portfolio construction using sharpe's model and risk analysis

Part-A
1.MUTUAL FUND OVERVIEW
1.1.MUTUAL FUND AN INVESTMENT PLATFORM
Mutual fund is an investment company that pools money from small investors and invests in
a variety of securities, such as stocks, bonds and money market instruments. Most open-end
Mutual funds stand ready to buy back (redeem) its shares at their current net asset value,
which depends on the total market value of the fund's investment portfolio at the time of
redemption. Most open-end Mutual funds continuously offer new shares to investors. It
is also known as an open-end investment company, to differentiate it from a closed-end
investment company.
Mutual funds invest pooled cash of many investors to meet the fund's stated investment
objective. Mutual funds stand ready to sell and redeem their shares at any time at the fund’s
current net asset value: total fund assets divided by shares outstanding. In Simple Words,
Mutual fund is a mechanism for pooling the resources by issuing units to the investors
and investing funds in securities in accordance with objectives as disclosed in offer
document.
Investments in securities are spread across a wide cross-section of industries and sectors and
thus the risk is reduced. Diversification reduces the risk because not all stocks may move in
the same direction in the same proportion at the same time. Mutual fund issues units’ to the
investors in accordance with quantum of money invested by them. Investors of Mutual fund are
known as unit holders. The profits or losses are shared by the investors in proportion to their
investments. The Mutual funds normally come out with a number of schemes with different
investment objectives which are launched from time to time.
In India, A Mutual fund is required to be registered with Securities and Exchange Board of
India (SEBI) which regulates securities markets before it can collect funds from the public.
In Short, a Mutual fund is a common pool of money in to which investors with common
investment objective place their contributions that are to be invested in accordance with the
state d investment objective of the scheme. The investment manager would invest the
money collected from the investor in to assets that are defined/ permitted by the s tated
objective of the scheme.
1

1.2 ADVANTAGES OF MUTUAL FUND
Synod. Advantage Particulars
1.
Portfolio
Diversification
Mutual Funds invest in a well-diversified portfolio of
securities which enables investor to hold a diversified
investment portfolio (whether the amount of investment is big or
small).
2.
Professional
Management
Fund manager undergoes through various research works and
has better investment management skills which ensure higher
returns to the investor than what he can manage on his own.
3. Less Risk
Investors acquire a diversified portfolio of securities even with
a small investment in a Mutual Fund. The risk in a diversified
portfolio is lesser than investing in merely 2 or 3 securities.
4.
Low transaction
Costs
Due to the economies of scale (benefits of larger volumes),
mutual funds pay lesser transaction costs. These benefits are
passed on to the investors.
5. Liquidity
An investor may not be able to sell some of the shares held by
him very easily and quickly, whereas units of a mutual fund
are far more liquid.
6.
Choice of
Schemes
Mutual funds provide investors with various schemes with
different investment objectives. Investors have the option of
investing in a scheme having a correlation between its investment
objectives and their own financial goals. These schemes further
have different plans/options
7.
Transparency
Funds provide investors with updated information pertaining to
the markets and the schemes. All material facts are disclosed to
investors as required by the regulator.
8. Flexibility
Investors also benefit from the convenience and flexibility
offered by Mutual Funds. Investors can switch their holdings
from a debt scheme to an equity scheme and vice-versa. Option
of systematic (at regular intervals) investment and withdrawal is
also offered to the investors in most open-end schemes.
2

9. Safety
Mutual Fund industry is part of a well-regulated investment
environment where the interests of the investors are protected
by the regulator. All funds are registered with SEBI and
complete transparency is forced.
Table: 1.1
1.3 DISADVANTAGE OF INVESTING THROUGH MUTUAL FUNDS
S. No. Disadvantage Particulars
1.
Costs Control
Not in the
Hands of an
Investor
Investor has to pay investment management fees and fund
distribution costs as a percentage of the value of his investments
(as long as he holds the units), irrespective of the performance of
the fund.
2.
No Customize
Portfolios
The portfolio of securities in which a fund invests is a decision
taken by the fund manager. Investors have no right to interfere
in the decision making process of a fund manager, which some
investors find as a constraint in achieving their
financial objectives.
3.
Difficulty in
Selecting a
Suitable Fund
Scheme
Many investors find it difficult to select one option from the
plethora of funds/schemes/plans available. For this, they may
have to take advice from financial planners in order to invest in
the right fund to achieve their objectives.
Table: 1.2
1.4 CATEGORIES OF MUTUAL FUND
3

Figure: 1.2
Figure: 1.3
4
BASED ON THEIR STRUCTURE
OPEN-ENDED FUNDS CLOSED-ENDED FUNDS
BASED ON
INVESTMENT
OBJECTIVE
EQUITY FUND BALANCED FUND DEBT FUND
DEBT
EQUITY
INDEX FUND
EQUITY FUND
DIVEDEND FUND
THEMANTIC FUND
LEQUID FUNDS
INCOME FUNDS
GUILT FUNDS
FMPS FUNDS
SECTOR FUND
ELSS
FLOATING
ARBITAGE

Mutual funds can be classified as follow:
A. Based on their structure:
 Open-ended funds: Investors can buy and sell the units from the fund, at any point of
time.
 Close-ended funds: These funds raise money from investors only once. Therefore,
after the offer period, fresh investments cannot be made into the fund. If the fund is
listed on a stocks exchange, the units can be traded like stocks (E.g., Morgan Stanley
Growth Fund). Recently, most of the New Fund Offers of close-ended funds provided
liquidity window on a periodic basis such as monthly or weekly. Redemption of units can
be made during specified intervals. Therefore, such funds have relatively low liquidity.
B. Based on their investment objective:
 Equity funds: These funds invest in equities and equity related instruments. With
fluctuating share prices, such funds show volatile performance, even losses. However,
short term fluctuations in the market, generally smoothens out in the long term,
thereby offering higher returns at relatively lower volatility. At the same time, such
funds can yield great capital appreciation as, historically, equities have outperformed all
asset classes in the long term. Hence, investment in equity funds should be considered for
a period of at least 3-5 years. It can be further classified as:
1. Index funds- In this case a key stock market index, like BSE Sensex or Nifty is
tracked. Their portfolio mirrors the benchmark index in terms of both
composition and individual stock weightages.
2. Equity diversified funds- 100% of the capital is invested in equities spreading
across different sectors and stocks.
3. Dividend yield funds- it is similar to the equity-diversified funds except that they
invest in companies offering high dividend yields.
4. Thematic funds- Invest 100% of the assets in sectors which are related through
some theme.
e.g. -An infrastructure fund invests in power, construction, cements sectors etc.
5. Sector funds- Invest 100% of the capital in a specific sector. e.g. - A banking

sector fund will invest in banking stocks.
6. ELSS- Equity Linked Saving Scheme provides tax benefit to the investors.
 Balanced fund: Their investment portfolio includes both debt and equity. As a result, on
the risk-return ladder, they fall between equity and debt funds. Balanced funds are the
ideal mutual funds vehicle for investors who prefer spreading their risk across various
instruments. Following are balanced funds classes:
1. Debt-oriented funds -Investment below 65% in equities.
2.Equity-oriented funds -Invest at least 65% in equities, remaining in debt.
 Debt fund: They invest only in debt instruments, and are a good option for investors
averse to idea of taking risk associated with equities. Therefore, they invest exclusively in
fixed-income instruments like bonds, debentures, Government of India securities; and
money market instruments such as certificates of deposit (CD), commercial paper (CP)
and call money. Put your money into any of these debt funds depending on your
investment horizon and needs.
1.Liquid funds- These funds invest 100% in money market instruments, a large
portion being invested in call money market.
2. Gilt funds ST- They invest 100% of their portfolio in government securities of
and T-bills.
3. Floating rate funds - Invest in short-term debt papers. Floaters invest in debt
instruments, which have variable coupon rate.
4.Arbitrage fund- They generate income through arbitrage opportunities due to
miss- pricing between cash market and derivatives market. Funds are allocated to
equities, derivatives and money markets. Higher proportion (around 75%) is put
in money markets, in the absence of arbitrage opportunities.
5.Gilt funds LT- They invest 100% of their portfolio in long-term government
securities.
6.Income funds LT- Typically, such funds invest a major portion of the portfolio
in long-term debt papers.
7.MIPs- Monthly Income Plans have an exposure of 70%-90% to debt and an
exposure of 10%-30% to equities.

8.FMPs- fixed monthly plans invest in debt papers whose maturity is in line with
that of the fund.
How are funds different in terms of their risk profile:
Equity Funds High level of return, but has a high level of risk too
Debt funds Returns comparatively less risky than equity funds
Liquid and Money
Market funds
Provide stable but low level of return
Table:1.3
1.5 INVESTMENT STRATEGIES
1. Systematic Investment Plan: Under this, a fixed sum is invested each month on a fixed
date of a month. Payment is made through post-dated cheques or direct debit facilities. The
investor gets fewer units when the NAV is high and more units when the NAV is low. This is
called as the benefit of Rupee Cost Averaging (RCA)
2. Systematic Transfer Plan: Under this, an investor invest in debt-oriented fund and give
instructions to transfer a fixed sum, at a fixed interval, to an equity scheme of the same
mutual fund.
3. Systematic Withdrawal Plan: if someone wishes to withdraw from a mutual fund then he
can withdraw a fixed amount each month.
1.6. ORGANISATION OF MUTUAL FUND:

Figure:1.4
THE STRUCTURE CONSISTS OF:
SPONSOR
Sponsor is the person who acting alone or in combination with another body corporate
establishes a mutual fund. Sponsor must contribute at least 40% of the net worth of the
Investment managed and meet the eligibility criteria prescribed under the Securities and
Exchange Board of India (Mutual Fund) Regulations, 1996. The sponsor is not responsible or
liable for any loss or shortfall resulting from the operation of the Schemes beyond the initial
contribution made by it towards setting up of the Mutual Fund.
TRUST
The Mutual Fund is constituted as a trust in accordance with the provisions of the Indian
Trusts Act, 1882 by the Sponsor. The trust deed is registered under the Indian Registration
Act, 1908.
TRUSTEE
Trustee is usually a company (corporate body) or a Board of Trustees (body of individuals).
The main responsibility of the Trustee is to safeguard the interest of the unit holders and
ensure that the AMC functions in the interest of investors and in accordance with the Securities
and Exchange Board of India (Mutual Funds) Regulations, 1996, the provisions of the Trust
Deed and the Offer Documents of the respective Schemes. At least 2/3rd directors of the
Trustee are independent directors who are not associated with the Sponsor in any manner.
ASSET MANAGEMENT COMPANY (AMC)
The AMC is appointed by the Trustee as the Investment Manager of the Mutual Fund. The

AMC is required to be approved by the Securities and Exchange Board of India (SEBI) to act
as an asset management company of the Mutual Fund. At least 50% of the directors of the
AMC are independent directors who are not associated with the Sponsor in any manner. The
AMC must have a net worth of at least 10 cores at all times.
REGISTRAR AND TRANSFER AGENT
The AMC if so authorized by the Trust Deed appoints the Registrar and Transfer Agent to the
Mutual Fund. The Registrar processes the application form, redemption requests and dispatches
account statements to the unit holders. The Registrar and Transfer agent also handles
communications with investors and updates investor records.
ASSET UNDER MANAGEMENT:
ASSET UNDER MANAGEMENT OF TOP AMC,S as on Jun 30, 2013
Mutual Fund Name No. of schemes Corpus (Rs.Crores)
Reliance Mutual Fund 263 108,332.36
SBI Mutual Fund 202 78,197.90
ICICI Prudential Mutual Fund 325 70,169.46
UTI Mutual Fund 207 67,978.19
Birla Sun Life Mutual Fund 283 56,282.87
Hdfc Mutual Fund 130 34,061.04
LIC Mutual Fund 70 32,414.92
Kotak Mahindra Mutual Fund 124 30,833.02
Franklin Templeton Mutual Fund 191 25,472.85
IDFC Mutual Fund 164 21,676.29
Tata Mutual Fund 175 21,222.81
Table1.4
The graph indicates the growth of assets over the years.

Figure:1.5
1.7 DISTRIBUTION CHANNELS:
Mutual funds posses a very strong distribution channel so that the ultimate customers doesn’t
face any difficulty in the final procurement. The various parties involved in distribution of
mutual funds are:
1. Direct marketing by the AMCs: the forms could be obtained from the AMCs directly.
The investors can approach to the AMCs for the forms. some of the top AMCs of India are;
Reliance ,Birla Sunlife, Tata, Hdfc magnum, Kotak Mahindra, SBI, Sundaram, ICICI, Mirae
Assets, Canara Robeco, Lotus India, LIC, UTI etc. whereas foreign AMCs include: Standard
Chartered, Franklin Templeton, Fidelity, JP Morgan, HSBC, DSP Merill Lynch, etc.

2. Broker/ sub broker arrangements: the AMCs can simultaneously go for broker/sub-
broker to popularize their funds. AMCs can enjoy the advantage of large network of these
brokers and sub brokers.
3. Individual agents, Banks, NBFC: investors can procure the funds through individual
agents, independent brokers, banks and several non- banking financial corporations too,
whichever he finds convenient for him.

Part-B
2.Optimal portfolio construction
Portfolio is a combination of securities such as stocks, bonds and money market instruments. The
process of blending together the broad asset classes so as to obtain optimum return with minimum risk
is called portfolio construction. Diversification of investments helps to spread risk over many assets. A
diversification of securities gives the assurance of obtaining the anticipated return on portfolio. In a
diversified portfolio, some securities may not perform as expected, but others may exceed the
expectation and making the actual return of the reasonably close to the anticipated one.
Keeping a portfolio of single security may lead to a greater likelihood of the actual return sonic what
different from that of the expected return. Hence it is a common practice to diversify securities in the
portfolio. Keeping this fact in mind throve tried to construct portfolio with diversification of
investments in all sectors.
The steps followed in constructing optimal portfolio are as follows:
 Determination of objectives
 Selection of securities based on the objectives
 Choose a suitable approach for construction portfolio
 Apply the approach and construct the portfolio
 Assessment of risk and return

2.1. Value of a stock
There are various factors that determine the value of a stock understanding these helps to pay a price
that reflects the true value of a stock.
 Demand and supply:
In the short term the basic economic theory of demand and supply determines a stock's worth so when
the demand for a stock exceeds its supply (that is there are more buyers than sellers), its price tends to
rise and when supply overtakes demand that is, sellers exceed buyers), the stock loses value. However
these are short term marker trend to get evened out over a period of time. In the medium to long term, a
stock is driven by the companies fundamental strength i.e. business potential, past performance,
competence and credibility of its promoters and management etc.
 Growth potential:
Investors are willing to pay a premium for stocks of companies that have the potential to increase
their revenues and net profit the greater this growth potential, the higher the premium given to the
stock, if a company proves that it is capable of sustaining growth the market will continue to give it
high valuations and that's likely to be the major driver for stock valuation,
 Fundamentals:
A company’s growth outlook is linked to its business prospects and how well its management is
capitalizing on the existing opportunities. The quality of company’s management is crucial so attention
should be paid to the management practices of a company and its level of corporate governance.
2.2. Data Collection
The top 30 companies constituting the Nifty index have been chosen for applying Sharpe's single
index model and hence construct optimal portfolio. The National Stock Exchange (NSE) is India's
leading stock exchange covering various cities and towns across the country. NSE was set up by
leading institutions to provide a modern, fully automated screen-based trading system with national
reach. The Exchange has brought about unparalleled transparency, speed & efficiency, safety and
market integrity. It has set up facilities that serve as a model for the securities industry in terms of
systems, practices and procedures.

List of Companies constituting Nifty Index
Sector Company
Pharmaceuticals Lupin
Automobile Hero motorcorp
FMCG ITC
Automobile Bajaj Auto
Paints Asian Paints
IT HCL Tech
Pharmaceuticals Reddy Labs
Refineries BPCL
Automobile Mah and Mah
IT Infosys
Pharmaceuticals Cipla
Automobile Maruti Suzuki
Cement Ambuja Cements
Steel Jindal steel
Aluminium Hindalco
Cement ACC
Infra Larsen
Diversified Grasim
Oil and gas GAIL
Infra Jaiprakash
Oil and gas Cairn India
Oil and gas ONGC
Construction DLF
Minerals NMDC
Infra BHEL
Power Power Grid
Power NTPC
Telecom Bharti Airtel
FMCG HUL
Minerals Coal India
2.3. Single index model

Casual observations of the stock prices over a period of time reveals that most of the stock prices move
with the market index when the sensex increases, stock prices also tend to increase and vice-versa. This
indicates that some underlying factors affect the market index and this relationship could be used to
estimate the return on stock. Towards this purpose the following equation can be used:
Ri = αi + βiRm + ei
Where,
Ri – actual return on security i,
αi – intercept of the straight line or alpha co-efficient i.e., the amount by which a fund has
outperformed its bench mark taking into account its exposure to market risk.
βi – slope of straight line or beta co-efficient i.e., a measure of a fund's sensitivity to market
movements.
Rm – the rate of return on market index
ei – error term.
According to the equation the return of the stock can be divided into 2 components, the return due to
the market and the return independent of the market.
βi indicates the sensitiveness of the stock return to the changes in the market return..
The co variance of returns between securities i and j = βi βj
The variance of security's return, (σi2) = βi2 x σm2 + σei2
The variance of the security has two components namely, systematic risk or market risk and
unsystematic risk or unique risk. The variance explained by the index is referred to systematic risk and
the unexplained variance is called residual variance or unsystematic risk.
Systematic risk = βi2 * variance of market index.
= βi2 x σm2
Unsystematic risk = total variance - systematic risk
σei2 = σi2 – βi2 x σm2
From this point the portfolio variance can be derived
σp2 = [ (Xi βi)2 σm2 + Xi2 σei2]

were i vary from I to N
σp2 = variance of portfolio
σm2 = expected variance of index
σei2 = variation in security 's return not related to the market index
Xi = the portion of stock I in the portfolio.
2.4. Sharpe’s Optimal Portfolio
Sharpe had provided a model for the selection of appropriate securities in a portfolio. The selection of
any stock is directly related to its excess return to beta ratio.
Ri-Rf
βi
The excess return is the difference between the expected return on the stock and the risk less rate of
interest such as offered on government securities or treasury bill, the excess return to beta ratio
measures the additional return on a security (excess of the risk less asset return) per unit of systematic
risk or non-diversifiable risk. This ratio provides a relationship between potential risk and return.
Ranking of the stocks are done on the basis of their excess return to beta ratio. Portfolio managers
would like to include stocks with higher ratios. The selection of stocks depend on unique cut-off rate
such as all stocks with higher ratios of (Ri-Rf)/ βi are included and the stocks with lower rank are let
off, the cut-off point is denoted by C*. The stocks ranked above C*
have high excess returns to beta
and are included in the optimal portfolio.
2.4.1. Methodology
Step 1: A brief profile of each of the 30 companies of Nifty index is chosen.
Step 2: For a period of 5 years data of the each companies have been recorded.
Step 3: For applying Sharpe's index model Ri, Rm. σei2, βi, σm2, Rf values are required so all these
are calculated for further proceeding.

Step4: Excess to Beta ratio is calculated for all stocks and arranged in descending order.
Step 5: the unique value Ci is calculated for each stock using the formula below:
Ci = σm2 ∑[{(Ri – Rf)*βi}/ σei2]
1 + σm2 ∑(βi2/σei2)
Step 6: The Ci values go on increasing up to a certain point and then start decreasing, the highest
point is called cut-off point (C*). The securities which are above C*
point are chosen to be included in
optimal portfolio.
Step 7: Once the securities for portfolio are chosen, the proportion in which they should be invested is
to be determined. This can be done using a formula where Xi denotes the proportion,
Xi = Zi
∑ Zi
Where,
Zi = (βi/σei2) x {(Ri – Rf)/βi – C*}
Step 8: Return of portfolio is then calculated as:
R = WƩ i * Rp
Where i = 1 to n
2.4.2. Risk Free Rate of Return
Risk free security has zero variance or standard deviation. The risk free securities have no risk of
default. The government T-bills or bonds are approximate examples of risk free securities as they have
no risk of default. The 364 days Treasury bill rate return is considered as the risk free rate of return for

our calculation purpose. The 364 days T-Bills rule for five years from 2008 to Dec 2012 is as shown
in the following table.
Year Average
2008 6.99
2009 7.33
2010 8.3
2011 7.25
2012 7.52
Therefore the risk free rate of return for whole five years is the average of all the values in the table
mentioned above.
Rf = 6.99 + 7.33 + 8.3 + 7.25 + 7.52
5
Rf = 7.478
2.4.3. Return on Market
The return on the market is the return obtained by the companies constituting the Nifty index. The
return of Nifty Index is considered and only the yearly values are shown in the table below for
calculating purpose. The detailed fluctuation of Nifty index points during five years period can be seen
clearly in the following table.
The volatility in the stock returns of index companies is given by:
σm
2
=Σ(rm– rm’)2
= 1585.80
N-1
2.4.4. Evaluation of companies
ACC

ACC Limited was incorporated in the year 1936. ACC is India's foremost manufacturer of cement and
concrete. The company has been a trendsetter and important benchmark for the cement industry in
respect of its production, marketing and personal management process. The company has 14 cement
plants all over India, three refractory plants and 6 Ready Mix Concrete plants near to four metro cities
of India. It has also extended its services overseas to the Middle East, Africa and South America where
it has provided technical and managerial consultancy to a variety of consumers, and also helps in the
operation and maintenance of cement plants abroad. The company has received Good Corporate Citizen
Award for the year 2005-06. ACC received this award in recognition of its corporate achievements and
its ongoing endeavors in improving the quality of life of the community.
Return (rp) = (ClosingPrice–OpeningPrice) X 100%
OpeningPrice
Rp’ = Σ Ri
N
Rp’ = 47.8951÷ 5 = 9.579
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 4755.488÷ 4 = 1188.872
βi= Σ(ri -rp’)(rmi –rm’) = 4723.08 =0.744
Σ (rmi – rm’)2
6343.216
Unsystematic Risk (σei
2
) = σrp
2
– βi*βi* σm
2
= 1188.872 – 0.744*0.744*1585.8041
=1188.872–879.187
=309.6848
Ambuja Cements
Started out as a .joint sector co. with public sector Gujarat Industrial Investment Corporation
(GIIC) and Narottam Sekhsaria & Associates in 1981. Later with private partners buying out GIIC's
stake , the company became a private sector venture. It is having six cement plants at Ambujanagar
(Gujrat), Darlaghat (Himachal Pradesh), Upperwahi (Maharashtra), Rabriyawas (Rajasthan),

Daburji (Punjab) and in Bhatinda district (Punjab). It is also having three Bulk Cement Terminals at
Muldwarka (Gujarat), Gavier (Gujarat) and in Ulwa (Maharashtra). The company has increased its
installed capacity of Cement by 440000 MT and with this expansion the total installed capacity of
Cement has been increased to 13300000 MT.
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 58.81489085÷ 5 = 11.76297817
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 5471.526÷ 4 = 1367.882
βi= Σ(rp-rp’)(rm– rm’ ) = 5387.124206 =0.849273283
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 1367.882 – 0.849*0.849*1585.8041
=1367.882 –1143.785
=224.0915475
Asian Paints
The company has come a long way since its small beginnings in 1942. It was set up as a partnership
firm by four friends who were willing to take on the world's biggest, most famous paint companies
operating in India at that time. Over the course of 25 years, Asian Paints became a corporate force and
India's leading paints company. Driven by its strong consumer-focus and innovative spirit, the
company has been the market leader in paints since 1968. Today, it is double the size of any other

paint company in India. Asian Paints manufactures a wide range of paints for decorative and industrial
use. Asian Paints was included in Forbes Magazine's - Asia's Fab 50 List of companies in 2011 and
2012.
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 209.6294734 ÷ 5 = 41.92589469
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 7674.179 ÷ 4 =1918.545
βi= Σ(rp-rp’)(rm– rm’ ) = 6316.281944 = 0.995753819
Σ (rm – rm’)2
6343.21639
2
) = σrp
2
– βi*βi* σm
2
= 1918.545 – 0.9957*0.9957*1585.8041
=4994.225 –1572.36
=346.28
Bajaj Auto
Manufactures and markets Bajaj scooters, motorcycles, three-wheelers and spare parts.
Incorporated in 1945 as a private limited company, it went public in 1960. Currently the
company has four plants at Akurdi, Waluj. Chakan and Pantnagar (Uttarakhand) with a
combined installed capacity to produce 4.050.000 nos. of two wheelers and three wheelers. Further
the company has an installed capacity to produce 65.20 MW of Wind power.
In 1974-75, Bajaj Auto co-promoted a joint-sector company, Maharashtra Scooters. A plant was set

up at Satara and production of Priya scooters commenced in 1976. The company introduced a new
ungeared scooter called Wave for which the engine is powered by DTSi. In 2006-07, Bajaj Auto
entered into a Joint Venture in Indonesia with a local financial consultancy group Boentaro and
formed PT. Bajaj Auto Indonesia, where the company has 95 per cent equity ownership. This joint
venture company will be used for assemble and sell three-wheelers and high-end motorcycles.
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 284.3294÷ 5 = 56.86588562
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 18026.38 ÷ 4 = 4506.595
βi= Σ(rp-rp’)(rm– rm’ ) = 9282.336036 = 1.463348476
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 4506.595 – 1.463348*1.463348*1585.8041
=4506.595 – 3395.823072
=1110.772
JAIPRAKASH
Jaiprakash Associates Limited, an infrastructural industrial conglomerate, engages in engineering and
construction, power, cement, hospitality, real estate, expressways, sports, and agri businesses in India.
The company constructs river valley and hydropower projects; and focuses on wind and thermal
power generation and sale, as well as operates transmission lines for distribution and consumption of
power. It also produces and sells cement, clinker, and cement products under the Jaypee Cement
name. Further, it develops golf centric real estate comprising Jaypee Greens, an integrated complex
consisting of an 18 hole Greg Norman golf course, as well as residences, commercial spaces,

corporate park, and entertainment venues; and an integrated township comprising one 18-hole and two
9-hole golf facility and residences. Additionally, the company constructs motorsports tracks and sports
facilities, and expressways; and is involved in fertilizers and chemicals, dairy, and soya and mustard
processing business; and mining of coal.
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = -7.553940807÷ 5 = -1.510788161
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 24027.04÷ 4 = 6006.76
βi= Σ(rp-rp’)(rm– rm’ ) = 11482.72007 = 1.810236222
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 6006.76 – 1.8102362*1.810236222*1585.8041
=6006.76 –5196.609
=810.149
BhartiAirtel
Was incorporated on 7th July, 1995, for promoting investments in diversified telecom service
projects. The company was formed as a 80:20 joint venture between the Bharti Group through its
subsidiary Bharti Telecom and STET International Netherlands NV, a company promoted by Telecom
Italia, Italy. Bharti is one of India's leading private sector provider of telecom services with more than
39.01 million customers in India comprising of 37 million mobile and approximately 1.9 million
broadband & telephone customers and is the first to have an all India presence. The company is
structured into three main units, Mobile Services which offers GSM Mobiles Services and Infotel
Services which provides broadband & Telephone, long distance and enterprise services which offers

carriers and corporal.. The company was first GSM Operator to have more than ten million.
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = -23.51338494÷ 5 = -4.702676987
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 891.8852÷ 4 = 222.9713
βi = Σ(rp-rp’)(rm– rm’ ) = 979.9283425 = 0.154484457
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 222.9713 – 0.154484*0.154484457*1585.8041
=222.9713 –37.84592
=185.12
BHEL
Incorporated as a government owned organization in 1950. After liberalization of Indian
economy, the government decided to divest a portion of its holding. In 1991-92, it has divested a part
of its equity shares to public and financial institutions. At present the government of India holds
67.72% in the total equity capital of the company.
BHEL is the largest engineering and manufacturing enterprise in India in the energy
related/infrastructure sector today. The company's operations are organized around three business
sectors, namely Power, Industry (includes Transmission, Transportation, Telecommunication and
Renewable Energy) and Overseas Business. This enables the organization to have a strong customer
orientation, to be sensitive to his needs and respond quickly to the changes in the market.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = -50.49087626÷ 5 = -10.0981752
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 6056.822÷ 4 = 1514.205
βi= Σ(rp-rp’)(rm– rm’ ) = 5281.696629 = 0.832652759
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 1514.205 – 0.83265275*0.8326527*1585.8041
=1514.205 –1099.455
=414.75
BPCL
Bharat Petroleum Corporation Limited engages in the refining of crude oil and marketing of petroleum
products, as well as exploration and production of hydrocarbons. The company offers liquefied
petroleum gas (LPG), naphtha, motor spirit, special boiling point spirit/hexane, benzene, toluene,
polypropylene feedstock, and regassified-LNG; aviation turbine fuel, superior kerosene oil, high speed
diesel, light diesel oil, and mineral turpentine oil; and furnace oil, low sulphur heavy stock, bitumen,
and lubricants. It serves the automotive industry; household consumers, residential complexes, and
commercial and industrial establishments; various industrial customers comprising industries from the
public and private sectors; government establishments, such as defense, railways, state transport
undertakings, and state electricity boards; and domestic and international airlines.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 69.37041458÷ 5 = 13.87408292
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 1405.184÷ 4 = 351.296
βi= Σ(rp-rp’)(rm– rm’ ) = 2781.341532 = 0.438474957
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 351.296 – 0.4384749*0.438474957*1585.8041
=351.296 –304.8872
=46.408
Cairn India
Cairn India Limited, an independent oil and gas exploration and production company, engages in
surveying, prospecting, acquiring, drilling, exploring, developing, producing, maintaining, refining,
storing, trading, supplying, transporting, marketing, distributing, importing, exporting, and dealing
minerals, oils, petroleum, gas, and related by-products in India. It holds interests in various oil and gas
blocks/fields located in Krishna-Godavari basin, the Rajasthan onshore basin, the Mumbai offshore
basin, the Palar-Pennar basin, and the Cambay offshore basin in India; Mannar basin, Sri Lanka; and
Orange Basin, South Africa. The company also operates a crude oil evacuation pipeline system. Cairn
India Limited sells its products to public and private sector refineries. The company was incorporated
in 2006 and is based in Gurgaon, India. Cairn India Limited is a subsidiary of Vedanta Resources Plc.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 15.93451654÷ 5 = 3.186903308
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 3506.075÷ 4 = 876.5187
βi= Σ(rp-rp’)(rm– rm’ ) = 4171.349546 = 0.657607953
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 876.5187 – 0.657607*0.657607953*1585.8041
= 876.5187 –685.7782
= 190.790
JINDAL STEEL
Jindal Steel and Power Limited (JSPL) is one of India's major steel producers with a significant
presence in sectors like Mining, Power Generation and Infrastructure.
With an annual turnover of over US$ 3.5 billion, JSPL is a part of the US$ 18 billion diversified O. P.
Jindal Group and is consistently tapping new opportunities by increasing production capacity,
diversifying investments, and leveraging its core capabilities to venture into new businesses. The
company has committed investments exceeding US$ 30 billion in the future and has several business
initiatives running simultaneously across continents.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 106.9599934÷ 5 = 21.39199868
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 64612.18÷ 4 = 16153.05
βi= Σ(rp-rp’)(rm– rm’ ) = 17892.36774 = 2.820709029
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 16153.05 – 2.820709*2.820709029*1585.8041
=16153.05 –12617.29
=3535.74
Cipla
Cipla Limited engages in the manufacture and sale of pharmaceutical products in India and
internationally. The company offers various prescription pharmaceutical products for various diseases;
and animal health care products, including active pharmaceutical ingredients, aqua products,
disinfectants and sanitizers, equine products, feed and feed additives, herbal products, dog treats and
chews, poultry products, products for companion animals and livestock animals, and surgical products
and equipment, as well as herbal specialities and therapeutic groups. It also provides OTC products,
such as child care, eye care, food supplements, foot and hair care, health drinks, life style products,
sweeteners, nutraceuticals and tonics, oral hygiene, pain care, probiotics/indigestion, skin care, sports
care/muscle building, and vitamins and minerals, as well as cough, cold, and flu products.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 61.99086475÷ 5 = 12.39817295
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 2285.791÷ 4 = 571.4478
βi= Σ(rp-rp’)(rm– rm’ ) = 3203.948505 = 0.505098409
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 571.4478 – 0.5050984*0.50509849*1585.8041
= 571.4478 –404.5773
= 166.87
Coal India
Coal India Limited (CIL) as an organized state owned coal mining corporate came into being in
November 1975 with the government taking over private coal mines. With a modest production of 79
Million Tonnes (MTs) at the year of its inception CIL today is the single largest coal producer in the
world. Operating through 81 mining areas CIL is an apex body with 7 wholly owned coal producing
subsidiaries and 1 mine planning and consultancy company spread over 8 provincial states of India.
CIL also fully owns a mining company in Mozambique christened as 'Coal India Africana Limitada'.
CIL also manages 200 other establishments like workshops, hospitals etc. Further, it also owns 26
technical & management training institutes and 102 Vocational Training Institutes Centres. Indian
Institute of Coal Management (IICM) as a state-of-the-art Management Training 'Centre of

Excellence' - the largest Corporate Training Institute in India - operates under CIL and conducts multi
disciplinary management development programmes.
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = -11.94403117÷ 5 = -2.388806234
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 121.4926÷ 4 = 30.37316
βi= Σ(rp-rp’)(rm– rm’ ) = 46.86986988 = 0.007388975
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 30.37316 – 0.007388*0.007388975*1585.8041
=30.37316 –0.08658
=30.28
GAIL
GAIL (India) Limited operates as a natural gas company in India and internationally. It engages in the
exploration, production, processing, transmission, distribution, and marketing of natural gas. The
company also offers liquefied petroleum gas (LPG) and other liquid hydrocarbons, and
petrochemicals. It owns approximately 9,500 kilometers of natural gas pipelines; 2 LPG pipelines
covering 2040 kilometers; 7 gas processing plants for production of LPG and other liquid
hydrocarbons; and a gas based integrated petrochemical plant for producing polymer. The company
also has participating interests in 31 oil and gas exploration and production blocks. In addition, GAIL
(India) Limited provides telecommunication services through its high speed optic-fiber network of
approximately 13,000 kilometers; and generates electric power through a joint venture. The company,
formerly known as Gas Authority of India Ltd, was founded in 1984 and is based in New Delhi, India.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 19.9945342÷ 5 = 3.99890684
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 4875.32÷ 4 = 1218.83
βi= Σ(rp-rp’)(rm– rm’ ) = 5042.931815 = 0.79501179
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 1218.83 – 0.79501179*0.79501179*1585.8041
=1218.83 –1002.298
=216.52
HUL
Hindustan Unilever Limited, a fast moving consumer goods company, primarily offers home care,
personal care, and food products in India and internationally. The company offers soaps, detergent
bars, detergent powders, detergent liquids, and scourers; and personal products, such as oral care, skin
care, and hair care products, as well as deodorants, talcum powders, color cosmetic products, and
Ayush health care and personal care products. It also offers packaged foods, such as atta, salt, rice, and
bread; ice creams and frozen desserts; culinary products comprising tomato based products, fruit based
products, and soups; and beverages, including tea and coffee. In addition, the company exports marine
and leather products, as well as offers chemicals, such as glycerin and fine chemicals; agri
commodities; Pureit in-home water purifiers; and salon services..

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 89.86708238÷ 5 = 17.97341648
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 1257.995÷ 4 = 314.4988
βi= Σ(rp-rp’)(rm– rm’ ) -470.5614974 = -0.074183422
Σ (rm – rm’)2
6343.216
Unsystematic Risk(σei
2
) = σrp
2
– βi*βi* σm
2
= 314.4988 – -0.074183422*-0.07418*1585.8041
=314.4988 –8.726966
=305.77
LARSEN
Larsen & Toubro Limited operates as a technology, engineering, construction, and manufacturing
company. The company engages in the design, engineering, and construction of hydrocarbon
upstream, mid and downstream, and construction and pipelines projects; coal and gas based power
plants; and refinery, petrochemical, fertilizers, modular process plant, and gas processing projects. It is
also involved in the construction of infrastructure, buildings and factories, power transmission and
distribution, metallurgical and material handling, and realty projects; manufacture and supply of
equipment and systems for refinery, oil and gas, fertilizer, coal gasification, aerospace, thermal power
plant, nuclear power plant, and defense industries; and provision of solutions for power projects, such
as thermal, hydropower, nuclear, plant automation, power transmission and distribution, and power
development

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 54.38304921÷ 5 = 10.87660984
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 19122.48÷ 4 = 4780.62
βi= Σ(rp-rp’)(rm– rm’ ) = 10876.86038 = 1.714723212
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 4780.62 – 1.714723212*1.714723212*1585.8041
=4780.62 –4662.701
=117.9
DLF
DLF Limited, together with its subsidiaries, engages in the business of colonization and real estate
development in India. Its activities include identification and acquisition of land; and planning,
execution, construction, and marketing of projects, such as residential, commercial, and retail
properties. It develops super luxury, luxury, and premium homes, which comprise condominiums,
duplexes, row houses, and apartments; commercial complexes in the vicinity of residential areas; and
IT parks and retail malls. The company has a land bank of 348 msf. It is also involved in the rental of
offices and retail properties; and owns and operates Aman Resorts. In addition, the company owns
wind farms, which include 150 megawatt (MW) wind power project located in Kutch, Gujarat; 11.2
MW wind power project located in Gadag, Karnataka; 33 MW wind power project located in Osisan
and Ratan Ka Baas, Rajasthan; and 34.5 MW wind power project located in Elavanthi and Panapatti,
Tamilnadu.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = -24.81723814÷ 5 = -4.963447628
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 11941.57÷ 4 = 2985.392
βi= Σ(rp-rp’)(rm– rm’ ) = 8449.041195 = 1.331980603
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 2985.392 – 1.33198060*1.3319806*1585.8041
=2985.392 –2813.49
=171.90
Reddy Labs
Dr. Reddy’s Laboratories Limited operates as an integrated pharmaceutical company. It operates in
three segments: Pharmaceutical services and Active Ingredients (PSAI), Global Generics, and
Proprietary Products. The PSAI segment develops active pharmaceutical ingredients (APIs) and
intermediaries, which are used as principal ingredients for finished pharmaceutical products. It offers a
range of APIs for use in amyotrophic lateral sclerosis, anti-inflammatory, anti-allergic, anti-asthmatic,
anticoagulant, anti-convulsant, anti-diabetic, anti-emetic, anti-fungal, anti-gout, anti-migraine, ARV
and anti-viral, benign prostate hyperlasia, cardiovascular, erectile dysfunction, expectorant,
expectorant, gastro-intestinal, genitourinary, hyperparathyroidism, immunology and inflammation,
multiple sclerosis, muscle relaxant, neuropsychiatry, oncology, ophthalmic, osteoporosis, steroid, and
urinary incontinence products.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 177.858247÷ 5 = 35.57164941
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 21169.8÷ 4 = 5292.451
βi= Σ(rp-rp’)(rm– rm’ ) = 11092.94666 = 1.748788939
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 5292.451 – 1.748788*1.748788939*1585.8041
=5292.451 –4849.806
=442.64
HERO MOTOCORP
Hero MotoCorp Limited, formerly Hero Honda Motors Limited is an India-based company engaged in
the manufacture of motorcycles. The Company is engaged in manufacturing of two wheelers and its
parts and ancillary services. The Company’s bikes are manufactured across three manufacturing
facilities. Two of these are based at Gurgaon and Dharuhera, which are located in the state of Haryana
in northern India. The third manufacturing plant is based at Haridwar, in the hill state of Uttrakhand.
The Company has 17 different products across 100 cubic centimeter (cc), 125cc, 150cc, 225cc and
scooter category. The Company offers a range of bikes which include CD Dawn, CD Deluxe,
Splendor Plus, Splendor NXG, super splendor and Passion Pro. In April 2013, Hero Motocorp Ltd
incorporated an off-shore investment subsidiary in the Netherlands. In July 2013, Hero Motocorp Ltd
announced has incorporated a wholly owned subsidiary in the United States by the name of HMCL
(NA), Inc.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 129.5342444÷ 5 = 25.90684888
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 9348.194÷ 4 = 2337.048
βi= Σ(rp-rp’)(rm– rm’ ) = 2923.721939 = 0.460921047
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 2337.048 – 0.460921*0.460921047*1585.8041
=2337.048 –336.9012
=2000.14
INFOSYS
Infosys Limited (Infosys), formerly Infosys Technologies Limited, provides business consulting,
technology, engineering and outsourcing services. Its end-to-end business solutions include consulting
and systems integration comprising consulting, enterprise solutions, systems integration and advanced
technologies; business information technology (IT) services consisting application development and
maintenance, independent validation services, infrastructure management, engineering services
comprising product engineering and life cycle solutions and business process management; products,
business platforms and solutions, including Finacle, its banking product, which offers solutions to
address core banking, mobile banking and e-banking needs of retail, corporate and universal banks
globally, and areas, such as cloud computing, enterprise mobility and sustainability.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 89.90751566÷ 5 = 17.98150313
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 6453.134÷ 4 = 1613.283
βi= Σ(rp-rp’)(rm– rm’ ) = 5993.239735 = 0.944826625
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 1613.283 – 0.9448266*0.94482665*1585.8041
=1613.283 –1415.643
=197.6
LUPIN
Lupin Limited, a pharmaceutical company, produces a range of generic and branded formulations and
active pharmaceutical ingredients. The company offers various formulations in cephalosporins,
cardiovascular, central nervous system, anti-asthma, anti-tuberculosis, diabetology, dermatology,
gastro intestinal, pediatrics, oncology, anti-biotics, anti-infectives, and NSAID therapy segments. Its
drug delivery platforms include bioadhesive/gastroretentive extended release, laser-drilled extended
release, matrix/coated extended release, taste masking technologies, and improved bioavailability
through solubilization and nano-particle technology. The company also engages in the novel drug
discovery and development programs for metabolic/endocrine diseases, pain/inflammation, auto-
immune diseases, and central nervous system disorders. The company was formerly known as Lupin

Chemicals Ltd. and changed its name to Lupin Limited in 2001 as a result of its amalgamation with
Lupin Laboratories Ltd.
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 248.2905753÷ 5 = 49.65811505
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 9842.978÷ 4 = 2460.745
βi= Σ(rp-rp’)(rm– rm’ ) = 6376.919947 = 1.005313323
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 2460.745 – 1.00531332*1.005313323*1585.80
=2460.745 –1602.701
=858.04
GRASIM
Grasim Industries Limited, together with its subsidiaries, engages in the manufacture and sale of
viscose staple fiber, chemicals, cement, and textiles in India and internationally. The company offers
viscose staple fiber, a biodegradable fiber for use in apparels, home textiles, dress material, knitted
wear, and non-woven applications; and cement products comprising grey and white cement, ready mix
concrete, and putty. Its chemical products consist of rayon grade caustic soda; stable bleaching powder
used in water purification, sanitation, and as a bleaching agent; poly aluminum chloride used in water
treatment, paper sizing, and effluent treatment; and chloro sulphonic acid used in vinyl sulphate, the
raw material for dyes and intermediates, saccharin, drugs, and pharmaceuticalsThe company was
incorporated in 1947 and is based in Nagda, India.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 37.21089568÷ 5 = 7.442179137
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 8274.164÷ 4 = 2068.541
βi= Σ(rp-rp’)(rm– rm’ ) = 6927.747438 = 1.092150577
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 2068.541 – 1.09215057*1.092150577*1585.80
=2068.541 –1891.536
=177.00
HCL Tech
HCL Technologies Limited provides a range of software services, business process outsourcing, and
infrastructure product and management services in India, the United States, Europe, and
internationally. It manages information technology infrastructure management services, such as end
user computing, data center and mainframe, integrated operations management, cross functional,
security and network, and cloud computing services. The company’s custom application services
include application development, management, support, re-engineering, modernization, migration, and
independent verification and validation. It offers end-to-end engineering services and solutions in
hardware, embedded, mechanical, and software product engineering.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 285.3023829÷ 5 = 57.06047658
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 57383.15÷ 4 = 14345.79
βi= Σ(rp-rp’)(rm– rm’ ) = 18867.33294 = 2.974411052
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 14345.79 – 2.974411052*2.974411052*1585.804
=14345.79 –14029.8
=315.98
HINDAL CO.
Hindalco Industries Limited, together with its subsidiaries, engages in the production and sale of
aluminum and copper in India and internationally. It offers various aluminum products that include
rolled products, extrusions, foils, primary aluminum ingots, billets, wire rods, and aluminum slabs;
and alumina chemicals, such as standard alumina, standard hydrate, and specialty aluminas and
hydrates for use in refractories, ceramics, fire retardant plastics, alum, and zeolite applications. The
company also provides aluminum foil and packaging solutions for the pharmaceuticals, healthcare,
dairy, confectionery, processed foods, personal products, and tobacco industries, as well as to the heat,
ventilation, and air conditioning segments. Its aluminum products are used in the architectural,
electrical, industrial, transport, defense, consumer durables, packaging, building and construction, and
general engineering sectors

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 103.2248179÷ 5 = 20.64496359
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 55792.94÷ 4 = 13948.24
βi= Σ(rp-rp’)(rm– rm’ ) = 18004.73849 = 2.838424134
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 13948.24– 2.838424134*2.83842414*1585.80
=13948.24 –12776.27
=1171.93
ITC
ITC Limited engages in fast moving consumer goods, paperboards and packaging, hotels, and agri
businesses in India and internationally. The company offers cigarettes under the Insignia, India Kings,
Lucky Strike, Classic, Gold Flake, Navy Cut, Players, Scissors, Capstan, Berkeley, Bristol, Flake, Silk
Cut, and Duke & Royal brands; Armenteros hand rolled cigars; ready to eat foods, staples,
confectionery products, and snack foods under the Aashirvaad, Sunfeast, Bingo!, Kitchens of India,
mint-o, Candyman, and Yippee! brands; personal care products under the Essenza Di Wills, Fiama Di
Wills, Vivel, Engage, and Superia brands; education and stationary products under the Classmate,
Paperkraft, and Colour Crew brands; safety matches under the Aim and i Kno brands; and agarbattis
under the Mangaldeep brand. It also engages in retailing formals, casuals, sports ware, party ware,
evening ware, designer wear, edgy denims, and accessories through Wills Lifestyle and John Players
stores.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 130.1279927÷ 5 = 26.02559854
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 2051.742÷ 4 = 512.9355
βi= Σ(rp-rp’)(rm– rm’ ) = 2958.186289 = 0.466354308
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 512.9355 – 0.466354308*0.466354308*1585.8
=512.9355 –344.8907
=168.04
MAH & MAH
Mahindra & Mahindra Limited engages in the automotive and farm equipment businesses in India and
internationally. The company offers aerospace components, assemblies, and aircrafts; automotive
services and pre-owned cars; and crop care, fresh produce services, seed distribution, and seed potato
inputs. It also provides commercial vehicles, such as Alfa, Gio, Mahindra Navistar Trucks, Bolero
Maxi Trucks, Genio, Loadking, Maxximo, and Tourister Buses; personal vehicles, including Bolero,
REVA Electric Cars, Scorpio, Thar, Verito, Xylo, Actyon, Actyon Sports, Chairman W, Korando,
Kyron, Rexton, Rodius, XUV 500, and Quanto; contract sourcing and engineering services; and
components, such as alloy steel, blankings, castings, composites, ferrites and magnetic, forgings,
gears, ring rolling, and stamping

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 171.4155909÷ 5 = 34.28311818
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 23281.93÷ 4 = 5820.483
βi= Σ(rp-rp’)(rm– rm’ ) = 12079.28524 = 1.904283962
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 5820.483 – 1.904283962*1.904283962*1585.8
=5820.483 –5750.597
=69.88
Maruti Suzuki
Maruti Suzuki India Limited manufactures, purchases, and sells motor vehicles and spare parts
primarily in India and internationally. It offers 15 brands and approximately 150 variants, primarily
including passenger cars, vans, utility vehicles, sedans, SUVs, MUVs, and life utility vehicles under
the Maruti 800 brand, Alto, Alto K10, A-star, Estilo, WagonR, Ritz, Swift, Swift DZire, SX4, Omni,
Eeco, Kizashi, Grand Vitara, Gypsy, and Ertiga brands. The company is also involved in the
facilitation of pre-owned car sales, fleet management, and car financing. It operates through a sales
network of 1,100 outlets 801 cities; and 2,958 service points in 1,408 cities in India. The company,
formerly known as Maruti Udyog Limited, was founded in 1981 and is headquartered in New Delhi,
India. Maruti Suzuki India Limited is a subsidiary of Suzuki Motor Corporation.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 59.51114174÷ 5 = 11.90222835
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 5571.108÷ 4 = 1392.777
βi= Σ(rp-rp’)(rm– rm’ ) = 5278.63365 = 0.832169884
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 1392.777 – 0.8321698*0.832169884*1585.804
=1392.777 –1098.18
=294.5
NMDC
NMDC Limited engages in the exploration, production, sale, and export of various minerals in India
and internationally. It explores for iron ore, copper, rock phosphate, lime stone, dolomite, gypsum,
bentonite, magnesite, diamond, tin, tungsten, graphite, and beach sands. The company also focuses on
coal and gold properties, as well as platinum group of elements, and bauxite. It primarily has interests
in Bailadila iron ore deposits in Dantewada, Chhattisgarh; Donimalai iron ore mines in Bellary,
Karnataka; diamond mining projects in Panna, Madhya Pradesh; sponge iron unit in Khammam,
Andhra Pradesh; and Panthal magnesite mine in Jammu. The company, formerly known as National
Mineral Development Corporation Limited, was founded in 1958 and is headquartered in Hyderabad,
India.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = -42.80351027÷ 5 = -8.560702054
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 13036.74÷ 4 = 3259.186
βi= Σ(rp-rp’)(rm– rm’ ) = 8912.838827 = 1.40509771
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 3259.186 – 1.40509771*1.40509771*1585.804
=3259.186 –3130.852
=128.33
NTPC
NTPC Limited engages in the generation, distribution, and sale of bulk power to state power utilities
in India. It generates power from coal, gas, hydro, and liquid fuel sources. The company also
undertakes consultancy and turnkey project contracts that comprise engineering, project management,
construction management, and operation and maintenance of power plants. In addition, it engages in
the oil and gas exploration, and coal mining activities. The company has approximately 39,174
megawatts of installed capacity. NTPC Limited was founded in 1975 and is based in New Delhi,
India.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = -28.01269412÷ 5 = -5.602538823
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 638.4769÷ 4 = 159.6192
βi= Σ(rp-rp’)(rm– rm’ ) = 1555.367406 = 0.245201694
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 159.6192 – 0.24520164*0.245201694*1585.8041
=159.6192 –95.34468
=64.27
ONGC
Oil and Natural Gas Corporation Limited engages in the exploration, development, production, and
refining of oil and gas in India and internationally. The company’s products include crude oil, natural
gas, liquified petroleum gas, naphtha, ethane/propane, kerosene oil, low sulphur heavy stock, high
speed diesel, motor spirit, aviation turbine fuel, liquid diesel oil, and mineral turpentine oil. It is also
involved in power generation, liquefied natural gas supply, and pipeline transportation activities; and
the provision of petrochemicals. Oil and Natural Gas Corporation was incorporated in 1993 and is
headquartered in Dehradun, India.

OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 18.22403257÷ 5 = 3.644806514
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 2103.269÷ 4 = 525.8172
βi= Σ(rp-rp’)(rm– rm’ ) = 3530.690922 = 0.556608935
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 525.8172 – 0.556608935*0.5566089*1585.804
=525.8172 –491.3035
=34.51
POWER GRID CO.
Power Grid Corporation of India Limited, a central transmission utility, engages in the transmission of
power in India. The company involves in planning, coordinating, supervising, and controlling inter-
state transmission systems; and operating unified load dispatch centers and regional load dispatch
centers. It owns and operates about 95,329 circuit kilometers (kms) of transmission lines and 156 sub-
stations with transformation capacity of about 1,38,673 MVA. The company also owns and operates a
telecom network of approximately 25,000 kms connecting approximately 206 cities in India that offers
bandwidth capacity leasing, Internet access lines, Ethernet private leased lines, multi protocol label

switching based VPN, and broadband Internet services to telecom service providers, government
agencies, and international telecom players
OpeningPrice
Rp’ = Σ Rp
N
Rp’ = 4.067291681÷ 5 = 0.813458336
σrp
2
=Σ(rp– rp’)2
N-1
σrp
2
= 327.0742÷ 4 = 81.76855
βi= Σ(rp-rp’)(rm– rm’ ) = 1220.154135 = 0.192355748
Σ (rm – rm’)2
6343.216
2
) = σrp
2
– βi*βi* σm
2
= 81.76855 – 0.19235574*0.192355748*1585.80
=81.76855 –58.67592
=23.09
2.4.5. Findings
Step1: In order to determine the cut-off point, the excess return to beta ratio is calculated for each
company and the companies are ranked in decreasing order of the ratio.

Step2: Ci value is calculated for each is calculated using the formula:
Ci = σm2 ∑{(Ri – Rf)βi/ σei2)}
1 + σm2 ∑(βi2/σei2)

Step 3: The Ci values go on increasing upto a point and then starts decreasing. The largest value of Ci
after ehich the values decrease is taken as the cut off (C*) which comes out to be 33.66. All the
companies above the cut off are included in the portfolio. The following are those Companies:
S. No. Company Ci
1 Lupin 27.33
2 Hero Motor Corp 28.03
3 ITC 32.77
4 Asian Paints 33.63
5 Bajaj Auto 33.66
Step 4: Calculation of Zi
Zi = (βi/σei2) x {(Ri – Rf)/βi – C*}
S. No. Company Zi
1 Lupin 0.97248

3 ITC 1.697849
5 Bajaj Auto 0.01271
Total Zi = 3.09727Ʃ
Step 5: Calculation of Xi
Xi = Zi
ZiƩ
S. No. Company Xi
1 Lupin 0.31398
3 ITC 0.54818
5 Bajaj Auto 0.0041
Total Xi = 1Ʃ
Step 6: Return of portfolio
R = WƩ i * Rp
S. No. Company Wi Rp
1 Lupin 31.398% 49.65
2 Hero Motor Corp 4.707% 25.90
3 ITC 54.818% 26.02
4 Asian Paints 8.667% 41.92
5 Bajaj Auto 0.41% 56.86
Total Wi = 100%Ʃ Return = 34.93%
Part-C

3.Risk Return Analysis
3.1 MEASURING & EVALUATING MUTUAL FUNDS PERFORMANCE:
3.1.1 PURPOSE OF MEASURING AND EVALUATING
Every investor investing in the mutual funds is driven by the motto of either wealth creation or
wealth increment or both. Therefore it’s very necessary to continuously evaluate the funds’
performance with the help of factsheets and newsletters, websites, newspapers and professional
advisors like SBI AMC. If the investors ignore the evaluation of funds’ performance then he can
lose hold of it any time. In this ever-changing industry, he can face any of the following problems:
1. Variation in the funds’ performance due to change in its management/ objective.
2. The funds’ performance can slip in comparison to similar funds.
3. There may be an increase in the various costs associated with the fund.
4. Beta, a technical measure of the risk associated may also surge.
5. The funds ratings may go down in the various lists published by independent rating agencies.
6. It can merge into another fund or could be acquired by another fund house.
Performance measures:
Equity funds: the performance of equity funds can be measured on the basis of: NAV Growth,
Total Return; Total Return with Reinvestment at NAV, Annualized Returns and Distributions,
Computing Total Return (Per Share Income and Expenses, Per Share Capital Changes, Ratios,
Shares Outstanding), the Expense Ratio, Portfolio Turnover Rate, Fund Size, Transaction Costs,
Cash Flow, Leverage.
Debt fund: Likewise, the performance of debt funds can be measured on the basis of: Peer Group
Comparisons, The Income Ratio, Industry Exposures and Concentrations, NPAs, besides NAV

Growth, Total Return and Expense Ratio.
Liquid funds: the performance of the highly volatile liquid funds can be measured on the basis
of: Fund Yield, besides NAV Growth, Total Return and Expense Ratio.
Concept of benchmarking for performance evaluation:
Every fund sets its benchmark according to its investment objective. The funds performance is
measured in comparison with the benchmark. If the fund generates a greater return than the
benchmark then it is said that the fund has outperformed benchmark , if it is equal to
benchmark then the correlation between them is exactly 1. and if in case the return is lower than
the benchmark then the fund is said to be underperformed.
Some of the benchmarks are:
1. Equity funds: market indices such as S&P CNX nifty, BSE100, BSE200, BSE-PSU, BSE 500
index, BSE bankex, and other sectoral indices.
2. Debt funds: Interest Rates on Alternative Investments as Benchmarks, I-Bex Total Return Index,
JPM T-Bill Index Post-Tax Returns on Bank Deposits versus Debt Funds.
3.Liquid funds: Short Term Government Instruments’ Interest Rates as Benchmarks, JPM TBill
Index.
To measure the fund’s performance, the comparisons are usually done with:
i) with a market index.
ii) Funds from the same peer group.
iii) Other similar products in which investors invest their funds.
3.1.2 WHY HAS IT BECOME ONE OF THE LARGEST FINANCIAL
INSTRUMENTS?
If we take a look at the recent scenario in the Indian financial market then we can find the market
flooded with a variety of investment options which includes mutual funds, equities, fixed income
bonds, corporate debentures, company fixed deposits, bank deposits, PPF, life insurance, gold, real
estate etc. all these investment options could be judged on the basis of various parameters such as-
return, safety convenience, volatility and liquidity. Measuring these investment options on the basis
of the mentioned parameters, we get this in a tabular form.

Return Safety Volatility Liquidity Convenience
Equity
Bonds
Co. Debentures
Co. FDs
Bank Deposits
High Low High High Moderate
Moderate High Moderate Moderate High
Moderate Moderate Moderate Low Low
Moderate Low Low Low Moderate
Low High Low High High
PPF
Life Insurance
Gold
Real Estate
Mutual Funds
Moderate High Low Moderate High
Low High Low Low Moderate
Moderate High Moderate Moderate Gold
High Moderate High Low Low
High High Moderate High High
We can very well see that mutual funds outperform every other investment option. On three
parameters, it scores high whereas it’s moderate at one. comparing it with the other options, we
find that equities gives us high returns with high liquidity but its volatility too is high with low safety
which doesn’t makes it favorite among persons who have low risk- appetite. Even the

convenience involved with investing in equities is just moderate.
Now looking at bank deposits, it scores better than equities at all fronts but lags badly in the
parameter of utmost important ie; it scores low on return , so it’s not an happening option for person
who can afford to take risks for higher return. The other option offering high return is real estate but
that even comes with high volatility and moderate safety level, even the liquidity and convenience
involved are too low. Gold have always been a favorite among Indians but when we look at it as an
investment option then it definitely doesn’t gives a very bright picture. Although it ensures high
safety but the returns generated and liquidity are moderate. Similarly, the other investment options
are not at par with mutual funds and serve the needs of only a specific customer group.
Straightforward, we can say that mutual fund emerges as a clear winner among all the options
available.
The reasons for this being:
I) Mutual funds combine the advantage of each of the investment products: mutual fund is one
such option which can invest in all other investment options. Its principle of diversification allows
the investors to taste all the fruits in one plate. just by investing in it, the investor can enjoy the
best investment option as per the investment objective.
II) Dispense the shortcomings of the other options: every other investment option has more or
less some shortcomings. Such as if some are good at return then they are not safe, if some are safe then
either they have low liquidity or low safety or both….likewise, there exists no single option which can
fit to the need of everybody. But mutual funds have definitely sorted out this problem. Now everybody
can choose their fund according to their investment objectives.
III) Returns get adjusted for the market movements: as the mutual funds are managed by experts
so they are ready to switch to the profitable option along with the market movement. Suppose they
predict that market is going to fall then they can sell some of their shares and book profit and can
reinvest the amount again in money market instruments.
IV) Flexibility of invested amount: Other then the above mentioned reasons, there exists one
more reason which has established mutual funds as one of the largest financial intermediary and that
is the flexibility that mutual funds offer regarding the investment amount. One can start investing
in mutual funds with amount as low as Rs. 500 through SIPs and even Rs. 100 in some cases.
Not all award-winning funds may be suitable for everyone

Many investors feel that a simple way to invest in Mutual funds is to just keep investing in award
winning funds. First of all, it is important to understand that more than the
awards; it is the methodology to choose winners at is more relevant.
A rating firm generally elaborates on the criteria for deciding the winner’s that is consistent
performance, risk adjusted returns, total returns and protection of capital. Each of these factors is
very important and has its significance for different categories of funds.
Besides, each of these factors has varying degree of significance for different kinds of investors.
For example, consistent return re ally focuses on risk. If someone is afraid of negative returns,
consistency will be a more import ant measure than tot al ret urn i.e. Growth in NAV as well as
dividend received.
A fund can have very impressive total ret urns overtime, but can be very volatile and tough for a
risk adverse investor. Therefore, all the ward winning funds in different categories may not be
suitable for everyone. Typically, when one has to select funds, the first step should be to consider
personal goals and objectives. Invest ors need to decide which element they value the most and the n
prioritize the other criteria
Once one knows what one is looking for, one should go about selecting the funds according to the
asset allocation. Most investors need just a few funds, carefully picked, watched and managed over
period of time.
3.1.3 EVALUATING PORTFOLIO PERFORMANCE
It is important to evaluate the performance of the portfolio on an on-going basis. The following
factors are important in this process:
Consider long-term record of accomplishment rather than short -term performance. It is important
because long-term track record moderates the effects which unusually good or bad short -term
performance can have on a fund's track record. Besides, longer-term track record compensates for the

effects of a fund manager's particular investment style.
Evaluate the record of accomplishment against similar funds. Success in managing a small or in a
fund focusing on a particular segment of the market cannot be re lied upon as an evidence of
anticipated performance in managing a large or a broad based fund.
Discipline in investment approach is an important factor as the pressure to perform can make a fund
manager susceptible to have a n urge to change tracks in terms of stock selection as well a s
investment strategy.
The objective should be to differentiate investment skill of the fund manager from luck and to
identify those funds with the greatest potential of future success.
3.1.4 HOW TO REDUCE RISK WHILE INVESTING:
Any kind of investment we make is subject to risk. In fact we get return on our investment purely and
solely because at the very beginning we take the risk of parting with our funds, for getting higher value
back at a later date. Partition it self is a risk. Well known economist and Nobel Prize recipient William
Sharpe tried to segregate the total risk faced in any kind of investment into two parts
systematic(Systemic) risk and unsystematic (Unsystematic) risk.
Systematic risk is that risk which exists in the system. Some of the biggest examples of systematic risk
are inflation, recession, war, political situation etc.
Inflation erodes returns generated from all investments e .g. If return from fixed deposit is 8 percent
and if inflation is 6 per cent then real rate of return from fixed deposit is reduced by 6 percent.
Similarly if returns generated from equity market is 18 percent and inflation is still 6 per cent then
equity returns will be lesser by the rate of inflation. Since inflation exists in the system there is no way
one can stay away from the risk of inflation.
Economic cycles, war and political situations have effects on all forms of investments. Also these exist
in the system and there is no way to stay away from them. It is like learning to walk. Anyone who
wants to learn to walk has to first fall; you cannot learn to walk without falling. Similarly, anyone who
wants to invest has to first face systematic risk. Therefore, one can never make any kind of investment
without systematic risk.
Another form of risk is unsystematic risk. This risk does not exist in the system and hence is not
applicable to all forms of investment.

Unsystematic risk is associated with particular form of investment. Suppose we invest in stock market
and the market falls, then only our investment in equity gets affected OR if we have placed a fixed
deposit in particular bank and bank goes bankrupt, than we only lose money placed in that bank.
While there is no way to keep away from risk, we can always reduce the impact of risk.
Diversification helps in reducing the impact of unsystematic risk. If our investment is distributed
across various asset classes, the impact of unsystematic risk is reduced.
If we have placed fixed deposit in several banks, then even if one of the banks goes bankrupt our entire
fixed de posit investment is not lost. Similarly if our equity investment is in Tata Motors, HLL,
Infosys, adverse news about Infosys will only impact investment in Infosys, all other stocks will not
have any impact. To reduce the impact of systematic risk, we should invest regularly. By investing
regularly, we average out the impact of risk. Mutual fund, as an investment vehicle gives us benefit of
both diversification and averaging. Portfolio of mutual funds consists of multiple securities and hence
adverse news about single security will have nominal impact on overall portfolio.
By systematically investing in mutual fund, we get benefit of rupee cost averaging. Mutual fund as an
investment vehicle helps reduce, both, systematic as well a s unsystematic risk
3.1.5. STUDY OF PORTFOLIO ANALYSIS FROM THE POINT OF FUND
MANAGER:
Effective use of portfolio management disciplines improves customer satisfaction, reduces the
number of risks problems, and increases success. The goal of portfolio analysis is to realize these
same benefits at the portfolio level by applying a consistent structured management approach.
The considerations underlying the portfolio analysis is a matter of concern to the fund managers,
investors, and researchers alike. This study attempts to answer two questions relating to the
portfolio analysis:

 Make an average (or fair) return for the level of risk in the portfolio
 To find out the portfolio which best meets the purpose of the investor.
At a minimum, any comprehensive mutual fund selection and analysis approach should include
the following generalized processes:
 Fund selection
 Fund prioritize/ reprioritize
 Selection of the acceptable and required fund
 Fund analysing and monitoring
 Corrective action management
The fund portfolio analysis gives the ability to select funds that are aligned with the investor’s
strategies and objectives. It helps the fund manager to make the best use of available opportunities
by applying to the highest priority of the investor. A fund manager can regularly assess how
securities and stocks are contributing to portfolio health and can make the corrective action to keep
the portfolio in compliance with the investor’s interest and objectives.
Mutual funds do not determine risk preference. However, once investor determines his/her return
preferences, he/she can choose a mutual fund a large and growing variety of alternative funds
designed to meet almost any investment goal. Studies have showed that the funds generally were
consistent in meeting investors stated goals for investment strategies, risk, and return. The major
benefit of the mutual fund is to diversify the portfolio to eliminate unsystematic risk. The instant
diversification of the funds is especially beneficial to the small investors who do not have the
resources to acquire 100 shares of 12 or 15 different issues required to reduce unsystematic risk.
Mutual funds have generally maintained the stability of their correlation with the market because
of reasonably well diversified portfolios. There are some measures for the analysis and each of
them provides unique perspectives. These measures evaluate the different components of
performance.
3.1.6 MEASURES OF RISK AND RETURN:
Risk is variability in future cash flows. It is also known as uncertainty in the distribution of

possible outcomes. A risky situation is one, which has some probability of loss or unexpected results.
The higher the probability of loss or unexpected results is, the greater the risk.
Portfolio risk management includes processes that identify, analyse, respond to, track, and control
any risk that would prevent the portfolio from achieving its business objectives. These processes
should include reviews of project level risks with negative implications for the portfolio, ensuring
that the project manager has a responsible risk mitigation plan.
Additionally, it is important to do a consolidated risk assessment for the portfolio overall to
determine whether it is within the already specified limits. Since portfolio and their environments are
dynamic, managers should review and update their portfolio risk management plans on a regular
basis through the fund life cycle.
Simple measure of returns:
The return on mutual fund investment includes both income (in the form of dividends or investment
payments) and capital gains or losses (increase or decrease in the value of a security). The return is
calculated by taking the change in a fund’s Net Asset Value, which is the market value of securities
the fund holds divided by the number of the fund’s shares during a given time period, assuming the
reinvestment all income and capital gains distributions, and dividing it by the original net asset value.
The return is calculated net of management fees and other expenses charged to the fund. Thus, a
fund’s monthly return can be expressed as follows:
Rt= (NAVt- NAVt-1)/NAVt-1
Where,
Rt is the return in month t
NAVt is the closing net asset value of the fund on the last trading day of the month
NAVt-1 is the closing net asset value of the fund on the last day of the previous month
Measure of risk
Investors are interested not only in fund’s return but also in risk taken to achieve those returns.
So risk can be thought as the uncertainty of the expected return, and uncertainty is generally
equated with variability. Variability and the risk are correlated; hence high returns will tend to high

variability.
 Standard deviation:
in simple terms standard deviation is one of the commonly used statistical parameter to measure
risk, which determines the volatility of a fund. Deviation is defined as any variation from a mean
value (upward & downward). Since the markets are volatile, the returns fluctuate every day. High
standard deviation of a fund implies high volatility and a low standard deviation implies low
volatility.
S.D. =√1/T× (Rt-AR) ²
Where,
S.D. is the periodic standard deviation,
AR is the average periodic return,
T is the number of observations in the period for which the standard deviation is being
calculated.
Rt is the return in month t
 Beta analysis: Beta Co-efficient:
Systematic risk is measured in terms of Beta, which represents fluctuations in the NAV of the fund
vis-à-vis market. The more responsive the NAV of a Mutual Fund is to the changes in the market;
higher will be its beta. Beta is calculated by relating the returns on a Mutual Fund with the returns in
the market. While unsystematic risk can be diversified through investments in a number of
instruments, systematic risk cannot. By using the risk return relationship, we try to assess the
competitive strength of the Mutual Funds vis-à-vis one another in a better way.
(Beta) is calculated as = [N (XY) – XY]/ [N (X2
) – (X) 2
]
Beta is used to measure the risk. It basically indicates the level of volatility associated with the
fund as compared to the market. In case of funds, as compared to the market. In case of funds,
beta would indicate the volatility against the benchmark index. It is used as a short term decision

making tool. A beta that is greater than 1 means that the fund is more volatile than the benchmark
index, while a beta of less than 1 means that the fund is more volatile than the benchmark index.
A fund with a beta very close to 1 means the fund’s performance closely matches the index or
benchmark.
The success of beta is heavily dependent on the correlation between a fund and its benchmark. Thus,
if the fund’s portfolio doesn’t have a relevant benchmark index then a beta would be grossly
inappropriate. For example if we are considering a banking fund, we should look at the beta against a
bank index.
 R-Squared (R2):
R squared is the square of ‘R’ (i.e.; coefficient of correlation). It describes the level of
association between the fun’s market volatility and market risk. The value of R- squared ranges
from0 to1. A high R- squared (more than 0.80) indicates that beta can be used as a reliable
measure to analyze the performance of a fund. Beta should be ignored when the r- squared is low
as it indicates that the fund performance is affected by factors other than the markets.
For example:
Case 1 Case 2
R2 0.65 0.88
B 1.2 0.9
In the above tableR2 is less than 0.80 in case 1, implies that it would be wrong to mention that
the fund is aggressive on account of high beta. In case 2, the r- squared is more than 0.85 and beta
value is 0.9. it means that this fund is less aggressive than the market.
 Portfolio turnover ratio:
Portfolio turnover is a measure of a fund's trading activity and is calculated by dividing the lesser
of purchases or sales (excluding securities with maturities of less than one year) by the average

monthly net assets of the fund. Turnover is simply a measure of the percentage of portfolio value
that has been transacted, not an indication of the percentage of a fund's holdings that have been
changed. Portfolio turnover is the purchase and sale of securities in a fund's portfolio. A ratio of
100%, then, means the fund has bought and sold all its positions within the last year. Turnover is
important when investing in any mutual fund, since the amount of turnover affects the fees and
costs within the mutual fund.
 Total expenses ratio:
A measure of the total costs associated with managing and operating an investment fund such as a
mutual fund. These costs consist primarily of management fees and additional expenses such as
trading fees, legal fees, auditor fees and other operational expenses. The total cost of thefund is
divided by the fund's total assets to arrive at a percentage
amount, which represents the TER:
Total expense ratio = (Total fund Costs/ Total fund Assets)
The most important and widely used measures of performance are:
 The Sharpe Measure
 The Treynor’ Measure
 Jenson Model
 Fama Model
 The Sharpe Measure :- In this model, performance of a fund is evaluated on the basis of
Sharpe Ratio, which is a ratio of returns generated by the fund over and above risk free rate of
return and the total risk associated with it.
According to Sharpe, it is the total risk of the fund that the investors are concerned about. So, the
model evaluates funds on the basis of reward per unit of total risk. Symbolically, it can be written as:
Sharpe Ratio (Si) = (Ri - Rf)/Si
Where,

Si is standard deviation of the fund,
Ri represents return on fund, and
Rf is risk free rate of return.
While a high and positive Sharpe Ratio shows a superior risk-adjusted performance of a fund, a low
and negative Sharpe Ratio is an indication of unfavourable performance.
 The Treynor Measure :- Developed by Jack Treynor, this performance measure evaluates
funds on the basis of Treynor's Index.
This Index is a ratio of return generated by the fund over and above risk free rate of return
(generally taken to be the return on securities backed by the government, as there is no credit risk
associated), during a given period and systematic risk associated with it (beta). Symbolically, it can
be represented as:
Treynor's Index (Ti) = (Ri - Rf)/Bi.
Where,
Ri represents return on fund,
Rf is risk free rate of return, and
Bi is beta of the fund.
All risk-averse investors would like to maximize this value. While a high and positive Treynor's
Index shows a superior risk-adjusted performance of a fund, a low and negative Treynor's Index is
an indication of unfavorable performance.
Comparison of Sharpe and Treynor
Sharpe and Treynor measures are similar in a way, since they both divide the risk premium by a
numerical risk measure. The total risk is appropriate when we are evaluating the risk return
relationship for well-diversified portfolios. On the other hand, the systematic risk is the relevant
measure of risk when we are evaluating less than fully diversified portfolios or individual stocks.
For a well-diversified portfolio the total risk is equal to systematic risk. Rankings based on total

risk (Sharpe measure) and systematic risk (Treynor measure) should be identical for a well-
diversified portfolio, as the total risk is reduced to systematic risk. Therefore, a poorly diversified
fund that ranks higher on Treynor measure, compared with another fund that is highly diversified,
will rank lower on Sharpe Measure.
 Jenson Model :- Jenson's model proposes another risk adjusted performance measure. This
measure was developed by Michael Jenson and is sometimes referred to as the differential Return
Method. This measure involves evaluation of the returns that the fund has generated vs. the
returns actually expected out of the fund1 given the level of its systematic risk. The surplus between
the two returns is called Alpha, which measures the performance of a fund compared with the actual
returns over the period. Required return of a fund at a given level of risk (Bi) can be calculated as:
E(Ri) = Rf + Bi (Rm - Rf)
Where,
E(Ri) represents expected return on fund, and
Rm is average market return during the given period,
Rf is risk free rate of return, and
Bi is Beta deviation of the fund.
After calculating it, Alpha can be obtained by subtracting required return from the actual return of
the fund.
αp= Ri –[ Rf + Bi (Rm - Rf) ]
Higher alpha represents superior performance of the fund and vice versa. Limitation of this model
is that it considers only systematic risk not the entire risk associated with the fund and an ordinary
investor cannot mitigate unsystematic risk, as his knowledge of market is primitive.
 Fama Model:-The Eugene Fama model is an extension of Jenson model. This model
compares the performance, measured in terms of returns, of a fund with the required return
commensurate with the total risk associated with it. The difference between these two is taken as a

measure of the performance of the fund and is called Net Selectivity.
The Net Selectivity represents the stock selection skill of the fund manager, as it is the excess returns
over and above the return required to compensate for the total risk taken by the fund manager.
Higher value of which indicates that fund manager has earned returns well above the return
commensurate with the level of risk taken by him.
Selectivity: measures the ability of the portfolio manager to earn a return that is consistent with
the portfolio’s market (systematic) risk. The selectivity measure is:
Ri –[ Rf + Bi (Rm - Rf) ]
Diversification: measures the extent to which the portfolio may not have been completely
diversified. Diversification is measured as:
[Rf +(Rm - Rf)(αi/ αm)]-[Rf + Bi (Rm - Rf)]
If the portfolio is completely diversified, contains no unsystematic risk, then diversification
measure would be zero. A positive diversification measure indicates that the portfolio is not
completely diversified; it would contain unsystematic risk and it represents the extra return that
the portfolio should earn for not being completely diversified. The performance of the portfolio
can be measured as:
Net selectivity = selectivity - diversification
Net selectivity measures, how well the portfolio managers performed at earning a fair return for
the portfolio’ systematic risk and diversifying away the unsystematic risk. Positive net selectivity
indicates that the fund earned a better return.
The comparison, done based on sharpe ratio, Treynor measure, Jensen alpha, and Fema measure
notifies that the portfolio performance can be evaluated on the following basis:
 Sahrpe ratio: measures the reward to total risk trade off
 Treynor: measures the reward to systematic risk trade off

 Jensen’s alpha: measures the average return over and above that predicted.
 Fema measure: measures return of portfolio for its systematic risk and diversifying away
unsystematic risk.
Among the above performance measures, two models namely, Treynor measure and Jenson model
use Systematic risk is based on the premise that the Unsystematic risk is diversifiable. These models
are suitable for large investors like institutional investors with high risk taking capacities as they do
not face paucity of funds and can invest in a number of options to dilute some risks. For them, a
portfolio can be spread across a number of stocks and sectors. However, Sharpe measure and
Fama model that consider the entire risk associated with fund are suitable for small investors, as the
ordinary investor lacks the necessary skill and resources to diversify. Moreover, the selection of the
fund on the basis of superior stock selection ability of the fund manager will also help in
safeguarding the money invested to a great extent
3.2. RESEARCH METHODOLOGY
3.2.1. NEED FOR THE STUDY
The Mutual Fund Companies periodically build up a study, which can prioritize and analyse the
portfolio of the mutual funds. This study is helpful in having a comparison among the mutual
funds based on the risk bearing capacity and expected return of the investor and will also carry out
an analysis of the portfolio of the selected mutual fund.
The mutual fund industry is growing globally and new products are emerging in the market with
all captivating promises of providing high return. It has become difficult for the investors to choose
the best fund for their needs or in other words to find out a fund which will give maximum return
for minimum risk. Therefore, they turn to their financial adviser to get precise direct investment.
Hence, the company asked me to prepare a model, which will facilitate them to analyse the fund
and to have reasonable estimation for the fund performance.
The driving force of Mutual Funds is the ‘safety of the principal’ guaranteed, plus the added
advantage of capital appreciation together with the income earned in the form of interest or
dividend. The various schemes of Mutual Funds provide the investor with a wide range of
investment options according to his risk bearing capacities and interest besides; they also give handy
return to the investor. Mutual Funds offers an investor to invest even a small amount of money,

each Mutual Fund has a defined investment objective and strategy. Mutual Funds schemes are
managed by respective asset managed companies, sponsored by financial institutions, banks, private
companies or international firms. A Mutual Fund is the ideal investment vehicle for today’s
complex and modern financial scenario.
The study is basically made to analyze the various open-ended equity schemes of SBI Asset
Management Company to highlight the diversity of investment that Mutual Fund offer. Thus,
through the study one would understand how a common person could fruitfully convert a meagre
amount into great penny by wisely investing into the right scheme according to his risk taking
abilities.
Sharpe ratio is a performance measure, which reflects the excess return earned on a portfolio per
unit of its total risk (standard deviation). Treynor measure indicates the risk premium return per
unit risk of the portfolio. While Jensen alpha talks about the deviation of the actual return from its
expected one. Fema measure decomposes the portfolio total return into two main components:
systematic return and the unsystematic return. It determines whether the portfolio is perfectly
diversified or not. Hence, it is a significant measure to evaluate the performance of the fund
manager.
The analysis of the fund portfolio has been done to find out the influence of the top holdings on the
performance of the fund. All these measures give fair implication and results about the portfolio
performance and can show the ground reality to a rational investor.

3.2.2 OBJECTIVE OF THE STUDY
 Whether the growth oriented Mutual Fund are earning higher returns than the benchmark returns
(or market Portfolio/Index returns) in terms of risk.
 Whether the growth oriented mutual funds are offering the advantages of Diversification, Market
timing and Selectivity of Securities to their investors
 This study provides a proper investigation for logical and reasonable comparison and selection of
the funds.
 It also assists in analysing the portfolio of the selected funds.
3.2.3 LIMITATIONS OF THE STUDY
 The study is limited only to the analysis of different schemes and its suitability to different
investors according to their risk-taking ability.
 The study is based on secondary data available from monthly fact sheets, websites and other
books, as primary data was not accessible.
 The study is limited by the detailed study of six schemes of SBI.
 Many investors are all price takers.

 The assumption that all investors have the same information and beliefs about the distribution
of returns.
 Banks are free to accept deposits at any interest rate within the ceilings fixed by the Reserve
Bank of India and interest rate can vary from client to client. Hence, there can be inaccuracy in
the risk free rates.
 The study excludes the entry and the exit loads of the mutual funds.
3.2.4 DATA COLLECTION
The Methodology involves the selected Open-Ended equity schemes of SBI mutual fund for the
purpose of risk return and comparative analysis the competitive funds. The data collected for this
project is basically from secondary sources, they are;
The monthly fact sheets of SBI AMC fund house and research reports from banks.
The NAVs of the funds have been taken from AMFI websites for the period starting from 30st may
2013 to 30st june, 2013.
For the Benchmark prices, data has been taken from BSE and NSE sites.
3.3. CASE ANALYSIS
3.3.1 DATA INTERPRETATION
Risk returns analysis and comparative study of funds
In this section, a sample of SBI equity related funds have been studied, evaluated and analysed.
This study could facilitate to get a fair comparison.
The expectations of the study are to give value to the funds by keeping the risk in the view. Here
equity funds are taken as they bear high return with high risk.

Following are the products of SBI Mutual Fund, which have been taken the evaluation purpose.
1) SBI equity fund
2) SBI Capital Builder
3) SBI Growth Fund
4) SBI Long Term Advantage Fund
5) SBI Tax Saver Fund
6) SBI Top 200 Fund
 SBI equity fund
Investment Objective:-The investment objective of the Scheme is to achieve capital appreciation.
Basic Scheme Information
Table:3.1
Nature of Scheme Open Ended Growth Scheme
Inception Date Jan 01, 1995
Option/Plan Dividend Option, Growth Option,
Entry Load
(purchase / additional purchase / switch-
in)
NIL
(With effect from August 1, 2009)
Exit Load.
(as a % of the Applicable NAV)
Nil
Minimum Application Amount Rs.5000 and in multiples of Rs.100
thereof to open an account / folio.
Additional purchases is Rs. 1000 and in
multiples of Rs. 100 thereof
Lock-In-Period Nil
Net Asset Value Periodicity Every Business Day
Redemption Proceeds Normally despatched within 3 Business
days
Investment Pattern

The asset allocation under the Scheme will be as follows:
Table:3.2
SR NO. TYPE OF INSTRUMENTS NORMAL ALLOCATION
(%of net asset)
RISK
PROFILE
1 Equities & Equities related
Instruments
80-100 Medium to
high
2 Debt securities, money market
instruments & cash
0-100 Low to
medium
Investment in Securitised debt, if undertaken, would not exceed 20% of the net assets of the
scheme. The Scheme may also invest upto 25% of net assets of the Scheme in derivatives such as
Futures & Options and such other derivative instruments as may be introduced from time to time
for the purpose of hedging and portfolio balancing and other uses as may be permitted under the
Regulations.
Investment Strategy & Risk Control
In order to provide long term capital appreciation, the Scheme will invest predominantly in growth
companies. Companies selected under this portfolio would as far as practicable consist of medium to
large sized companies which: are likely achieved above average growth than the industry; enjoy
distinct competitive advantages, and have superior financial strengths.
The aim will be to build a portfolio, which represents a cross-section of the strong growth
companies in the prevailing market. In order to reduce the risk of volatility, the Scheme will
diversify across major industries and economic sectors.
Benchmark Index : S&P CNX 500. SBI Equity, which is benchmarked to S&P CNX 500 Index is
not sponsored, endorsed, sold or promoted by Indian Index Service & Products Limited (IISL).
SBI EQUITY FUND-GROWTH OPTION
Table:3.3
NAV S&P
CNX
500
Ri Rm Ri Rm Rm-Rm
av
sqr(Rm-
Rm av)
Rm2

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