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Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 207
CONSTRUCTION OF AN OPTIMAL PORTFOLIO USING SHARPE INDEX
MODEL FOR BSE LARGE CAP SECURITY
Mr. Vijay Bhatu
&
Ms. Hetal Mehta
&
Prof. Riddhi Sanghvi
Abstract In modern area the investment is too much importance. The portfolio construction in equity fund is
very risky because the equity shares provides higher return and also beard higher risk. The investor
need to find optimal portfolio that give best return at given risk. A portfolio is a grouping of
financial assets such as stocks, bonds and cash equivalents, as well as their funds counterparts,
including mutual, exchange-traded and closed funds. In this paper we selected S & P SENSEX is
market index and construct the portfolio using Sharpe’s ratio and beta of the stock. We are collect
data 31st march 2007 to 31
st march 2017 as period of securities. The total sampling company is 12.
The selection of securities is based on the higher market capitalization of the BSE listed securities.
The higher market capitalization company is which that well established and leading company so
investor more focused in that company. In this paper get an insight into the idea embedded in
Sharpe’s single index model and to construct an optimal portfolio empirically using this model. In
this research the price of securities and market return is selected on BSE website and risk free rate
is tacking from reserved bank of India website. After the data collection we find the return in
percentage, the time duration of data analysis is past 10 years. After the find the mean return and
risk of securities. Also find the covariance and beta of the securities in relation to BSE market.
Then after we have applied the Sharpe’s ratio that gives the base of portfolio selection. The sharps
ratio gives the idea about incremental return for incremental risk and reward to volatility of the
securities.
Keywords: sharpes index, beta, variyance, risk free rate.
Introduction of Portfolio A portfolio is a grouping of financial assets such as stocks, bonds and cash equivalents, as well as
their funds counterparts, including mutual, exchange-traded and closed funds. Portfolio is a
combination of securities such as stocks bonds and money market instruments. Diversification of
investments over different assets helps to reduce risk without sacrificing return. When determining
a proper asset allocation one aims at maximizing the expected return and minimizing the risk. The
ISSN No. 0974-035X
An Indexed Refereed Journal of Higher Education
Towards Excellence UGC-ACADEMIC STAFF COLLEGE,
GUJARAT UNIVERSITY, AHMEDABAD, INDIA
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 208
process of blending together the broad asset classes so as to obtain optimum return with minimum
risk is called portfolio construction.
These holdings are the result of individual preferences, decisions of the holders regarding risk,
return and most of other considerations. Modern portfolio theory has one central theme: ―In
constructing their portfolios investors need to look at the expected return of each investment in
relation to the impact that it has on the risk of the overall portfolio‖. Portfolio management concerns
the constructions and maintenance of a collection of investment. It is investment of funds in
different securities in which the total risk of the portfolio is minimized, while expecting maximum
return from it. It primarily involves reducing risk rather than increasing return.
Approaches to Portfolio Construction
There are two approaches to portfolio construction of the portfolio of securities vise, Traditional
approach and Modern approach
In traditional approach, investor‘s needs in terms of income and capital appreciation are evaluated
and appropriate securities are selected to meet the needs of the investor. The common practice in
the traditional approach is to evaluate the entire financial plan of the individual.
In modern approach, portfolios are constructed to maximize the expected return for a given level of
risk. It views the portfolio construction in terms of the expected return and the risk associated with
obtaining the expected return.
Portfolio Management Process
1. Specification of investment objectives and constraints
The first step the typical objectives sought by investor are current income, capital appreciation, and
safety of principal. Also relative importance of those objective should be specified. After the
constraint from liquidity, time horizon, tax, and special circumstances must be identified.
2. Quantification of capital market expectation
The second step to address the asset mix question you need relatively long term estimates of returns
and risk of various assets classes. Choice the asset mix
The most importance decision in portfolio management is the asset mix decision. That is concern
with the proportion of stock and bonds and other assets of portfolio on the basis of risk and return.
3. Formulation of portfolio strategy
Once a certain asset mix is chosen, an appropriate strategy has to formulate. Two board choices are
available: an active strategy or a passive portfolio strategy.
4. Selection of securities
After a formulation portfolio strategy, generally investor pursues an active stance with respect of
security selection. For example the factor of selecting bonds is yield to maturity, credit rating, and
term of maturity, tax shelter and liquidity.
5. Portfolio execution
This is phase of portfolio management which is concerned with implementing the portfolio plan by
buying specific securities.
6. Portfolio revision
The value of a portfolio as well as its composition - the relative proportion of assets are change in
term of risk and return, in response to such changes periodic rebalancing of portfolio is required.
7. Performance evaluation
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 209
The performance of portfolio should be evaluated periodically. The key dimensions of portfolio
performance evaluation are risk and return. Such a review may provide useful feedback to improve
the quality of the portfolio management process on a continuing basis.
Types of Portfolio
1. The Aggressive Portfolio
An aggressive portfolio or basket of stocks includes those stocks with high risk/high reward
proposition. Stocks in the category typically have a high beta, or sensitivity to the overall market.
Higher beta stocks experience larger fluctuations relative to the overall market on a consistent basis.
If you’re individual stock has a beta of 2.0, it will typically move twice as much in either direction
to the overall market - hence, the high-risk, high-reward description.
2. The Defensive Portfolio
Defensive stocks do not usually carry a high beta, and usually are fairly isolated from broad market
movements. Cyclical stocks, on the other hand, are those that are most sensitive to the underlying
economic "business cycle." For example, during recessionary times, companies that make the
"basics" tend to do better than those that are focused on fads or luxuries. Despite how bad the
economy is, companies that make products essential to everyday life will survive.
3. The Income Portfolio
An income portfolio focuses on making money through dividends or other types of distributions
to stakeholders. These companies are somewhat like the safe defensive stocks but should offer
higher yields. An income portfolio should generate positive cash flow. Real estate investment
trusts (REITs) and master limited partnerships (MLP) are excellent sources of income producing
investments.
4. The Speculative Portfolio
A speculative portfolio is the closest to a pure gamble. A speculative portfolio presents more risk
than any others discussed here. Finance gurus suggest that a maximum of 10% of one's investable
assets be used to fund a speculative portfolio. Speculative "plays" could be initial public
offerings (IPOs) or stocks that are rumoured to be takeover targets.
5. The Hybrid Portfolio
Building a hybrid type of portfolio means venturing into other investments, such as bonds,
commodities, real estate and even art. Basically, there is a lot of flexibility in the hybrid portfolio
approach. Traditionally, this type of portfolio would contain blue chip stocks and some high grade
government or corporate bonds. a hybrid portfolio would include a mix of stocks and bonds in a
relatively fixed allocation proportions. This type of approach offers diversification benefits across
multiple asset classes as equities and fixed income securities tend to have a negative
correlation with one another.
Capital Market
Capital markets are markets for buying and selling equity and debt instruments. Capital markets
channel savings and investment between suppliers of capital such as retail
investors and institutional investors, and users of capital like businesses, government and
individuals. Capital markets are vital to the functioning of an economy, since capital is a critical
component for generating economic output. Capital markets include primary markets, where new
stock and bond issues are sold to investors, and secondary markets, which trade existing securities.
Capital markets are a broad category of markets facilitating the buying and selling of financial
instruments. In particular, there are two categories of financial instruments that capital in which
markets are involved. These are equity securities, which are often known as stocks, and debt
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 210
securities, which are often known as bonds. Capital markets involve the issuing of stocks and bonds
for medium-term and long-term durations, generally terms of one year or more.
Capital markets are overseen by the Securities and Exchange Commission in the United States or
other financial regulators elsewhere. Though capital markets are generally concentrated in financial
centers around the world, most of the trades occurring within capital markets take place through
computerized electronic trading systems. Some of these are accessible by the public and others are
more tightly regulated.
Other than the distinction between equity and debt, capital markets are also generally divided into
two categories of markets, the first of which being primary markets. In primary markets, stocks and
bonds are issued directly from companies to investors, businesses and other institutions, often
through underwriting. Primary markets allow companies to raise capital without or before holding
an initial public offering so as to make as much direct profit as possible.
Bombay Stock Exchange This Stock Exchange, Mumbai, popularly known as "BOMBAY STOCK EXCHANGE (BSE)" was
established in 1875 as ''The Native Share and Stock Brokers Association", as a voluntary non-profit
making association. It has evolved over the years into its present status as the premiere Stock
Exchange in the country. It may be noted that the Stock Exchange is the oldest one in Asia, even
older than the Tokyo Stock Exchange, which was founded in 1878.
The exchange, while providing an efficient and transparent market for trading in securities, upholds
the interests of the investors and ensures redressed of their grievances, whether against the
companies or its own member brokers. It also strives to educate and enlighten the investors by
making available necessary informative inputs and conducting investor education programmers.
A governing board comprising of 9 elected directors, 2 SEBI nominees, 7 public representatives
and an executive director is the apex body, which decides the policies and regulates the affairs of
the exchange.
The Executive director as the chief executive officer is responsible for the day to day administration
of the exchange.
BSE Indices
In order to enable the market participants, analysts etc., to track the various ups and downs in the
Indian stock market, the Exchange introduced in 1986 an equity stock index called BSE-SENSEX
that subsequently became the barometer of the moments of the share prices in the Indian stock
market. It is a "Market capitalization-weighted" index of 30 component stocks representing a
sample of large, well established and leading companies. The base year of SENSEX is 1978-79.
The SENSEX is widely reported in both domestic and international markets through print as well as
electronic media.
SENSEX is calculated using a market capitalization weighted method. As per this methodology, the
level of the index reflects the total market value of all 30 component stocks from different
industries related to particular base period. The total market value of a company is determined by
multiplying the price of its stock by the number of shares outstanding. Statisticians call an index of
a set of combined variables a composite Index. An Indexed number is used to represent the results
of this calculation in order to make the value easier to work with and track over a time. It is much
easier to graph a chart based on Indexed values than one based on actual values world over majority
of the well-known Indices are constructed using "Market capitalization weighted method".
Sharpe’s Single Index Model
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 211
Sharpe‘s single index model was developed by William Sharpe for the construction of optimal
portfolio using less number of inputs. The simplicity is the most important feature of the Sharpe’s
single index model over Markowit‘z model. Markowitz‘s model uses large number of covariance.
Taking idea from the Markowit‘z, suggested that index to which securities are related can be used
for covariance generation, William Sharpe formulated single index model.
Research Objectivies 1. To construct an optimal portfolio using Sharpe Index Model.
2. To analyze the Portfolio risk and Portfolio return of stocks listed at BSE.
3. To study the volatility of companies in comparison with the market.
4. To examine the efficiency of Sharpe single index portfolio evaluation model in relation to
an optimum portfolio.
Literature Review Saurabh Singh, Jayant Gautam, (2014) studied that Risk and return plays an important role in
making any investment decisions. In this present study 10 companies listed at National Stock
Exchange and CNX Bank Price Index was selected taking Jan 2009 to Dec 2013 as period of study.
The monthly closing prices of the selected securities were used for the Dec 2013. Application of
Single Index Model for the empirical analysis identified a portfolio of two companies based on the
cut-off point.
Laxmi Kanta Giri, Dr. Gayadhar Parhi, (2017) studied that Investment decision requires
consideration of two parameters - risk and return, under modern portfolio construction. The same is
applicable both for selecting an individual security as well as a portfolio comprising of securities.
Every investor seeks to maximize her return at a given level of risk or minimize the risk at a given
level of return. In this paper the author attempts to construct an optimum Portfolio with the help of
Sharpe’s single index model. The daily closing prices of all 50 stocks along With the Nifty Index
were considered for the period of one year. Results from the analysis shows that out of 50 stocks,
only 5 stocks were included in the optimum portfolio.
Niranjan Mandal, (2013) studied that paper get an insight into the idea embedded in Sharpe’s single
index model and to construct an optimal portfolio empirically using this model. Taking BSE
SENSEX as market performance index and considering daily indices along with the daily prices of
sampled securities for the period of April 2001 to March 2011, the proposed method formulates a
unique cut-off rate and selects those securities to construct an optimal portfolio whose excess return
to beta ratio is greater than the cut-off rate. Then, proportion of investment in each of the selected
securities is computed on the basis of beta value, unsystematic risk, and excess return to beta ratio
and cut-off rate of each of the securities concerned.
Chintan A. Shah, (2015) studied that process of blending together the broad asset classes so as to
obtain optimum return with minimum risk if called portfolio construction. Diversification of
investments helps to spread risk over many assets. Sharpe Model has simplified this process by
relating the return in a security to a single Market index. For the fulfilment of our research
objectives which are, to construct an optimal portfolio, evaluate the performance of BSE 15
securities, author have used the Descriptive Research Design and used the Secondary data
Sharp's Ratio = E(RP) – RF/σp
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 212
collection methods. Finally, the results will be drawn out on the basis of expected risk & return
with help of Sharpe index model and comparison between Sharpe index model & CAPM model.
Research Methodology Research Design : Descriptive and Quantitative
Sources of Data : Secondary
Data Collection based : Market Capitalization
Sample Size : On based high capitalization based
Time period : 14 years
Sampling Methods : Non – probability methods
Mode of analysis : Sharpen single index methods
Steps in construction of optimal portfolio
This model firstly ranks the securities based on their excess return to beta ratio. After that all
securities are arranged according to their ranks. Then cut-off rate is calculated and it is compared
with excess return to beta for deciding whether to select the security for investment or not. The
model explains the weight that should be allocated to each security to obtain optimal portfolio.
Step 1: Calculate excess return to beta ratio for each security under consideration
Excess return to beta ratio = (Ri-Rf)/βi
Where:
Ri = Expected return of Security
Rf = Risk free rate of return Present MIBOR rate is taken as risk free rate
Rf βi = the Beta co-efficient of the security or excess return of the security over market index
Step 2: Rank the securities based on the excess return to beta ratio.
Step 3: Calculate the cut of rate using the formulae. Highest cut off rate will be regarded as C*
Where,
σm 2 = Market variance
Ri - Rf = Market risk premium
σei2 = Unsystematic risk of the
security
Step 4: Selection of securities for investment.
If (Ri- Rf)/βi is greater than cut off rate then the security will be included in the portfolio.
Step 5: Calculate the proportion to be invested in each security is calculated.
Here,
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms. Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 213
Data Analysis Table 1: Company price and market capitalization
S
R.
n
o Company
Market
cap
in(Cr.) 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
1 RELIANCE. 559526.3 1,368.35 2264.5 1523.2 1074.65 1047.8 748.25 773.7 929.5 824.7 1045.25 1319.2
2 TCS 517489.4 1,208.60 810.9 540 780.8 1182.5 1167.85 1571.8 2128.25 2547.05 2516.05 2431.1
3 HDFC Bank 470454.7 890 1319.95 967.85 1932.5 2342.95 520.05 624.1 748.85 1022.85 1071.2 1442.3
4 ITC LTD. 318468.4 150.4 206.35 184.8 263.15 181.45 226.85 309.1 352.95 325.45 328.05 280.45
5 SBI 287619.9 992.9 1598.85 1066.55 2079 2767.9 2095 2072.75 1918.3 267 194.3 292.6
6 HUL 279380.0 205.25 228.7 238.2 238.7 284.6 409.9 466.1 603.65 872.9 869.5 909.75
7 HDFCL 272402.3 1,870.80 2383.75 1411.2 2712.85 698.9 673.6 825.75 883.8 1311.25 1105.55 1502.4
8 SUZUKI 246646.8 819.7 829.55 775.1 1416.15 1227.5 1349.1 1279.7 1971.4 3699.25 3719.1 6024.3
9 ONGC 244858.1 878.15 981.35 779.7 1098.5 290.1 267.3 311.55 318.7 306.8 214.75 185.05
10 INFOSYS 220649.1 2,012.60 1430.15 1324.1 2615.1 3236.75 2864.95 2889.9 3278.85 2216.6 1217.95 1020.8
11
ICICI
BANK 204488.9 853.1 770.1 332.6 952.7 1112.75 784.3 1045.35 1245.45 315.3 236.55 277.1
12 AIRTEL 200589.5 763.2 826.1 625.8 311.9 357.5 336.75 291.8 318.9 393.9 350.9 349.95
13 S & P BSE 13,072.10 15644.4 9708.5 17527.8 19445.2 17404.2 18835.8 22386.3 27957.5 25341.9 29620.5
(Source: BSE and NSE official Website)
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 214
Table 2: Company Return
Name R(2008) R(2009) R(2010) R(2011) R(2012) R(2013) R(2014) R(2015) R(2016) R(2017)
Reliance 65.49129 -32.736 -29.448 -2.4985 -28.588 3.40127 20.137 -11.275 26.7431 26.209
TCS -32.9058 -33.407 44.5926 51.4472 -1.2389 34.5892 35.4021 19.6781 -1.2171 -3.3763
HDFC 48.30899 -26.675 99.6694 21.2393 -77.804 20.0077 19.9888 36.5894 4.72699 34.6434
ITC 37.2008 -10.443 42.3972 -31.047 25.0207 36.2574 14.1863 -7.7915 0.79889 -14.51
SBI 61.0283 -33.293 94.9276 33.1361 -24.311 -1.0621 -7.4515 -86.081 -27.228 50.5919
HUL 11.42509 4.15391 0.20991 19.2292 44.0267 13.7107 29.5108 44.6037 -0.3895 4.6291
HDFCL 27.41875 -40.799 92.2371 -74.237 -3.62 22.5876 7.02997 48.365 -15.687 35.8962
SUZUKI 1.201659 -6.5638 82.7055 -13.321 9.90631 -5.1442 54.0517 87.6458 0.5366 61.9827
ONGC 11.75198 -20.548 40.8875 -73.591 -7.8594 16.5544 2.29498 -3.7339 -30.003 -13.83
INFOSYS -28.9402 -7.4153 97.5002 23.7716 -11.487 0.87087 13.4589 -32.397 -45.053 -16.187
ICICI -9.72922 -56.811 186.44 16.7996 -29.517 33.2845 19.1419 -74.684 -24.976 17.1423
AIRTEL 8.241614 -24.246 -50.16 14.6201 -5.8042 -13.348 9.28718 23.5183 -10.916 -0.2707
BSE 19.67 -37.94 80.54 -100.00 -10.50 -11.73 18.85 24.89 19.93 -10.32
(Source: BSE and NSE official Website)
Table 3: BSE and Risk and Return**
BSE
year Ri R bar ( Ri-R bar ) ( Ri-R bar )2
2008 19.67 -0.67 20.34 413.76
2009 -37.94 -0.67 -37.27 1,388.98
2010 80.54 -0.67 81.21 6,595.23
2011 -100 -0.67 -99.33 9,866.25
2012 -10.5 -0.67 -9.83 96.61
2013 -11.73 -0.67 -11.06 122.3
2014 18.75 -0.67 19.42 377.18
2015 24.89 -0.67 25.56 653.36
2016 19.93 -0.67 20.6 424.4
2017 -10.32 -0.67 -9.65 93.1
TOTAL -6.71 TOTAL 20,031.17
MEAN -0.67 VARI = 2225.69
S.D= 47.18
(Source: BSE official Website)
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 215
Table 4: T-Bills interest rates
T – BILL
Year 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
% 7.31 4.95 4.42 7.23 8.98 8.02 9.19 8.31 7.27 5.86
(Source: BSE and NSE official Website)
(Source: BSE and NSE official Website)
Table 6: TATA CONSULTANCY SERVICES LTD Risk and Return
Table 5: Reliance Risk & Return
RELIANCE INDUSTRY BSE
Year Ri ( Ri-R bar ) ( Ri-R bar )2 ( Ri-R bar)
( Ri-R bar )* ( Ri-R
bar)
2008 65.4912851 61.74766075 3812.773609 20.34 1,255.95
2009 -32.7357032 -36.47932762 1330.741343 -37.27 1,359.58
2010 -29.4478729 -33.19149727 1101.675491 81.21 -2,695.48
2011 -2.49848788 -6.24211225 38.96396534 -99.33 620.03
2012 -28.5884711 -32.33209545 1045.364396 -9.83 317.82
2013 3.40126963 -0.342354741 0.117206769 -11.06 3.79
2014 20.137004 16.39337964 268.7428959 19.42 318.36
2015 -11.274879 -15.01850334 225.5554425 25.56 -383.87
2016 26.7430581 22.99943371 528.9739511 20.6 473.79
2017 26.2090409 22.46541653 504.6949398 -9.65 -216.79
TOTAL 37.4362437
8857.603241 TOTAL 1,053.17
% = 3.74362437 VARI= 984.1781378 VARI 117.02
S.D= 31.37
(Source: BSE and NSE official Website)
Findings
Co- Re = 0.079066
BETA = 0.052577
Sharpe’s ratio = -0.108714556
TATA CONSULTANCY SERVICES LTD. BSE
Year
Return
(in %) X-X BAR (X-X BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R
bar)
2008 -32.9058 -44.2622 1959.144 20.34 -900.29
2009 -33.4073 -44.7637 2003.789 -37.27 1,668.34
2010 44.59259 33.23621 1104.646 81.21 2,699.11
2011 51.44723 40.09085 1607.277 -99.33 -3,982.22
2012 -1.2389 -12.5953 158.6411 -9.83 123.81
2013 34.5892 23.23282 539.764 -11.06 -256.96
2014 35.40209 24.04571 578.196 19.42 466.97
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 216
Table 7: HDFC Bank Risk and Return
Table 8: ITC’s Risk and Return
2015 19.67814 8.321759 69.25168 25.56 212.70
2016 -1.21709 -12.5735 158.0923 20.6 -259.01
2017 -3.37632 -14.7327 217.0526 -9.65 142.17
TOTAL 113.5638 TOTAL 8395.854 TOTAL -85.38
% 11.35638 VARI = 932.87 CO-VARI -9.49
S.D = 30.54
(Source: BSE and NSE Official Website)
Findings
CO- RELA = --0.00659
BETA = -0.00426
shapes ratio =0.137602
HDFC BANK BSE
Year
Return
(in %) x- x bar (x- x bar)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 48.30899 30.23899 914.3965 20.34 615.0611
2009 -26.675 -44.745 2002.115 -37.27 1667.646
2010 99.6694 81.5994 6658.462 81.21 6626.687
2011 21.2393 3.1693 10.04446 -99.33 -314.807
2012 -77.804 -95.874 9191.824 -9.83 942.4414
2013 20.0077 1.9377 3.754681 -11.06 -21.431
2014 19.9888 1.9188 3.681793 19.42 37.2631
2015 36.5894 18.5194 342.9682 25.56 473.3559
2016 4.72699 -13.343 178.0359 20.6 -274.866
2017 34.6434 16.5734 274.6776 -9.65 -159.933
TOTAL 180.695
19579.96 TOTAL 9591.418
MEAN 18.07 VARI = 2175.55 VARI 1065.71
S.D = 46.64 CO - RELE
0.484309
(Source: BSE and NSE Official Website)
Findings
Beta = 0.478822
Sharpe’s ratio = 0.234048027
ITC LTD BSE
Year
Return
(in %) X- X BAR (X-X BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 37.2008 27.9908 783.48488 20.34 569.3329
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 217
Table 9: State Bank of India’s Risk and return
Table 10: Hindustan Unilever Ltd’s Risk and return
2009 -10.443 -19.653 386.24041 -37.27 732.4673
2010 42.3972 33.1872 1101.3902 81.21 2695.133
2011 -31.047 -40.257 1620.626 -99.33 3998.728
2012 25.0207 15.8107 249.97823 -9.83 -155.419
2013 36.2574 27.0474 731.56185 -11.06 -299.144
2014 14.1863 4.9763 24.763562 19.42 96.63975
2015 -7.7915 -17.0015 289.051 25.56 -434.558
2016 0.79889 -8.41111 70.746771 20.6 -173.269
2017 -14.51 -23.72 562.6384 -9.65 228.898
TOTAL 92.06979 TOTAL 5820.4814 COV= 7258.808
MEAN 9.21 VARI = 646.72
S.D = 25.43 COR = 0.672231
(Source: BSE and NSE Official Website)
Findings
Beta = 0.362375
Sharpe’s ratio = 0.08084939
STATE BANK OF INDIA BSE
Year
Return
(in %) (RI- R BAR) (RI- R BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 61.0283 55.0033 3025.363011 20.34 1118.767
2009 -33.293 -39.318 1545.905124 -37.27 1465.382
2010 94.9276 88.9026 7903.672287 81.21 7219.78
2011 33.1361 27.1111 735.0117432 -99.33 -2692.95
2012 -24.311 -30.336 920.272896 -9.83 298.2029
2013 -1.0621 -7.0871 50.22698641 -11.06 78.38333
2014 -7.4515 -13.4765 181.6160523 19.42 -261.714
2015 -86.081 -92.106 8483.515236 25.56 -2354.23
2016 -27.228 -33.253 1105.762009 20.6 -685.012
2017 50.5919 44.5669 1986.208576 -9.65 -430.071
TOTAL 60.2573
25937.55392
3756.544
MEAN = 6.025 VARI = 2881.95 COV = 417.39
SD= 53.68 COR = 0.164805
(Source: BSE and NSE Official Website)
Findings
Beta = 0.187533
Sharpe’s ratio = -0.021032042
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 218
Table 11: Housing Development Finance ‘s Risk and return
HINDUSTAN UNILEVER LTD. BSE
Year
Return
(in %) (RI- R BAR) (RI- R BAR)2 ( Ri-R bar)
(X-X BAR) * (
Ri-R bar)
2008 11.42509 -5.68491 32.3182017 20.34 -115.631
2009 4.15391 -12.95609 167.860268 -37.27 482.8735
2010 0.20991 -16.90009 285.613042 81.21 -1372.46
2011 19.2292 2.1192 4.49100864 -99.33 -210.5
2012 44.0267 26.9167 724.508739 -9.83 -264.591
2013 13.7107 -3.3993 11.5552405 -11.06 37.59626
2014 29.5108 12.4008 153.779841 19.42 240.8235
2015 44.6037 27.4937 755.90354 25.56 702.739
2016 -0.3895 -17.4995 306.2325 20.6 -360.49
2017 4.6291 -12.4809 155.772865 -9.65 120.4407
TOTAL 171.1096
2598.03525
-739.195
MEAN = 17.11 VARI = 288.670583 COV = -82.13
SD = 16.99 COR = -0.10246
(Source: BSE and NSE Official Website)
Findings
Beta = -0.0369
Sharpe’s ratio = 0.58599176
HOUSING DEVELOPMENT FINANCE BSE
Year
Return
(in %) (RI- R BAR) (RI- R BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 27.41875 17.49875 306.206252 20.34 355.92458
2009 -40.799 -50.719 2572.41696 -37.27 1890.2971
2010 92.2371 82.3171 6776.10495 81.21 6684.9717
2011 -74.237 -84.157 7082.40065 -99.33 8359.3148
2012 -3.62 -13.54 183.3316 -9.83 133.0982
2013 22.5876 12.6676 160.46809 -11.06 -140.1037
2014 7.02997 -2.89003 8.3522734 19.42 -56.12438
2015 48.365 38.445 1478.01803 25.56 982.6542
2016 -15.687 -25.607 655.718449 20.6 -527.5042
2017 35.8962 25.9762 674.762966 -9.65 -250.6703
TOTAL 99.19162
19897.7802
17431.858
MEAN = 9.92 VARIANCE 2210.86447 COV= 1936.87
S.D.= 47.02 COR= 41.052777
(Source: BSE and NSE Official Website)
Findings
Beta = 0.8702335
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 219
Table 12: Maruti Suzuki India Ltd’s Risk and Return
Table 13: ONGC’s Risk and return
Sharpe’s ratio = -0.00426
MARUTI SUZUKI INDIA LTD. BSE
Year
Return
(in %)
(RI- R
BAR)
(RI- R
BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 1.201659 -26.0983 681.123403 20.34 -530.84
2009 -6.5638 -33.8638 1146.75695 -37.27 1262.104
2010 82.7055 55.4055 3069.76943 81.21 4499.481
2011 -13.321 -40.621 1650.06564 -99.33 4034.884
2012 9.90631 -17.3937 302.540452 -9.83 170.98
2013 -5.1442 -32.4442 1052.62611 -11.06 358.8329
2014 54.0517 26.7517 715.653453 19.42 519.518
2015 87.6458 60.3458 3641.61558 25.56 1542.439
2016 0.5366 -26.7634 716.27958 20.6 -551.326
2017 61.9827 34.6827 1202.88968 -9.65 -334.688
TOTAL 273.0013
14179.3203
10971.38
MEAN
= 27.3
VARI 1575.48 COV= 1219.043
S.D. 39.69 COR = 0.650998
(Source: BSE and NSE Official Website)
Findings
Beta = 0.093705
Sharpe’s ratio= -0.487100977
OIL AND NATURAL GAS CORPORATION LTD. BSE
Year
Return
(in %) (RI- R BAR) (RI- R BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R
bar)
2008 11.75198 19.55198 382.2799 20.34 397.6873
2009 -20.548 -12.748 162.5115 -37.27 475.118
2010 40.8875 48.6875 2370.473 81.21 3953.912
2011 -73.591 -65.791 4328.456 -99.33 6535.02
2012 -7.8594 -0.0594 0.003528 -9.83 0.583902
2013 16.5544 24.3544 593.1368 -11.06 -269.36
2014 2.29498 10.09498 101.9086 19.42 196.0445
2015 -3.7339 4.0661 16.53317 25.56 103.9295
2016 -30.003 -22.203 492.9732 20.6 -457.382
2017 -13.83 -6.03 36.3609 -9.65 58.1895
TOTAL -78.0764
8484.636
10993.74
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 220
Table 14: Infosys Ltd’s Risk and return
Table 15: ICICI Bank Ltd’s Risk and Return
MEAN = -7.8 VARI 942.7373 COV 1221.527
S.D. 30.7 COR 0.843348
(Source: BSE and NSE Official Website)
Findings
Beta = 0.200149
Sharpe’s ratio = -0.178977667
INFOSYS LTD. BSE
Year
Return
(in %) (RI- R BAR) (RI- R BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 -28.9402 -28.9402 837.5352 20.34 -588.644
2009 -7.4153 -7.4153 54.98667 -37.27 276.3682
2010 97.5002 97.5002 9506.289 81.21 7917.991
2011 23.7716 23.7716 565.089 -99.33 -2361.23
2012 -11.487 -11.487 131.9512 -9.83 112.9172
2013 0.87087 0.87087 0.758415 -11.06 -9.63182
2014 13.4589 13.4589 181.142 19.42 261.3718
2015 -32.397 -32.397 1049.566 25.56 -828.067
2016 -45.053 -45.053 2029.773 20.6 -928.092
2017 -16.187 -16.187 262.019 -9.65 156.2046
TOTAL -5.87793
14619.11
4009.185
% -0.0588 VARIANCE 1624.35 COV 445.47
S.D. 40.3 COR 0.234291
(Source: BSE and NSE Official Website)
Findings
Beta = 0.653806
Sharpe’s ratio = 0.007713047
ICICI BANK LTD. BSE
Year
Return
(in %) (RI- R BAR) (RI- R BAR)2 ( Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 -9.72922 -17.438328 304.0952834 20.34 -354.696
2009 -56.811 -64.520108 4162.844336 -37.27 2404.664
2010 186.44 178.730892 31944.73176 81.21 14514.74
2011 16.7996 9.090492 82.6370448 -99.33 -902.959
2012 -29.517 -37.226108 1385.783117 -9.83 365.9326
2013 33.2845 25.575392 654.100676 -11.06 -282.864
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 221
Table 16: Bharti Airtel Ltd’s Risk and Return
Conclusion
Table 17: Summary
PARTICULAR RETURN S.D. COV COR BETA SHARPE’S
RATIO
RELIANCE 3.74 31.37 117.02 0.079066 0.053 -0.109
2014 19.1419 11.432792 130.7087329 19.42 222.0248
2015 -74.684 -82.393108 6788.624246 25.56 -2105.97
2016 -24.976 -32.685108 1068.316285 20.6 -673.313
2017 17.1423 9.433192 88.98511131 -9.65 -91.0303
TOTAL 77.09108
46610.82659
13096.53
MEAN = 7.709108 VARIANCE 5178.980732 COV 1455.17
S.D. 71.97 COR 0.428553
(Source: BSE and NSE Official Website)
Findings
Beta = -0.18424
Sharpe’s ratio = -0.167594423
BHARTI AIRTEL LTD. BSE
Year
Retrun
(in %) (RI- R BAR) (RI- R BAR)2 (Ri-R bar)
(X-X BAR) * ( Ri-R bar)
2008 8.241614 13.14938 172.9063 20.34 267.4585
2009 -24.246 -19.3382 373.9671 -37.27 720.7358
2010 -50.16 -45.2522 2047.764 81.21 -3674.93
2011 14.6201 19.52787 381.3377 -99.33 -1939.7
2012 -5.8042 -0.89643 0.803587 -9.83 8.811907
2013 -13.348 -8.44023 71.23748 -11.06 93.34894
2014 9.28718 14.19495 201.4966 19.42 275.6659
2015 23.5183 28.42607 808.0415 25.56 726.5703
2016 -10.916 -6.00823 36.09883 20.6 -123.77
2017 -0.2707 4.63707 21.50242 -9.65 -44.7477
TOTAL -49.0777
4115.156
-3690.56
MEAN = -4.90777 VARIANCE 457.2395 COV -410.063
S.D. 71.97 COR -0.12076
(Source: BSE and NSE Official Website)
Findings
Beta = -0.00426
Sharpe’s ratio = 0.137602489
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 222
TC 11.35638 30.54 -9.49 -0.00659 -0.00426 0.137602489
HDFC Bank Ltd 18.07
46.64
1065.71
0.484309
0.478822
0.234048027
ITC LTD. 9.21
25.43
806.534
0.672231
0.362375
0.08084939
SBI 6.025
53.68
417.39
417.39
0.187533
-0.021032042
HUL 17.11
16.99
-82.13
-0.10246
-0.0369
0.58599176
HDFC LTD 9.92
47.02
1936.87
41.052777
0.8702335
0.058826031
MARUTI
SUZUKI
27.3
39.69
1219.043
0.650998
0.547714
0.507583774
ONGC -7.8
30.7
1221.527
0.843348
0.093705
-0.487100977
INFOSYS LTD. -0.0588
40.3
445.47
0.234291
0.200149
-0.178977667
ICICI BANK 7.709108
71.97
1455.17
0.428553
0.653806
0.007713047
BHARTI
AIRTEL
-4.90777
71.97
-410.063
-0.12076
-0.18424
-0.167594423
According to our objectives we find that out of 10 companies MARUTI SUZUKI provide higher
return which is 27.3 %, then after HDFC Bank that give 18.07% return and last one is HUL that
provide 17.11% return. Also the HDFC LTD & ONGC Company is positive correlation with the
market. In terms of market volatility the three company is negatively co related which is TCS,
HUL and BHARTI AIRTEL, and HDFC LTD is highly positive related with the market.
According to reward to volatility ratio the HDFC LTD and MARUTI SUZUKI is provide higher
return to take more risk.
References
1. http://www.bseindia.com/
2. https://www.rbi.org.in/
3. www.icaiknowledgegateway.org/...7-portfolio-theory.pdf
4. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2376319
5. http://ijarcsms.com/docs/paper/volume3/issue10/V3I10-0002.pdf
6. http://ijrar.com/upload_issue/ijrar_issue_196.pdf
7. http://www.garph.co.uk/IJARMSS/Dec2014/7.pdf
8. Investment analysis and portfolio management (4th
edition) – PRASANNA CHANDRA
9. Strategic financial management --- RAVI M. KISHORE
Towards Excellence: An Indexed Refereed Journal of Higher Education/ Mr. Vijay Bhatu & Ms.
Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223
FEB, 2018. VOL.10. SPECIAL ISSUE FOR
ICGS-2018 www.ascgujarat.org Page | 223
Mr. Vijay Bhatu
Student, MBA Semester 3
Noble Group of Institutions,
Junagadh
Ms. Hetal Mehta
Student, MBA Semester 3
Noble Group of Institutions,
Junagadh
Prof. Riddhi Sanghvi
Assistant Professor,
Noble Group of Institutions,
Junagadh