TERM PAPER: Portfolio Management
BY
Vishalakshi Verma F 82
Sharpe’s Optimum Portfolio
Systematic risk
Unsystematic risk
•The sharpe’s single-index
model (SIM) is a simple asset
pricing model commonly
used in the finance industry
to measure risk and return
of a stock.
•It sometimes called as
market risk, aggregate
risk, or undiversifiable risk, is
the risk associated
with aggregate market
returns.
•sometimes called
specific risk,
idiosyncratic risk,
residual risk, or
diversifiable risk, is
the company-specific
or industry-specific
risk in a portfolio,
which is uncorrelated
with aggregate
market returns
Capital asset pricing model (William
Sharpe (1961, 1964) and John Lintner
(1965)):
•Model is used to determine a theoretically
appropriate required rate of return of an
asset, if that asset is to be added to an
already well-diversified portfolio, given
that asset has non-diversifiable risk. The
model takes into account the asset's
sensitivity to non-diversifiable risk (also
known as systematic risk or market risk),
often represented by the quantity beta (β)
in the financial industry, as well as the
expected return of the market and the
expected return of a theoretical risk-free
asset.
What are the
assumptions in CAPM?
•No transaction cost.
•No tax
•Borrowing and lending
at risk free rate
•Buying and selling
security at competitive
rate
•Homogenous volatility
•Investors chooses
efficient portfolio
Efficient frontier:
The efficient frontier is a concept in modern
portfolio theory introduced by Harry
Markowitz and others. A combination of
assets, i.e. a portfolio, is referred to as
"efficient" if it has the best possible expected
level of return for its level of risk.
Here, every possible combination of risky
assets, without including any holdings of the
risk-free asset, can be plotted in riskexpected return space, and the collection of
all such possible portfolios defines a region
in this space.
The upward-sloped part of the left boundary
of this region, a hyperbola, is then called the
"efficient frontier".
The efficient frontier is the positively sloped
portion of the opportunity set that offers the
highest expected return for a given level of
risk. The efficient frontier lies at the top of
the opportunity set or the feasible set
Portfolio is consider efficient if
 Fully diversified, only systematic risk
 Because supply of security must equal demand
for securities, CAPM implies that market
portfolio is an efficient portfolio.
Under CAPM, CML is the line through risk
free security and market portfolio
A stock picking rule of thumb is to buy assets whose
Sharpe ratio is above the CML and sell those whose
Sharpe ratio is below. Indeed, from the efficient
market hypothesis it follows that we cannot beat the
market. Therefore, all portfolios should have a Sharpe
ratio less than or equal than the market's. In
consequence, if there is a portfolio (or asset) whose
Sharpe ratio is bigger than the market's then this
portfolio (or asset) gives more return for unity of risk
(i.e. the volatility σ), which contradicts the efficient
market hypothesis
What is CML and CML under CAPM?
CML is the set of portfolios with the
highest possible return for any level of
volatility.




To Study various companies from different
sectors listed in NSE
To find out the company which gives maximum
return with minimum risk
To study the volatility of companies in
comparison with the market.
To construct a portfolio and analyze the risk and
return, to meet the requirements of the investor
1. Beta Coefficient
Beta coefficient is the relative measure of
non diversifiable risk. It is an index of the
degree of movement of an asset’s return in
response to a change in the market’s return.
2. RETURN
The total gain or loss experienced on an
investment over a given period of time,
calculated by dividing the asset’s cash
distributions during the period, plus change
in value, by its beginning-of-period
investment value is termed as return.
3. Efficient Portfolio
A portfolio that maximizes return for a given
level of risk or minimizes risk for a given level
of return is termed as an efficient portfolio.
4. Correlation
A statistical measure of the relationship
between any two series of numbers
representing data of any kind is known as
correlation.
5. Risk-free Rate of Return (RF)
Risk-free rate of return is the required return
on a risk free asset, typically a three month
treasury bill.
•
•
Totally 15 securities of the companies
selected which comprised in National Stock
Exchange (NSE)
The return provided of which had been
tracked continually for the period from
August 2006 to August 2009
Pharmaceutical
BFSI
Infrastructure
FMCG
Oil & Gas
Ranbaxy
Axis
L&T
Cadbury
BPCL
Torent pharma
ICICI
Hindustan
ITC
HPCL
Dishman
HDFC
Reliance
P&G
IOCL
Cut off Points
Stock
Ranbaxy
Selection of stocks among 15 companie
C
3.00E-04
HDFC
0.0052
Reliance
0.0083
L&T
0.011
Axis
0.04
ICICI
0.044
BPCL
0.042
Hindustan
0.037
Torent pharma
0.035
HPCL
0.031
IOCL
0.027
Dishman
0.024
Cadbury
0.024
ITC
2.31E-02
P&G
2.30E-02
Stocks
Cutoff Points
Ranbaxy
0.00032
HDFC
0.0052
Reliance
0.0083
L&T
0.011
Axis
0.034
Proportion of Investment in selected stocks
Stock
Ranbaxy
HDFC
Reliance
L&T
Axis
Proportion of
Investment
31.19
29.33
21.6
10.95
6.93
100
The performance of all the five sectors namely pharmaceuticals, banking, oil & gas, Construction and
FMCG are calculated and in each sector one or two companies performing better than the market
Individual return of each stock is more than the market return in the entire portfolio.
Especially the performance of banking sector is remarkable with return more than 10% return for two
companies and for the third company also it is more than the market performance.
The stocks of higher risk yield higher return.Especially Ranbaxy pharmacy and Axis bank. Both the
companies have higher risk and yields higher return obviously.
The excess return to beta ratio is positive for few companies which are selected for the investment
and remaining stocks have got negative value.
The performance of Construction industry stocks is also good. Two out of three
companies are selected for the investment.
Except for the two stocks, all other stocks have beta less than one i.e. less than market
beta
The portfolio is made of one pharmaceutical company and two stocks from banking and
two stocks from construction industry. Hence the portfolio is a well diversified portfolio
The highest investment about 31% is allotted to SUN Pharmacy and the lowest
percentage of investment can be made on L&T stocks for about 7%
As the beta value of few companies is
in negative value which is has the least
risk on investments, investor should
not invest for short term due to less
return.
Ranbaxy has high proportion of investment
and it is the best option for investor to
invest in this company giving a first
priority. The proportion of about 31.13 % of
the investment has to be made.
All companies have beta value less than one, except for Ranbaxy and AXIS
bank, which means risk, is comparatively low so diversification of portfolio
may help the investor to eliminate the controllable risk associated with all
these companies stocks.
About 29.27% of the total
investment has to be made
in HDFC Bank
Next in the list of stocks
are AXIS Bank and Reliance
Construction with an
investment of 21.84% and
10.85% each.
The lower proportion of
investment of about 6.91%
has to be invested in L&T
Construction.