1. INTRODUCTION:

Financial success is based on saving money. Investors spend their valuable time and energy for earning money but it is also important to save money through savings and investment. But taking correct investment decision is more critical. Every investment decision should be based on the risk and return of the securities; risk varies with types of investments. Markowitz (1952)¹ postulates that portfolio risk can be reduced by diversification, later Sharpe (1964)², Lintner (1965)³, Mossin (1969)⁴ propounded that risk can divided into systematic and unsystematic risk. If systematic risk (beta) of security is stable then Capital Asset Pricing Model (CAPM) works in capital market. Beta means a security covariance with market portfolio/variance of the market portfolio or percentage change in security returns/ percentage in market returns. Beta measures a stock's volatility, the degree to which its price fluctuates in relation to the overall market. In other words, it gives a sense of the stock's market risk compared to the greater market.

Beta is also used to compare a stock's market risk to that of other stocks. A beta of 1 indicates that the security's price tends to move with the market. Stability of the beta over time is an important area of study and many researchers tried to find whether the security betas remain stable irrespective of time. Blume (1971)⁵ found that 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. Sharpe and Cooper (1972)⁶ examined the stationarity of individual betas by employing transition matrices. Based on transition matrices, which are somewhat analogous to rank correlations, Sharpe and Cooper concluded that there is substantial stationarity over time, even at the level of individual securities. Fama and French (1992)⁷ argued that the beta is no longer relevant to explain the security returns. A few studies are available in the Indian context to examine the stability systematic risk. Gupta and Sehgal (1993)⁸ found that there is a relationship in the expected direction between systematic risk and variables such as debt-equity ratio, current ratio and net sales. Vaidyanathan (1995)⁹ observed that CAPM probably could not explain the risk-returns relations in the Indian capital market. Gupta and Mallick (1996)¹⁰ found evidence of year-wise instability in beta in a sample of 150 BSE listed companies during the period from April 1991 to March 1996. Vipul (1999)¹¹ 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. Ansari (2000)¹² inferred that beta leaves returns unexplained in the Indian capital markets during the study period. Chawla (2001)¹³ investigated the stability of beta using monthly data on returns for the period April 1996 to March 2000. The stability 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. He rejected the hypothesis of stable beta in case 20 out of 36 companies. Haddad (2007)¹⁴ 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. Manjunatha (2010)¹⁵ attempted to test the stability of the beta during the period 1990 to 2005 in Indian capital market. The Beta analysis of all 66 companies that are/were part of the BSE Sensex shows that, beta was not stable during the study period. The analysis of individual company beta over the period 1993 to 2005 for each of the company shows that it does not remain constant. Deb and Misra (2011)¹⁶ examined the stability of beta coefficients over time in Indian equity market. Authors studied the beta stability for cross calendar periods and for sub periods based on bull and bear phases in the market. Their results revealed that betas are instable over shorter time horizons. This instability reduces when the beta estimation period increases. Similar results were obtained in case of portfolio betas as well. Mallikarjunappa and Vasantha (2013)¹⁷ used ordinary least square technique on Nifty index based company share prices and the Nifty index to assess the beta stability for different time periods. They explored the stability issue at the individual security level taking the data from NSE for the period covering from 1990-91 to 2011-12 and found evidence for instability of betas in Indian capital market. They advised further research on the stability of portfolio betas.

From an empirical perspective, a substantial academic literature explores the importance of beta and its stability. Literature is available on the studies over the beta stability for individual securities as well as portfolios. We also found studies carried on over the entire sample period and comparison of betas over sub-sample periods. A few studies compared the beta stability over different seasonal and economic phases like bull and bear and boom and recession. However the results were mixed in nature. Evidence was found to support that betas are unstable in the shorter period, while they are consistent when the estimation period is increased. Supporting results were also found on instability of individual betas and stability of portfolio betas. In the light of mixed results in the literature and the continued interest of beta in the capital market, the issue of beta stability continues to be a debatable one among academic and practical circles. This study tests the hypothesis of stable betas for individual securities and portfolios in the Indian capital market.

2. DATA, SAMPLE AND METHODOLOGY:

The study is based on Nifty companies that are part of the index for the study period of eleven years. Nifty consists of only 50 companies. The final sample companies is selected based on two criteria: a) The companies selected should have been constituents of Nifty Index and b) continuously traded for a minimum period of seven years during the study period. The daily adjusted share prices and index from January 1, 2009 to December 31, 2019 are used in the study.

Logarithm returns:

Natural logarithm of daily relative prices of companies and index is, thus, the measure of daily return and is used for this study. The log returns formula is

Mean return of security is given by:

Mean return of market m is given by:

We calculate beta by using market model.

Portfolio betas with equal weights:

Calculated companies betas for the historical prices of the study period are arranged in highest beta to lowest beta (Nifty index as market proxy) and then formed portfolios with equal weightage. In this set, portfolio 1 has been formed by choosing the first five securities having highest beta values (companies 1, 2, 3, 4 and 5). Portfolio 2 is formed by choosing the next five securities (6, 7, 8, 9, and 10) and so on. Using this process, 10 portfolios have been formed with equal weightage to each security upto portfolio 10. Similar process is done for Sensex based betas of companies for the study period. P11 is constructed from lowest beta values (companies 1, 2, 3, 4, 5). Similar process is done up to P20. Portfolios of P11 to P20 are having low to high betas of sample companies. Next set of portfolios are constructed by using highest- medium- low betas of sample companies. Portfolio P21 consist of first two companies 1 and 2 having highest betas, lowest beta values of two companies 49 and 50 and medium beta value of company 21. This portfolio consist of 5 companies betas. This process is done for portfolio P22 to P30. Portfolios of P21 to P30 are having high- medium- low betas of sample companies. Similar process is done for portfolio P31 to portfolio 40. Portfolios of P31 to P40 are having low - medium- high betas of sample companies. We have formed portfolio betas with equal weightage by using the following formula:

3. RESULTS AND ANALYSIS:

The main objective of the study is to find out the beta stability for individual companies and portfolios. We explore whether beta stabilizes over period of time during the study period in Indian capital market. The summarized results of the individual companies’ beta from 2009 to 2019, entire eleven years company wise beta and portfolio beta are presented in Table 1 to 6.

Table 1 Beta of Companies from 2017 to 2019 and All the Years from 2009 to 2019 (Nifty as Market Proxy)

Sl. No	Name of the Company	2017	2018	2019	2009-2019	SD
1	Adani Ports and Special Economic Zone Ltd.	1.55	1.41	1.20	1.02	0.23
2	Asian Paints Ltd.	0.77	0.93	0.92	0.53	0.19
3	Axis Bank Ltd.	1.19	1.26	1.31	1.38	0.08
4	Bharat Petroleum Corporation Ltd.	1.16	1.47	1.40	0.74	0.33
5	Bajaj Auto Ltd.	0.88	1.02	0.78	0.71	0.14
6	Bajaj Finance Ltd.	1.45	1.46	1.55	0.94	0.28
7	Bajaj Finserv Ltd.	1.36	1.41	1.37	0.70	0.34
8	Bharti Airtel Ltd.	1.01	1.11	0.94	0.86	0.11
9	Bharti Infratel Ltd.	0.19	0.24	0.08	0.07	0.18
10	Britannia Industries Ltd.	0.65	0.90	0.77	0.39	0.22
11	Cipla Ltd.	0.70	0.82	0.56	0.56	0.13
12	Coal India Ltd.	0.74	0.51	0.81	0.69	0.13
13	Dr. Reddy's Laboratories Ltd.	0.55	0.59	0.35	0.50	0.11
14	Eicher Motors Ltd.	1.07	1.22	1.57	0.70	0.36
15	GAIL (India) Ltd.	0.96	0.75	1.03	0.74	0.15
16	Grasim Industries Ltd.	1.13	1.19	1.48	0.82	0.27
17	HDFC Ltd	0.98	1.24	1.14	1.13	0.11
18	HCL Technologies Ltd.	0.23	0.53	0.29	0.83	0.27
19	HDFC Bank Ltd.	0.72	0.68	1.02	0.91	0.16
20	Hero MotoCorp Ltd.	0.96	0.89	1.23	0.71	0.22
21	Hindustan Unilever Ltd.	0.81	0.74	0.66	0.47	0.15
22	Hindalco Industries Ltd.	1.98	1.42	1.15	1.44	0.35
23	Indian Oil Corporation Ltd.	1.03	1.31	1.28	0.66	0.30
24	ICICI Bank Ltd.	1.54	1.32	1.41	1.51	0.10
25	IndusInd Bank Ltd.	0.92	0.95	1.79	1.23	0.40
26	Infosys Ltd.	0.70	0.58	0.31	0.69	0.18
27	ITC Ltd.	1.16	0.85	0.75	0.69	0.21
28	JSW Steel Ltd.	1.72	1.28	1.56	1.44	0.19
29	Kotak Mahindra Bank Ltd.	0.77	1.04	0.97	1.19	0.18
30	Larsen & Toubro Ltd.	1.33	1.09	1.30	1.27	0.11
31	Mahindra & Mahindra Ltd.	0.95	1.18	1.44	1.06	0.21
32	Maruti Suzuki India Ltd.	1.07	1.12	1.41	0.83	0.24
33	Nestle India Ltd.	0.34	0.71	0.61	0.37	0.18
34	NTPC Ltd.	0.73	0.61	0.56	0.70	0.08
35	Oil & Natural Gas Corporation Ltd.	0.69	1.03	1.08	0.90	0.17
36	Power Grid Corporation of India Ltd.	0.55	0.54	0.32	0.64	0.14
37	Reliance Industries Ltd.	0.96	1.38	0.98	1.14	0.19
38	State Bank of India	1.71	1.40	1.74	1.31	0.22
39	Sun Pharmaceutical Industries Ltd.	1.01	0.88	0.61	0.59	0.21
40	Tata Motors Ltd.	1.69	1.28	2.00	1.40	0.32
41	Tata Steel Ltd.	1.58	1.37	1.63	1.47	0.11
42	Tata Consultancy Services Ltd.	0.30	0.43	0.31	0.70	0.19
43	Tech Mahindra Ltd.	0.55	0.62	0.32	0.74	0.18
44	Titan Company Ltd.	1.32	0.89	0.91	0.77	0.24
45	UltraTech Cement Ltd.	1.12	1.13	1.37	0.79	0.24
46	UPL Ltd.	1.04	1.42	0.77	0.92	0.28
47	Vedanta Ltd.	1.95	1.35	1.56	1.42	0.27
48	Wipro Ltd.	0.41	0.38	0.31	0.65	0.15
49	Yes Bank Ltd.	1.20	1.35	1.98	1.48	0.34
50	Zee Entertainment Enterprises Ltd.	0.96	0.79	0.82	0.79	0.08
	Yearly average beta	1.01	0.99	1.03	0.88	0.20

Note: Column 3 to 6 shows beta values calculated based on market proxy as Nifty and Sensex using regression equation as explained in methodology of chapter 3 and column 7 shows standard deviation (SD) of beta to know the variation of beta for the year from 2009 to 2012. Same explanation holds good for table 2 of this paper.

Graph 1 Beta of Companies from 2017 to 2019 and All the Years from 2009 to 2019 (Nifty as Market Proxy)

Table and Graph 1 shows IndusInd Bank Ltd has maximum variation in beta from 0.92 to 1.79 and Axis Bank Ltd has lowest variation in beta from1.19 to1.38, Zee Entertainment Enterprises Ltd also has lowest variation in beta from 0.79 o 0.96 and average beta for the above table varies between 1.01 to 0.88. We have also compared companies beta for the entire study period from 2009 to 2019. It is found that it is not conforming standard CAPM model. We accept null hypothesis

Table 2 Beta of Portfolios formed from High Beta and Low Beta Stocks

Sl. No	Portfolios	Portfolio beta with Nifty as proxy	Portfolio beta with Sensex as proxy
1	P1	1.47	1.45
2	P2	1.36	1.35
3	P3	1.15	1.17
4	P4	0.94	0.98
5	P5	0.83	0.86
6	P6	0.76	0.76
7	P7	0.70	0.71
8	P8	0.68	0.69
9	P9	0.59	0.59
10	P10	0.36	0.44

Graph 2 Beta of Portfolios formed from High Beta and Low Beta Stocks

Table and Graph 3 shows that beta of portfolios formed from high beta and low beta stocks compared with Nifty and Sensex indices. We found that portfolio beta values do not vary much when we compare portfolio beta with Nifty index and Sensex index with few exceptions. Analysis of portfolio beta shows that beta is stable. We accept alternate hypotheses.

4. SUMMARY OF FINDINGS:

As per the research design and sample data we have done the beta analysis of NSE Nifty securities for each year from 2009 to 2019. Also we have calculated securities beta for the combined period of eleven years to test whether securities beta stable or not. Later we have formed portfolio betas based on the combined year’s securities beta. The results of the major findings are shown below.

· Betas of companies with Nifty index are having too much variation during the study period from 2016 to 2019 and same is compared to beta of companies from 2009 to 2019.

Based on above analysis we found that securities betas are not stable hence we accept null hypothesis.

· Portfolio betas values do not vary much during the study period from 2009 to 2019

Based on above analysis we found that portfolio betas are stable than securities beta during the study period with few exceptions.

5. CONCLUSION:

This study examined the stability of beta coefficients over time in Indian equity market across the calendar period. The issue of beta stability is important, as it determines the predictive accuracy of beta with respect to near term practical application. There are wide spread usage of beta estimates based on historical returns both in investment industry and academic field. We explored the stability issue at the individual security level taking the data from NSE for the period covering from 2009 to 2019. From our analysis, we found evidence for instability of betas in Indian capital market. But portfolio betas are stable in Indian capital market with few exceptions. Further research can be done to investigate the stability of portfolio betas and the various sources or causes of instability or variation in the beta value across time. Future research can also be extended by considering different return frequencies like weekly or monthly.

6. REFERENCES:

1. Markowitz, Harry M, Portfolio Selection, Journal of Finance, 1952; 7(1), 77-91.

2. Sharpe, William F. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, Journal of Finance 1964; 19(3), 425-442.

3. Lintner, John. Security Prices, Risk, and Maximal Gains from Diversification, Journal of Business 1965; 20, 294-419.

4. Mossin, Jan. Optimal Mult-Period Portfolio Policies, Journal of Business 1969; 4(2), 215-229.

5. Blume, Marshal E. On the Assessment of Risk, Journal of Finance 1971; 26(1), 1-11.

6. Sharpe William F and Cooper Guy M.. “Risk-return classes of New York stock exchange common stocks” Financial Analysts Journal 1972; 28(2), 46-54.

7. Fama Eugene, F. and French Kenneth, R. (), “The cross-section of expected stock returns”, The Journal of Finance, 1992; 47(2), 427-465.

8. Gupta, O.P. and Sehgal, Sanjay, An Empirical Testing of Capital Asset Pricing Model in India, Finance India 1993; 7, 863-874.

9. Vaidyanathan, R. Capital Asset Pricing Model: The Indian Context, The ICFAI Journal of Applied Finance 1995; 1(2), 221-224.

10. Gupta, A. and Mallick, A.K. “Interrelation between markets based security risk measure and accounting information: A study on selected Indian companies”, Decision, 1996; 23(1-4), 1-24.

11. Vipul. “Systematic risk: do size, industry and liquidity matter?” Prajanan, 1999; 27(2), 31-149.

12. Ansari Valeed A. Capital Asset Pricing Model: Should We Stop Using It? Vikalpa 2000; 25(1), 55-64.

13. Chawla, D. “Testing the stability of beta in the Indian stock market”, Decision, 2001; 28(2), 1-22.

14. Haddad, M. “An inter- temporal test of the beta stationary: the case of Egypt”, Middle East Business and Economic Review, 2007; 19(1), 1-7.

15. Manjunatha T. An analysis of Beta Stability in the Indian Capital Market, Samridhi- The Velammal Journal of Management, 2010; Issue No 2, 37-42

16. Deb Soumya Guha and Misra Sagarika. “Are equity beta stable? Evidence from Indian equity market”, The IUP Journal of Applied Finance, 2011; 17(4), 5-25.

17. Mallikarjunappa, T and Vasantha. “Are Beta Stable?”, Aims Internal journal Management, 2013; 7(1), 57-70

Webliography.

1. http://www.capitalmarket.com/. Dated: January 16, 2020.

2. https://cdbmsi.reservebank.org.in/cdbmsi/servlet/login/statistics. Dated: January 20, 2020.

3. http://bseindia.com/mktlive/indiceshighlights.asp. Dated: January 23, 2020.

4. http://nseindia.com/I I S L Indices/ S&P CNX Nifty. Dated: January 24, 2020.

Received on 15.05.2021 Modified on 29.05.2021

Asian Journal of Management. 2021;12(4):452-456.

DOI: 10.52711/2321-5763.2021.00069