1. INTRODUCTION:

Investment in equity stocks has been done for capital appreciation and/or dividend income. Empirical studies found that stock return in the capital market is highly variable. The investor’s risk-return trade-off can be achieved by diversification of equity stocks. The process of investing funds in several stocks is known as diversification. Diversification is the act of holding many stocks in order to reduce risk. Markowitz (1952) developed a mathematical concept of diversification by using the variance of returns as a measure of risk for portfolio construction. He proved that if investors balanced their investment among several stocks, it was possible to reduce risk. This helps investors constitute portfolios that attain the expected return for a given level of risk or the minimum risk for a given level of expected return.

The portfolio theory is based on the assumption that investors care only about the mean and variance of return. Investors are mean-variance optimizers, and therefore, they seek and prefer portfolio with least return variance for a given level of expected return.

1.1 Studies on Optimising of Portfolio in Developed Capital Markets:

Researchers in stocks market have attempted to understand the diversification of stocks and the way portfolio risk is reduced in the efficient portfolios of the capital market. The studies conducted in developed capital markets in various form of portfolio analysis. Markowitz (1959) found that diversification reduces the portfolio risk in the U S capital market. Sharpe (1964), Lintner (1965), Jensen (1968), Treynor and Black (1973) debated on the use of the original sample covariance matrix to estimate the risk of an asset portfolio. Lakonishok, Shlifer and Vishny (1994) found that diversification reduces the portfolio risk in Japanese capital market. Rom and Ferguson (1994); Chan et al (1999); Ulucan (2007) show that mean variance efficient investment portfolio performed better for long term period. DeMiguel et al (2009); Santhos and Tessari (2012), Araújo and Montini (2015) questioned the use of the variance of returns as a proxy for investment risk. Dare et al (2017) analysed gold, oil, silver and platinum and found that diversifying in gold minimizes higher risk and achieve more benefits than other assets in the portfolio.

, Oil, Silver and Platinum. It is observed that diversifying in Gold minimizes higher risk and achieve more benefits than other assets in the portfolio, which made portfolio1 of the constructed portfolios to be optimal. In view of these facts, it means diversifying in gold acts as hedge/safe haven for investors during economic recession.

1.2 Studies of Optimising of Portfolio in Indian Capital Markets:

Though there are many studies in the developed capital markets on the Risk Optimising of Portfolio, there are few studies in Indian capital market. Studies by Obaidulla (1994) and Ansari (2000) conducted in Indian Capital markets in various form of portfolio analysis. Varadarajan (2011) constructed an optimal equity portfolio of sector stocks. Manjunatha (2011) found that while systematic risk cannot be eliminated, unsystematic risk can be reduced much by diversification. Saravanan and Natarajan (2012) constructed portfolio of Nifty stocks. Portfolio constructed based on the cut-off rate of return, proportions of investments for each stocks were decided. Debasish et al (2012) arrived at an optimal portfolio. Proportions of investment were decided based on the factors like beta value, return, risk free rate of return and unsystematic risk. Niranjan and Dutta (2013) constructed an optimal portfolio using the Sharpe's model. Stocks above a cut-off rate were considered and proportions of investments in selected stocks were computed. Nageswari et al (2013) determined future risk and return of stocks to form an optimal portfolio which significantly reduces variability of returns. Mangram (2013) analysed the impact of the number of stocks on diversification of a portfolio and found that while systematic risk cannot be eliminated, unsystematic risk can be reduced much by diversification. Gopalakrishna (2014) compared the traditional and modern portfolio theory for selection of a portfolio. The study shows that undervalued stocks will help to revise the existing portfolio. Nalini (2014) constructed portfolio based on Ci values. Purvisha et al. (2015) found that returns increases and reduces risk in an optimum portfolio when asset allocation, diversification and valuation timing are used properly. Kavitha and Rao (2016) constructed an optimal portfolio by using Sharpe single index model. Simranjeet et al. (2018) stated that implementation of Markowitz model is much more time-consuming and more complex by the number of estimate required. Further they found that the framework of Sharpe’s index model for optimal portfolio construction is very simple and useful. Vishweswarsastry and Binoy (2019) attempted an application of Harry Markowitz portfolio Risk and Return techniques for the construction of an optimal portfolio.

The literature survey in India indicates that the optimum portfolio has been constructed different types of models using listed stocks of BSE/ NSE. There is no evidence that researchers in India have used NSE Nifty index 50 stocks prices on daily basis. Hence we are motivated to study NSE Nifty Index stocks returns and risk for the comparison to the return and risk associated with portfolios. The empirical study analyses the long-term daily share price data of NSE Nifty Index 50 Stocks which will contribute to the existing literature. The paper is organized in four parts. Part 1 is the introduction; literature survey, objectives, hypotheses, data and sample; part 2 presents methodology, calculation of percentage returns, standard deviation of individual stocks, portfolio returns and risk with equal weights ; part 3 analyses the results; part 4 presents the summary and conclusions; References are given part 5.

1.3 Objectives:

· To test risk return relations of individual stocks in the Indian capital market

· To test whether diversification of stocks reduces the risk in the Indian capital market.

1.4 Data and Sample:

The study is based on NSE Nifty stocks that are part of the NSE Nifty index. The final list of 50 stocks is selected based on two criteria: stock should have been (a) the constituents of NSE Nifty Index and (b) traded for minimum six months in a year during the study period. The NSE Nifty stocks represent almost 65 percent of the NSE’s total market capitalization (http://nseindia.com/mktlive/indiceshighlights.asp. Last accessed on April 10, 2017) and our sample stocks come from 28 industry groups. These stocks are heavily traded on the exchange and come from diverse industry groups. The daily adjusted share prices from January 1, 1997 to December 31, 2015 are used for the study. The method of computing these variables are explained in the methodology section. The data were collected from the capital line database, NSE and India Infoline.com websites. Over the years, researchers have used quarterly, monthly and weekly data to study the empirical relationship of portfolio risk and return in the portfolio theory. Following Brown and Warner’s (1995) suggestion that the daily prices are better as quarterly, monthly, and weekly data do not provide a very meaningful relationship between risk and return and hence, daily price data are used in this study. Only capital gains component has been used in estimating return as dividend information of stocks is not available for all stocks for all the years of the study period. Moreover, ignoring dividends would not pose a serious estimation bias in the light of the fact that the Indian stocks’ exhibit very low dividends yield ratios over the sample period.

2. METHODOLOGY:

The portfolio return and risk analysis has been analysed systematically by Markowitz (1952, 1959) and Lakonishok, Shlifer and Vishny (1994). The Methodology used in this study is more or less similar to that used by them.

2.1 Calculations of percentage returns:

Percentage of daily relative prices of Nifty Stocks and Nifty index of daily return are calculated by using following models:

Mean return of stocks is given by:

Mean return of market m is given by:

2.2 Calculation of individual stocks standard deviation

σ =√ [R₁ – E(R)]² + [R₂ – E(R)]² + … + [R_n – E(R)]²...4

2.3 Calculation of individual stocks variance

σ² = [R₁ – E(R)]² + [R₂ – E(R)]² + … + [R_n – E(R)]²...5

Where,

R_it = Return on stocks i during time period t; R_mit= Return on market index (Nifty Index) m during time period t; P_it = Adjusted closing price of stocks i for time t; P_it-1 = Adjusted closing price of stocks i for time t-1; I_it= Adjusted closing value of market index corresponding to the period of stocks i for time t; I_it-1 = Adjusted closing value of market index corresponding to the period of stocks i for time t-1; N = Number of observations (returns).

2.4 Portfolio returns with equal weights:

Markowitz (1959) found that diversification reduces the portfolio risk in the U S capital market. Lakonishok, Shlifer and Vishny (1994) found that diversification reduces the portfolio risk in Japanese capital market. Both of these studies have formed their portfolios with equal weightage. We use similar method to form different set of portfolios such as ‘set A portfolios’; ‘set B portfolios’; ‘set C portfolios’; ‘set D portfolios’; ‘set E portfolios’; ‘set F portfolios’. We form these portfolios with equal weightage. The portfolio return is given by the following formula

R_p=W₁*R₁+W₂*R₂ +…+W_n*R_n …6

Where

R_p= Expected return on portfolio

W₁=Percentage of funds invested in stocks1

W₂=percentage of funds invested in stocks 2

R₁=expected return on stocks 1

R₂=expected return on stocks 2

The portfolio risk is given by the following formula

Where

σ_p=Standard deviation of the portfolio

W₁₌percentage of funds invested in stocks 1

W₂₌Percentage of funds invested in stocks 2

σ₁ ₌standard deviation of the stocks 1

σ₂₌Standard deviation of the stocks 2

3. RESULTS AND ANALYSIS:

The present portfolio analysis study has been conducted by using a combination of stocks as done in Markowitz (1952, 1959) as well as Lakonishok, Shlifer and Vishny (1994) model to find out the extent of risk reduction by diversification. The results have been discussed in two parts, first part of the study deals with individual stocks daily return, stocks daily standard deviation for the study period of 9 years. The methodology of forming portfolios; calculation of portfolio return and risk has been discussed in the methodology. We calculated individual stocks average returns and standard deviation for the study period based on the number of observation of stocks returns. The results of the all the stocks return and standard deviation is Table1. Second part of the study discusses with portfolios return and risk analysis. We calculated portfolio average returns and standard deviation for the study period. The results of the 119 portfolio average returns, standard deviation, variance is presented in Table 2.

First Part: Empirical Results of Individual Stocks Return and Risk Analysis

Table 1: NSE Nifty Individual Stocks Average Return, Standard Deviation and Variance.

Sl no	Company Name	Average Return	Standard Deviation	Variance
1	ACC Ltd.	0.05	1.58	2.48
2	Adani Ports andSpecial Economic Zone Ltd.	0.13	2.47	6.09
3	Ambuja Cements Ltd.	0.04	1.83	3.37
4	Asian Paints Ltd.	0.13	1.76	3.10
5	Axis Bank Ltd.	0.13	1.96	3.85
6	Bajaj auto Ltd.	0.07	1.57	2.45
7	Bank Of Baroda.	0.07	2.52	6.34
8	Bharat Heavy Electricals Ltd.	0.02	2.47	6.10
9	Bharat Petroleum Corporation Ltd.	0.21	2.11	4.45
10	Bharati Airtel Ltd.	0.02	1.76	3.10
11	Bosch Ltd.	0.14	1.89	3.56
12	Cairn India Ltd.	-0.15	2.12	4.51
13	Cipla Ltd.	0.11	1.71	2.92
14	Coal India Ltd.	0.04	2.00	3.99
15	Dr. Reddy's Laboratories.	0.06	1.79	3.21
16	GAIL(India) Ltd.	0.04	2.02	4.09
17	Grasim Industries Ltd.	0.08	1.51	2.28
18	HCL Technologies Ltd.	0.08	1.93	3.74
19	HDFC Bank Ltd.	0.11	1.21	1.45
20	Hero MotoCorp Ltd.	0.06	1.55	2.39
21	Hindalco Industries Ltd.	-0.04	2.59	6.72
22	Hindustan Unilever Ltd.	0.09	1.49	2.21
23	H D F C Ltd.	0.11	1.76	3.11
24	ICICI Bank ltd.	0.05	1.87	3.48
25	Idea Cellular Ltd.	-0.01	2.23	4.96
26	Indulnd Bank Ltd.	0.18	1.66	2.76
27	Infosys ltd.	0.06	1.67	2.80
28	ITC Ltd.	0.02	1.54	2.36
29	Kotak Mahindra Bank Ltd.	0.15	1.70	2.89
30	Larsen and Toubro Ltd.	0.05	1.73	3.01
31	Lupin Ltd.	0.16	1.66	2.76
32	Mahindra and Mahindra Bank Ltd.	0.08	1.77	3.12
33	Maruti Suzuki India Ltd.	0.21	1.57	2.46
34	NTPC ltd.	0.03	1.81	3.27
35	Oil and Gas Corporation Ltd.	-0.01	2.09	4.37
36	Power Grid Corporation of India Ltd.	0.08	1.40	1.96
37	Punjab National Bank .	0.01	2.31	5.33
38	Reliance Industries Ltd.	0.04	1.62	2.61
39	State Bank Of India.	0.07	1.95	3.79
40	Sun Pharmaceutical Industries Ltd.	0.09	2.00	4.00
41	Tata Consultancy Services Ltd.	0.04	1.48	2.18
42	Tata Motors Ltd.	0.03	2.10	4.40
43	Tata Power Company Ltd.	-0.03	2.08	4.34
44	Tata Steel Ltd.	-0.07	2.34	5.46
45	Tech Mahindra Ltd.	0.04	1.72	2.95
46	Ultratech Cement Ltd.	0.11	1.80	3.25
47	Vedanta Ltd.	-0.12	2.78	7.74
48	Wipro Ltd.	0.01	1.49	2.21
49	Yes Bank Ltd.	0.16	2.27	5.16
50	Zee Entertainment Enterprises Ltd.	0.11	1.86	3.46

Note: The above table Second column shows names NSE Nifty Stocks, Third column shows average return, Fourth column demonstrations standard deviation and Fifth column shows variance of each stocks.

The Table 1 shows the characteristics of the percentage return, standard deviation and variance of individual stocks. We have found that ACC Ltd yielded returns of 0.05 percent; standard deviation of 1.58 percent; variance of 2.48 percent during the study period of 9 years, similar analysis holds for remaining stocks. Further analysis shows that while Cairn India Ltd stocks has given lowest (-0.15 percent) average return; HDFC Bank ltd stocks has lowest standard deviation (1.21) and lowest variance (1.45). Maruti Suzuki India Ltd stocks given a highest percentage of average return 0.21; with the standard deviation of 1.57 and variance of 2.46. These characteristics are depicted in the graph 1.

Graph 1: NSE Nifty Individual stocks Average Return and Standard Deviation.

Second part: Empirical Results of Portfolio Return and Risk

The individual stocks returns variation is too high and there is wide gap between the individual stocks risk and return. Hence the study further focuses on the portfolio way as suggested by Markowitz (1952; 1959), the following paragraphs deals about portfolio risk and return analysis.

Table 2: ‘Set A Portfolios’ Average Return, Standard Deviation andVariance

Sl No	Portfolios	Average Return (%)	Standard Deviation (%)	Variance (%)
1	Portfolio-A1	40.34	19.49	379.87
2	Portfolio-A2	56.38	22.30	497.08
3	Portfolio-A3	41.76	28.72	824.98
4	Portfolio-A4	31.73	45.45	2065.99
5	Portfolio-A5	37.17	41.78	1745.88
6	Portfolio-A6	35.51	38.10	1451.43
7	Portfolio-A7	30.21	39.89	1591.10
8	Portfolio-A8	26.24	38.97	1518.86
9	Portfolio-A9	30.04	41.15	1693.61
10	Portfolio-A10	28.34	39.31	1544.99
11	Portfolio-A11	31.07	38.62	1491.14
12	Portfolio-A12	26.79	42.68	1821.95
13	Portfolio-A13	27.61	41.35	1710.00
14	Portfolio-A14	26.55	40.06	1604.52
15	Portfolio-A15	26.84	38.74	1500.57
16	Portfolio-A16	25.53	37.96	1440.69
17	Portfolio-A17	25.55	36.91	1362.31
18	Portfolio-A18	28.09	38.11	1452.65
19	Portfolio-A19	28.96	37.30	1391.29
20	Portfolio-A20	30.20	37.10	1376.15
21	Portfolio-A21	28.89	37.00	1368.93
22	Portfolio-A22	30.36	36.90	1361.95
23	Portfolio-A23	30.38	36.41	1325.61
24	Portfolio-A24	30.31	35.63	1269.62
25	Portfolio-A25	30.82	36.23	1312.66

Note:-Third column shows average return, fourth column shows standard deviation and fifth column shows variance.

Table 2 shows the ‘set A portfolios’ average returns, standard deviation and variance. The Portfolio A1 has been formed by choosing the first one and last one stocks (stocks 1 and 50); portfolio A2 is formed by 4 stocks (stocks1, 2, 49 and 50); portfolio A3 is formed by 6 stocks (stocks1, 2, 3, 48, 49 and 50) and so on. Similar process is done for subsequent test of the portfolios. Using this process, 25 portfolios have been formed with equal weightage of each stocks. The portfolio A1 has portfolios average return of 40.34 percent, standard deviation of 19.49 percent and portfolio variance of 379.87 percent. The portfolio A2 has portfolios return of 56.38 percent, standard deviation of 22.30 percent and portfolio variance of 497.08 percent. When we compare the portfolio A1 and portfolio A2 we found that the portfolio standard deviation is marginally increasing in the portfolio A2.The portfolio A3 has portfolios return of 41.76 percent, standard deviation of 28.72 percent and variance of 842.98 percent. When we compare the portfolio A2 and portfolio A3, it is found that the portfolio standard deviation is marginally increasing in the portfolio A3. The portfolio A4 has portfolios return of 31.73 percent, standard deviation of 45.45 percent and portfolio variance of 2065.99 percent. When we compare the portfolio A3 and portfolio A4, it is found that the portfolio standard deviation is marginally increasing in the portfolio A4. The result shows that when we add more stocks to the portfolio (diversification of stocks), the standard deviation is gradually increasing. The analysis of the results for portfolio A1 to portfolio A5 gradually increasing in the standard deviation and then portfolio A6 has lower standard deviation and the other portfolios standard deviation is varies widely which has been depicted in the graph 2. This table it indicates that when we diversify it is not possible to reduce the risk. It is fail to fulfill the Markowitz model so we have to construct other portfolios.

Graph 2: ‘Set A Portfolios’ Average Return and Standard Deviation

4. SUMMARY AND CONCLUSIONS:

Based on the objectives we have tried to analyse the Markowitz diversification model which reduces the portfolio risk and maximize the portfolio return. Based on the tables we have found that following major observation, we offer suggestion to investors. Major findings are.

· The individual stocks result shows that variation of stocks return is too high and there is wide gap between the individual stocks risk and return. Hence we focused on the formation of different set of portfolios.

· In the ‘set A portfolios’ we found that portfolio A1 has lowest risk i.e. 19.49 percent and portfolio A4 has highest risk i.e. 45.45 percent. Further result show that in this set three portfolios risk is less than average risk of portfolios and twenty two portfolios risk is more than average risk of portfolios i.e. 31.73 percent.

· The overall result shows that 65 percent of the portfolios reduce the risk when more stocks are added to the portfolio. This shows that investors can scientifically diversify the stocks and build the efficient portfolios in the Indian capital market. The results of the present study are consistent with the studies undertaken by Markowitz (1952, 1959) and Lakonishok, Shlifer and Vishny (1994). The empirical findings of this paper would be useful to financial analysts as the portfolios reduces risk and increases returns. Our effort to document that diversification of stocks are explained by adding many stocks in the portfolios is not fully successful, but shows the direction for further research in portfolio model. Further research on the portfolio models is needed to enlarge the understanding of modern portfolio management.

5. REFERENCES:

1. Ansari, V.A. (2000), Capital asset pricing model: Should we stop using it?, Vikalpa, 25(1): 55-64.

2. Araújo, A.C. and Montini, A.A. (2015), Análise de métricas de risco na otimização de portf_olios deações, Revista De Administração, 50(2): 208-228.

3. Brown, Stephen J., and Warner (1985), Using Daily Stocks Returns, The Case of Event Studies, Journal of Financial Economics, 14(2): 3-31

4. Chan, L., Karceski, J. and Lakonishok, J. (1999), On portfolio optimization: forecasting covariances and choosing the risk model, Review of Financial Studies, 12(5):937-974.

5. Dare Jayeola, Zuhaimy Ismail, Suliadi Firdaus Sufahani (2017), Effects of diversification of assets in optimizing risk of portfolio, Malaysian Journal of Fundamental and Applied Sciences,13(4): 584-587

6. Debasish, Sathya Swaroop, Khan, and Jakki Samir (2012), Optimal portfolio construction in stocks market: An Empirical Study on selected stocks in Manufacturing sector in India, International Journal of Business Management, 2(2): 37-44.

7. DeMiguel, V., Garlappi, L. and Uppal, R. (2009), Optimal versus naive diversification: how inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22(5): 1915-1953.

8. Fama, Eugene F, and French Kenneth R (1992), The Cross-section of Expected Stocks Returns, Journal of Finance,47/2: 427-465.

9. Gopalakrishna Muthu, M (2014), Optimal portfolio selection using Sharpe's Single Index Model. Indian Journal of Applied Research, 4(1): 286-288.

10. Jack L. Treynor and Fischer Black (1973), How to Use Stocks Analysis to Improve Portfolio

11. Selection, The Journal of Business, 46(1): 66-86

12. Jensen, M. C. (1968), The performance of mutual funds in the period 1945–1964. The Journal of finance, 23(2): 389-416.

13. Lakonishok, Josef, Andrei Shleifer, and Robert Vishny W, (1994), Contrarian Investment Extrapolation and Risk journal of Finance, 49(5): 541-1578

14. Lintner J. (1965). The valuation of risk assets and the selection of risky investments in stocks portfolios and capital budgets, The review of economics and statistics, 47(1): 13-37

15. Kavitha Lal and S.R. Subba Rao (2016), Selecting an Optimal Portfolio for Investment in Stocks in India: A Sectoral Approach, Pacific Business Review International, 8(9): 109-115

16. Manjunatha T (2011), “Does Diversification of Stocks Reduce the Portfolio Risk in the Indian Capital Market?”; Anvesh Journal of Management, 4(2):11-17.

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

18. Markowitz, Harry M (1959), Portfolio Selection, Efficient Diversification of investments

19. (New Yark: john wiley and sons inc).

20. Mangram, M. E. (2013), A Simplified Perspective of the Markowitz Portfolio Theory.

21. Global Journal of Business Research, 7(1): 59-70.

22. Nageswari, P., Selvam, M., and Bhuvaneswari, P. (2013). An Empirical Analysis of Optimal Portfolio Selection Using Sharpe's Optimization. Asian Journal of Research in Business Economics and Management, 3(11): 209-221.

23. Nalini. (2014). Optimal Portfolio Construction using Sharpe's Single Index Model-Study of selected stocks from BSE. International Journal of Advanced Research in Management and Social Sciences, 3(12): 72-93.

24. Niranjan Mandal, and Dutta B.N. (2013), Sharpe's Single Index Model and its Application to Construct Optimal Portfolio: An Empirical Study. Great Lakes Herald. 7(1): 1-22.

25. Obaidullah M(1994), Indian stocks market: Theories and Evidence Hyderabad ,ICFAI

26. Purvisha Fadadu, Hiral Mathukiya, Chetna Parmar (2015), Portfolio Selection: Using Markowitz Model on selected Sectors Stocks in India, 2(12): 1-6.

27. Rom, B.M. and Ferguson, K.W. (1994), “Post-modern portfolio theory comes of age”, The Journal of Investing, Vol. 3 No. 3, pp. 11-17.

28. Santos, A.A.P. and Tessari, C. (2012), Técnicas quantitativas de otimização de carteiras aplicadas aomercado de ações brasileiro, Rev. Bras. Finanças, Vol. 10 No. 3, pp. 369-394.

29. Saravanan, A. and Natarajan, P. (2012). Optimal Portfolio Construction with Nifty Stocks (an analytical prescription for investors. Advances in Management. Pondicherry University.

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

31. Simranjeet Kaur Sandhar, Neetika Jain, Ruchi Kushwah (2018), Optimal Portfolio Construction: A Case Study of NSE, Journal of Emerging Technologies and Innovative Research, 5(8): 512-521

32. Treynor, J. L. (1965). How to rate management of investment funds. Harvard business review, 43(1):63-75.

33. Ulucan, A. (2007), An analysis of mean-variance portfolio selection with varying holding Periods. Applied Economics, 39(2): 1399-1407.

34. Varadarajan, P. (2011), Portfolio construction using the Sharpe Index Model with reference to banking and information technology sectors, Prime Journal of Business Administration and Management, 1(12): 392-398.

Websites

1. http://nseindia.com/I S L Indices/CNX NIFTY. Last accessed on 10.4.2017.

2. http://cdbmsi.reservebank.org.in cdbmsi/servlet/login/statistics/Sources of money Stocks. Last accessed on 11.10.2017.

3. http://nseindia.com/mktlive/indiceshighlights.asp. Last accessed on 16.4.2017.

Received on 22.05.2021 Modified on 10.06.2021

Asian Journal of Management. 2021;12(4):457-462.

DOI: 10.52711/2321-5763.2021.00070