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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Equity Portfolio Using The Sharpe Index Model With Reference To Banking And Information

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International Journal Of Business And Administration Research Review

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[4] Dileep, S. & Kesava Rao, G.V. (2013), “A Study On Sustainability Of William Sharpe’s Single

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[5] Gopalakrishna Muthu, M. (2014), “Optimal Portfolio Selection Using Sharpe’s Single Index

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Management, 3 (4), Pp: 88-98.

[7] Mandal, Niranjan (2013), “Sharpe’s Single Index Model & Its Application To Construct Optimal

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[8] Sarker, Mokta Rani (2013), “Optimal Portfolio Construction: Evidence From Dhaka Stock

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[10] Varadarajan, P. & Ganesh (2012), “Construction Of Equity Portfolio Of Large Cap Companies Of

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