CONSTRUCTION OF AN OPTIMAL PORTFOLIO USING SHARPE INDEX MODEL … Feb18/24.pdf · · 2018-02-21Sharpe’s single index model and to construct an optimal portfolio empirically using

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





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





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

http://www.investopedia.com/terms/a/aggressiveinvestmentstrategy.asp

http://www.investopedia.com/terms/b/beta.asp

http://www.investopedia.com/terms/d/defensivestock.asp

http://www.investopedia.com/terms/c/cyclicalstock.asp

http://www.investopedia.com/terms/s/stakeholder.asp

http://www.investopedia.com/terms/c/cashflow.asp

http://www.investopedia.com/terms/r/reit.asp

http://www.investopedia.com/terms/r/reit.asp

http://www.investopedia.com/terms/m/mlp.asp

http://www.investopedia.com/terms/i/ipo.asp

http://www.investopedia.com/terms/i/ipo.asp

http://www.investopedia.com/terms/t/takeover.asp

http://www.investopedia.com/terms/b/bluechip.asp

http://www.investopedia.com/terms/c/corporatebond.asp

http://www.investopedia.com/terms/n/negative-correlation.asp

http://www.investopedia.com/terms/n/negative-correlation.asp





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

http://www.investopedia.com/terms/l/longterm.asp

http://www.investopedia.com/university/tradingsystems/





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





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



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)





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


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)


Hetal Mehta & Prof. Riddhi Sanghvi / Page 207-223



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



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


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





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


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)


2008 37.2008 27.9908 783.48488 20.34 569.3329





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


Findings

Beta = 0.362375


STATE BANK OF INDIA BSE

Year

Return

(in %) (RI- R BAR) (RI- R BAR)2 ( 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


Findings

Beta = 0.187533






Table 11: Housing Development Finance ‘s Risk and return

HINDUSTAN UNILEVER LTD. BSE

Year

Return


(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


Findings

Beta = -0.0369


HOUSING DEVELOPMENT FINANCE BSE

Year

Return



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


Findings

Beta = 0.8702335





Table 12: Maruti Suzuki India Ltd’s Risk and Return

Table 13: ONGC’s Risk and return


MARUTI SUZUKI INDIA LTD. BSE

Year

Return

(in %)

(RI- R

BAR)

(RI- R

BAR)2 ( 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


Findings

Beta = 0.093705

Sharpe’s ratio= -0.487100977

OIL AND NATURAL GAS CORPORATION LTD. BSE

Year

Return


(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





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


Findings

Beta = 0.200149


INFOSYS LTD. BSE

Year

Return



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


Findings

Beta = 0.653806


ICICI BANK LTD. BSE

Year

Return



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





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


Findings

Beta = -0.18424


BHARTI AIRTEL LTD. BSE

Year

Retrun

(in %) (RI- R BAR) (RI- R BAR)2 (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


Findings

Beta = -0.00426






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





Mr. Vijay Bhatu

Student, MBA Semester 3

Noble Group of Institutions,

Junagadh

[email protected]

Ms. Hetal Mehta

Student, MBA Semester 3


Junagadh

[email protected]

Prof. Riddhi Sanghvi

Assistant Professor,


Junagadh

[email protected]

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