Construction of optimal portfolio by using Sharpe Single Index Model with special reference of NSE 50 securities.

1. SHARPE SINGLE
INDEX MODEL
with special reference to NSE 50 securities
Made By:
Fatima Choudhary
IV Semester (FA)

2. CONTENTS
• CONCEPTUAL FRAMEWORK
• REVIEW OF LITERATURE
• RATIONALE OF STUDY
• OBJECTIVES OF STUDY
• METHODOLOGY

3. CONCEPTUAL FRAMEWORK
• Security
• Portfolio
• Portfolio construction (Traditional and Modern
Approach)
• Portfolio Management

4. SECURITY
The term security was originally used to describe financial
instruments secured by physical assets.
Securities are broadly categorized into:
Debt securities (such as banknotes, bonds and debentures
Equity securities, e.g., common stocks; and
Derivative contracts, such
as forwards, futures, options and swaps.

5. PORTFOLIO
The term portfolio refers to any collection of financial
assets such as stocks, bonds, and cash. A portfolio is
designed according to the investor's risk tolerance, time
frame and investment objectives. A portfolio's asset
allocation may be managed by many of the investment
approaches and principles.

6. PORTFOLIO
CONSTRUCTION
Portfolio construction is investing in a variety of funds
or investment options that work together to meet the
requirements of the investor. As the risk element of
individual securities as well as portfolios change the
invinvestmentestor must periodically review and revise
the portfolios. Here the main focus is on Equity
portfolio construction. Portfolio constructions are of
two types, they are Traditional Approach and Modern
Approach

7. Traditional Vs. Modern Approach
Traditional Approach
• is based on Current Income,
Capital Appreciation, Tax
Considerations, Liquidity and
Safety
• begins with the analysis of
constraints
• determining the objectives of
investment
• type of portfolio is selected
• the risk and return of the
selected type is assessed
• diversification
Modern Approach
• Markowitz Model of
portfolio construction
• Sharpe Index Model of
portfolio construction .
• Capital Asset Pricing
Model of portfolio
construction

8. PORTFOLIO MANAGEMENT
• Portfolio management comprises all the processes involved in
the creation and maintenance of an investment portfolio.
• It deals specifically with the security analysis, portfolio
analysis, portfolio selection, portfolio revision & portfolio
evaluation.
• Portfolio management objectives can be divided into Risk
minimization, Safeguarding capital, Capital Appreciation,
Choosing optimal mix of securities and Keeping track on
performance.

9. SHARPE SINGLE INDEX
MODEL
By William Sharpe in 1963
The return of an individual security is assumed to depend on the return
on the market index. The return of an individual security may be
expressed as:
Ri = αi + βi Rm + ei
Where,
αi= The component of security’s return that is independent of the
market’s performance
Rm= The rate of return on the market index
Βi= The constant that measures the expected change in stock
return(Ri) given a change in market return(Rm).
ei= The error term representing the random or residual return, i.e. the
unexpected return resulting from influences not identified by the model

10. The desirability of any stock is directly related to its excess
return-to-beta ratio.
If the stocks are ranked from highest to lowest order by excess
return to beta that represents the desirability of any stock's
inclusion in a portfolio.
The number of stocks selected depends on a unique cutoff rate
such that all stocks with higher ratios will be included and all
stocks with lower ratios excluded

11. LITERATURE REVIEW
• AJ Du Plessis, M Ward (2009)
• G Van der Hoek, AHG Rinnooy Kan, GT Timmer (1983)
• Francesc J Ortí , José Sáez, Antonio Terceño (2002)
• Alina Lucia Trifan (2009) A Bilbao, M Arenas, M Jiménez,
B Perez Gladish and MV Rodriguez (2005)
• Varadharajan P (2011)
• Rajan Bahadur Paudel and Sujan Koirala (2006)

12. RATIONALE OF
STUDY
Through this research an attempt
has been made to construct an
optimal portfolio using Sharpe
Single Index Model with special
reference to NSE 50 securities
and to make the investors aware
of the functioning of various
securities which may help the
investors in taking decisions. The
report will try justifying that
rather keeping all the investment
in one security, the investor
should compare the risks and
expected yield on various
instruments while taking
investments decisions.

13. OBJECTIVE OF STUDY
Optimal Portfolio Construction using Sharpe Single Index
Model with special reference to NSE 100 securities

14. METHODOLOGY
THE STUDY
This research will be empirical in
nature. It will establish
relationship with various variables
and its impact on the others. The
variables under study would be
return (dependent variable) and
market return (independent
variable). These variables will be
studied over a period of time to
understand relationship between
these variables, which would help
the investors take timely decisions.
THE TOOLS
 FOR DATA
COLLECTION
 FOR DATA ANALYSIS
Mean
Standard deviation
 Beta
Sharpe Single Index
Model

15. CONCLUSION
As it is clear that the construction of optimal portfolio investment by
using Sharpe’s Single Index Model is an easy mechanism of
constructing an optimal portfolio of stocks for a rational investor by
analyzing the reason behind the inclusion of securities in the portfolio
with their respective weights. This model can show how risky a security
is, if the security is held in a well-diversified portfolio. This study is
made on the basis of small sample (n<100) i.e. 50 sampled securities. It
can be extended to a large sample to get a more accurate result. Hope
this study will contribute a little about a lot in the field of investment
finance.

16. Company Beta of the Portfolio Return of the Portfolio Variance of the Portfolio
Tata Motors ltd 0.0744 1.0889 0.0031
Adani 0.2613 3.8192 0.0385
Bharat Petroleum Corp ltd 0.0728 1.0647 0.0030
SBI 0.1275 1.8638 0.0094
Reliance 0.6608 9.6508 0.2878
Shree Cement ltd 0.0762 1.1129 0.0038
Maruti Suzuki India ltd 0.0635 0.9275 0.0027
M & M ltd 0.0701 1.0251 0.0034
ONGS ltd 0.0360 0.5261 0.0009
Bajaj Finance ltd 0.0229 0.3347 0.0004
UltraTech ltd 0.0362 0.5287 0.0010
Grasim Industries ltd 0.0245 0.3575 0.0004
Bharti Airtel ltd 0.0145 0.2118 0.0002
ICICI 0.0175 0.2553 0.0002
Eicher Motors ltd 0.0100 0.1458 0.0001
1.567935168 22.9127 0.3549
The beta, return and risk (in the form of variance) of the portfolio are:

17. REFERENCES
 Sharpe, William (January 1963). "A simplified Model of Portfolio Analysis". Management Science.
 http://www.primejournal.org/BAM/abstracts/2011/dec/Varadharajan.htm
 www.wikipedia.org/wiki/Single-index_mode
 Construction of equity portfolio of large caps companies of selected sectors in India with
reference to the Sharpe Index Model, IJPSS Journal, volume 2, issue 8, by P.Varadharajan and
Ganesh
 Application of Markowitz and Sharpe Models in Nepalese Stock Market, The Journal of Nepalese
Business Studies Vol. III No. 1 Dec. 2006 by Rajan Bahadur and Paudel Sujan Koirala
 http://oaithesis.eur.nl
 www.sage.com
 www.indianmba.com
 Security analysis and portfolio management, Punithavarthy Pandian
 Security analysis and portfolio management, Donald E. Ficher and Ronald J. Jordan