Research Paper Volume 3 Issue 3 November 2015 ... · PDF file692 ISSN: 2347-1697 International...
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691
Available online through - http://ijifr.com/searchjournal.aspx Published Online On: November 10, 2015
www.ijifr.com
International Journal of Informative & Futuristic Research ISSN: 2347-1697
Volume 3 Issue 3 November 2015 Research Paper
Abstract
Every investor always likes to purchase a bundle of stocks that provides the high rate of return and has low rate of risks. He wants to maintain a satisfactory reward to risk ratio. Traditionally analysts paid more care to the return concept of the stocks. Presently risk has received increased attention and analysts are providing estimates of risk as well as return. The scope of the present study is relating to optimal portfolio construction by selecting stocks from BSE. Optimal portfolio construction is a challenging task for the individual as well as the institutional investors. The importance of this study is to create awareness in the minds of investors about the use of Sharpe’s single index model in optimal portfolio construction. Twenty companies from the BSE Sensex index were selected for the study. The results of the present study have more utility value to the fund managers..
1. Introduction
In order to determine the variance of the portfolio, the covariance between each pair of securities
must be calculated, which is shown in a covariance matrix. Thus, increase in the number of
securities results in a big covariance matrix, which results in a more complex computation. If there
are n securities in a portfolio, the Markowitz’s model need n average or expected returns, n
variance terms and n (n-1)/2covariance terms (i.e. in total n(n+3)/2 data inputs). Due to these
difficulties analysts did not like to complete their task and they searched a simplified model to
Optimal Portfolio Construction Using
Sharpe’s Single Index Model - A Study
Of Selected Stocks From BSE
Paper ID IJIFR/ V3/ E3/ 001 Page No. 691-697 Subject Area Business
Administration
Key Words Sharpe’s Single Index Model, Cut-off rate, Beta, Excess Return to Beta Ratio
1st Dr .S. Poornima
HoD & Associate Professor,
Department of Business Administration,
PSGR Krishnammal College for Women
Coimbatore, Tamil Nadu
2nd
Aruna.P.Remesh
Research Scholar-M.Phil. ,
Department of Business Administration,
PSGR Krishnammal College for Women
Coimbatore, Tamil Nadu
692
ISSN: 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)
Volume - 3, Issue -3, November 2015 Continuous 27th Edition, Page No.:691-697
Dr. S. Poornima, Aruna. P. Remesh :: Optimal Portfolio Construction Using Sharpe’s Single Index Model - A Study Of Selected Stocks From BSE
perform their tasks, which is named as Sharp single Index Model given by William F. Sharp in
1963.
2. Need For The Study
While selecting securities for his portfolio, every investor undergoes confusion. Everyone faces
difficulties while deciding about the proportion of investment to be made in each security. To help
investors get out of such difficult situations the Sharpe’s Single Index Model may be used to
construct an optimal portfolio. This optimal portfolio helps the investor to find a suitable portfolio.
The present study is to establish that by applying this model an individual can construct a portfolio
not only with minimum risk but also with a maximum return.
3. Problem Statement
An investor making investment in securities is faced with the problem that how to allocate his funds
over a group of securities and how to choose the best one among a large number of securities. This
situation exists when the investor faces a problem of deciding which securities to hold and how
much to invest in each of them. So the present study is entitled as” Optimal Portfolio Construction
Using Sharpe’s Single Index Model”-A Study of Selected Stocks from BSE.
4. Research Methodology
This study is based on secondary data obtained from the website www.moneycontrol.com. Twenty
companies from the BSE Sensex index were selected for the study. The tools used are as follows
1) Estimate the return on stock. The equation to be used
Ri= (Pt-Po) ×100
Po where Pt=current year price, Po=previous year price
2) Excess return to beta ratio= (Ri-Rf)
βi
Where Ri=the expected return of stock I, Rf=risk free rate of return, βi=systematic risk of
stock i
3) Cut-off rate Ci is calculated by using the following equation
Where σ2m =Variance of the market index, σ2ei=stocks unsystematic risk.
5. Objective Of The Study
The main objectives of the study are:
I. To get an insight into the idea in Sharpe’s Single Index Model.
II. To construct an optimal portfolio empirically using the Sharpe’s Single Index Model.
III. To analyse return and risk of the optimal portfolio constructed by using Sharpe’s
Single Index Model .
693
ISSN: 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)
Volume - 3, Issue -3, November 2015 Continuous 27th Edition, Page No.:691-697
Dr. S. Poornima, Aruna. P. Remesh :: Optimal Portfolio Construction Using Sharpe’s Single Index Model - A Study Of Selected Stocks From BSE
6. Limitations Of The Study
The limitations of the present study are:
i.) The study uses yearly prices instead of monthly data
ii.) Only twenty companies have been selected for this study.
iii.) The results of the study may not be universally applicable
7. Data Analysis And Interpretation
This part brings out data analysis and interpretations relating to the present study. Secondary data
were used for this study. Twenty companies listed in the BSE Sensex were chosen. The companies
were selected listed below
Table 1: Sample Companies Name
Sr. No Name of Companies
1 Axis Bank Limited
2 Tata Consultancy Services Limited
3 Wipro Limited
4 HDFC Bank
5 ICICI Bank
6 State Bank Of India
7 Hindustan Unilever Limited
8 Infosys Limited
9 L &T Finance Limited
10 Kotak Mahindra Bank Limited
11 Tata Motors
12 Cipla Limited
13 Maruthi Suzuki
14 NTPC
15 Tech Mahindra
16 Reliance
17 ONGC
18 Colgate
19 YES Bank
20 SAIL
The above table 1represents the list of sample companies selected for the present study and the
historical stock prices for the last six years of the companies were collected from websites.
694
ISSN: 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)
Volume - 3, Issue -3, November 2015 Continuous 27th Edition, Page No.:691-697
Dr. S. Poornima, Aruna. P. Remesh :: Optimal Portfolio Construction Using Sharpe’s Single Index Model - A Study Of Selected Stocks From BSE
Table 2: Mean Return Of Sample companies stock (In %)and Beta values
Sr. No. Name of Companies Mean Return
(in %)
Beta
values
1 Axis Bank Limited 11.833 1.83
2 Tata Consultancy Services Limited 21.046 0.58
3 Wipro Limited 7.586 0.53
4 HDFC Bank 3.78 .93
5 ICICI Bank 8.020 1.14
6 State Bank Of India 26.970 1.28
7 Hindustan Unilever Limited 16.507 .40
8 Infosys Limited 6.037 .69
9 L &T Finance Limited 1.182 1.38
10 Kotak Mahindra Bank Limited 12.006 1.07
11 Tata Motors 1.582 1.41
12 Cipla Limited 16.818 .93
13 Maruthi Suzuki 29.822 .81
14 NTPC 7.387 .95
15 Tech Mahindra 22.208 .87
16 Reliance 1.941 1.12
17 ONGC 9.968 1.32
18 Colgate 3.157 .531
19 YES Bank 21.218 1.9
20 SAIL 18.453 1.56
Source: Mean Return Computed By The Author And Beta Values Collected From Each Company’s Websites
Table 2 shows the mean return of sample companies in percentage and the beta values of the
sample companies. A beta value lower than 1 indicates investment with volatility lower than the
market .Axis bank has the highest beta value.ie Axis bank is highly volatile. Similarly State bank of
India, ICICI bank, L&T finance, and Kotak Mahindra bank limited, Tata motors, Reliance, ONGC
and SAIL have beta values greater than 1.
Table 3: Ranking of the stocks based on excess return to Beta Ratio
Sr.
No.
Name of Companies Ri Ri-Rf β Ri-Rf
Β
Rank
1 Axis Bank Limited 11.833 -19.583 1.83 -10.701 15
2 Tata Consultancy Services
Limited
21.046 13.296 0.58 22.924 3
3 Wipro Limited 7.586 -0.164 0.53 -0.309 20
4 HDFC Bank 3.78 -3.970 .93 -4.268 19
5 ICICI Bank 8.020 -15.770 1.14 -13.833 13
6 State Bank Of India 26.970 -34.72 1.28 -27.125 8
7 Hindustan Unilever Limited 16.507 8.757 .40 21.892 2
8 Infosys Limited 6.037 -13.787 .69 -19.981 10
695
ISSN: 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)
Volume - 3, Issue -3, November 2015 Continuous 27th Edition, Page No.:691-697
Dr. S. Poornima, Aruna. P. Remesh :: Optimal Portfolio Construction Using Sharpe’s Single Index Model - A Study Of Selected Stocks From BSE
9 L&T Finance Limited 1.182 -6.568 1.38 -4.759 17
10 Kotak Mahindra Bank Limited 12.006 4.256 1.07 3.977 7
11 Tata Motors 1.582 -6.168 1.41 -4.374 18
12 Cipla Limited 16.818 9.068 .93 9.750 5
13 Maruthi Suzuki 29.822 22.072 .81 27.249 1
14 NTPC 7.387 -15.137 .95 -15.933 12
15 Tech Mahindra 22.208 14.458 .87 16.618 4
16 Reliance 1.941 -9.691 1.12 -8.652 16
17 ONGC 9.968 -17.718 1.32 -13.422 14
18 Colgate 3.157 -10.907 .531 -20.540 9
19 YES Bank 21.218 13.468 1.9 7.088 6
20 SAIL 18.453 -26.203 1.56 -16.796 11
Source: Computed By The Author
Table 4: Cut –off values of sample companies stock
Rank Name of Companies
1 Maruthi Suzuki 0.001990996 0.001990996 0.15
2 Hindustan Unilever Limited 0.00019042 0.002181416 0.41
3 Tata Consultancy Services Limited 0.000179927 0.002361343 0.59
4 Tech Mahindra 0.000881218 0.003242561 0.99
5 Cipla Limited 0.00121327 0.004455831 1.19
6 YES Bank 0.000982656 0.005438488 1.04
7 Kotak Mahindra Bank Limited 0.000280711 0.005719199 1.50
8 State Bank Of India 0.000154622 0.005873821 1.55
9 Colgate 0.00109679 0.006970611 1.80
10 Infosys Limited 0.001044982 0.008015593 2.31
11 SAIL 0.00301131 0.011026903 2.92
12 NTPC 0.000316102 0.011343005 3.11
13 ICICI Bank 0.000793461 0.012136466 3.87
14 ONGC 0.000317324 0.01245379 3.91
15 Axis Bank Limited 0.000371274 0.012825064 4.18
16 Reliance 0.000458381 0.013283445 4.26
17 L &T Finance Limited 0 0.013283445 4.32
18 Tata Motors 0 0.013283445 4.45
19 HDFC Bank 0 0.013283445 5.15
20 Wipro Limited 0 0.013283445 5.15
Source: Computed By The Author
Table.4 represents the Ci of sample companies. The Ci values goes on increasing from 4.18 to 5.15.
Therefore, the value of 5.15 is considered as the “Cut-off point”. The securities which come after
696
ISSN: 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)
Volume - 3, Issue -3, November 2015 Continuous 27th Edition, Page No.:691-697
Dr. S. Poornima, Aruna. P. Remesh :: Optimal Portfolio Construction Using Sharpe’s Single Index Model - A Study Of Selected Stocks From BSE
the cut-off point will not be considered for the optimal portfolio construction. Those securities
which have value of Ci more or equal to cut off point will be selected in optimal portfolio.
Table 5: Proportion of investment proposed
Company name Ci Zi Xi Return (%)
Axis bank limited 4.18 0.00671721 37.87 11.833
Reliance 4.26 0.005309255 10.59 1.941
L&T finance limited 4.32 0.005250465 19.32 1.182
Tata motors 4.45 0.012432076 2.40 1.582
HDFC bank 5.15 0.063458486 13.36 3.78
Wipro limited 5.15 0.029033426 16.46 7.586
ƸZi=0.122205 ƹXi=100.0
Figure 1: The Proportion Of Investment Made By The Investor
The above figure shows the proportion of investment made by the investor. From the figure we can
understand 38% of the investment made in Axis bank.17% made in Wipro, 19% made in L&T
finance,13% made in HDFC bank,11% made in Reliance and 2% in Tata motors.
8. Findings
The findings of the present study are listed below
i.) Axis bank has the highest return of 38% and the Tata motors has the lowest return of 2%.
ii.) The return from Axis bank has the highest beta value of 1.83 which means it is highly
volatile.
iii.) State Bank Of India, ICICI Bank ,L&T Finance ,Kotak Mahindra bank ,Tata motors,
Reliance, ONGC, Yes Bank, and SAIL also have beta values greater than 1.ie they are also
volatile.
iv.) The Ci values goes on increasing from 4.18 to 5.15. The Ci value is 5.15.based on the Ci
values only six securities were selected.
v.) HDFC bank and Wipro having the highest cut off value (5.15) and Maruthi Suzuki having
the lowest cut off value (0.15).
37.87
10.59 19.32
2.4
13.36
16.46
Axis bank limited Reliance L&T finance limited
Tata motors HDFC bank Wipro limited
697
ISSN: 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)
Volume - 3, Issue -3, November 2015 Continuous 27th Edition, Page No.:691-697
Dr. S. Poornima, Aruna. P. Remesh :: Optimal Portfolio Construction Using Sharpe’s Single Index Model - A Study Of Selected Stocks From BSE
vi.) 38% of the investment made in Axis bank.ie majority of the funds is to be invested in this
company.
9. Conclusion
From the study it is clear that the construction of optimal portfolio investment by using Sharpe’s
Single Index Model is more comfortable. Among the twenty companies only six were selected for
optimal portfolio. The results of the present study have more utility value to the fund managers.
10. References
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International Journal Of Business And Administration Research Review
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