency demonetization. Bai and Perron test to find the unknown breaks in the computed beta series. The study revealed that following major findings. The chow test results for 2008 crisis show that the 23 companies do not have structural break in the computed beta series. However, only three companies have structural break in the computed beta series. The currency demonetization has not affected the 26