A Study on the Performance of Mutual Fund Scheme in IndiaIJAEMSJORNAL
A mutual fund is a trust that encompasses the savings of a number of investors who share a common financial goal. The money thus collected is then invested in capital market instruments such as shares, debentures and other securities. The income earned through these investments and the capital appreciation realized is shared by its unit holders in proportion to the number of units owned by them. Thus, Mutual Fund is one of the most effective instruments for the small & medium investors for investment and offers opportunity to them to participate in capital market with low level of risk. It also provides the facility of diversification i.e. investors can invest across different types of schemes. Indian Mutual Fund has achieved a lot of popularity since last two decades. For a long time UTI enjoyed the monopoly in mutual fund industry. But with the passage of time many new players came in the market and thus the mutual fund industry faces a lot of competition. Now a day this industry has become the major player of the financial system. Therefore it becomes important to investigate the mutual fund performance at continuous basis. The wide variety of schemes floated by these mutual fund companies gave wide investment choice for the investors. Among wide variety of funds equity, diversified fund is considered as substitute for direct stock market investment. In present paper an attempt has been made to investigate the performance of the open ended, growth oriented, equity diversified schemes on the basis of return and risk evaluation. The analysis was achieved by assessing various financial tests like Average Return, Standard Deviation, Beta, Coefficient of Determination (R2), Alpha, Sharpe Ratio and Treynor Ratio whose results will be useful for investors for taking better investment decisions. The data has been taken from various websites of mutual fund schemes and from amfiindia.com. The analysis depicts that majority of funds selected for study have outperformed under Sharpe Ratio as well as Treynor Ratio.
A Study on the Performance of Mutual Fund Scheme in IndiaIJAEMSJORNAL
A mutual fund is a trust that encompasses the savings of a number of investors who share a common financial goal. The money thus collected is then invested in capital market instruments such as shares, debentures and other securities. The income earned through these investments and the capital appreciation realized is shared by its unit holders in proportion to the number of units owned by them. Thus, Mutual Fund is one of the most effective instruments for the small & medium investors for investment and offers opportunity to them to participate in capital market with low level of risk. It also provides the facility of diversification i.e. investors can invest across different types of schemes. Indian Mutual Fund has achieved a lot of popularity since last two decades. For a long time UTI enjoyed the monopoly in mutual fund industry. But with the passage of time many new players came in the market and thus the mutual fund industry faces a lot of competition. Now a day this industry has become the major player of the financial system. Therefore it becomes important to investigate the mutual fund performance at continuous basis. The wide variety of schemes floated by these mutual fund companies gave wide investment choice for the investors. Among wide variety of funds equity, diversified fund is considered as substitute for direct stock market investment. In present paper an attempt has been made to investigate the performance of the open ended, growth oriented, equity diversified schemes on the basis of return and risk evaluation. The analysis was achieved by assessing various financial tests like Average Return, Standard Deviation, Beta, Coefficient of Determination (R2), Alpha, Sharpe Ratio and Treynor Ratio whose results will be useful for investors for taking better investment decisions. The data has been taken from various websites of mutual fund schemes and from amfiindia.com. The analysis depicts that majority of funds selected for study have outperformed under Sharpe Ratio as well as Treynor Ratio.
A Study on Empirical Testing of Capital Asset Pricing ModelProjects Kart
A Study on Empirical Testing of Capital Asset Pricing Model is compared with many blue chip companies with the help of detailed questionnaire to understand the problem statement. Visit http://www.projectskart.com/p/contact-us.html for more information.
Insight Summit 2017: Intelligent Risk Taking - Active vs passive investing
Money management in equilibrium - Jonathan Berk, A.P. Giannini Professor of Finance, Graduate School of Business, Stanford University
Presented at the third annual Insight Summit conference held on 7 November 2017 by London Business School’s AQR Asset Management Institute.
Global Value Equity Portfolio (March 2011)Trading Floor
This month we have adjusted our Global Value Equity Portfolio to include the reinvestment of gross dividends and introduced dynamic weights for the constituents. This reduces transaction costs, enhances excess return and makes the portfolio easier to replicate for investors.
The Global Market Portfolio Composition Studygjohnsen
Eastgate Advisors, llc recently conducted a review of published literature on the likely composition of the global markets portfolio which theory says is the most mean variance efficient portfolio an investor can hold. Our purpose in doing so was to help update our strategic global asset allocation benchmarks.
Feel free to contact Greg Johnsen, CFA with comments or questions.
A Study on Factors Influencing Investment Decision Regarding Various Financia...ijtsrd
In the current era of financial inclusion, digitalization and economy driving towards a faster pace, the investors are very much concerned about their savings which can be transferred into investments. The main purpose of investment is to maximize the returns out of it with minimum expenses and risk. There are various factors which affect the investment decision like demographic factors and behavioural biases which decides the type, tenure, amount of the investment. This paper explores that return, advice, tax benefit, liquidity risk appetite of the investors altogether plays a significant part in influencing the investors. Is there any impact of demographic factors like age, gender and income on factors influencing investment decision tried to find out. The results show that factors influencing the investment decision are influenced by income level not by age and gender. Dr. Ankit Jain | Mr Raj Tandel "A Study on Factors Influencing Investment Decision Regarding Various Financial Products" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33678.pdf Paper Url: https://www.ijtsrd.com/management/accounting-and-finance/33678/a-study-on-factors-influencing-investment-decision-regarding-various-financial-products/dr-ankit-jain
Quantopian is Launching a Crowd-sourced Hedge Fundkelmstrom
Crowd-sourcing opens a fire hose of ideas.
Diversity of ideas will result in a diversified hedge fund portfolio.
Quantopian has unique access to tens of thousands of quants which allows for idea generation at an unprecedented scale.
Quantopian provides a platform for you to build, test, and execute trading algorithms. Live trading algorithms can become part of our crowd-sourced hedge fund where top quant talent is matched with outside investor capital.
https://www.quantopian.com/home
A Study on Empirical Testing of Capital Asset Pricing ModelProjects Kart
A Study on Empirical Testing of Capital Asset Pricing Model is compared with many blue chip companies with the help of detailed questionnaire to understand the problem statement. Visit http://www.projectskart.com/p/contact-us.html for more information.
Insight Summit 2017: Intelligent Risk Taking - Active vs passive investing
Money management in equilibrium - Jonathan Berk, A.P. Giannini Professor of Finance, Graduate School of Business, Stanford University
Presented at the third annual Insight Summit conference held on 7 November 2017 by London Business School’s AQR Asset Management Institute.
Global Value Equity Portfolio (March 2011)Trading Floor
This month we have adjusted our Global Value Equity Portfolio to include the reinvestment of gross dividends and introduced dynamic weights for the constituents. This reduces transaction costs, enhances excess return and makes the portfolio easier to replicate for investors.
The Global Market Portfolio Composition Studygjohnsen
Eastgate Advisors, llc recently conducted a review of published literature on the likely composition of the global markets portfolio which theory says is the most mean variance efficient portfolio an investor can hold. Our purpose in doing so was to help update our strategic global asset allocation benchmarks.
Feel free to contact Greg Johnsen, CFA with comments or questions.
A Study on Factors Influencing Investment Decision Regarding Various Financia...ijtsrd
In the current era of financial inclusion, digitalization and economy driving towards a faster pace, the investors are very much concerned about their savings which can be transferred into investments. The main purpose of investment is to maximize the returns out of it with minimum expenses and risk. There are various factors which affect the investment decision like demographic factors and behavioural biases which decides the type, tenure, amount of the investment. This paper explores that return, advice, tax benefit, liquidity risk appetite of the investors altogether plays a significant part in influencing the investors. Is there any impact of demographic factors like age, gender and income on factors influencing investment decision tried to find out. The results show that factors influencing the investment decision are influenced by income level not by age and gender. Dr. Ankit Jain | Mr Raj Tandel "A Study on Factors Influencing Investment Decision Regarding Various Financial Products" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33678.pdf Paper Url: https://www.ijtsrd.com/management/accounting-and-finance/33678/a-study-on-factors-influencing-investment-decision-regarding-various-financial-products/dr-ankit-jain
Quantopian is Launching a Crowd-sourced Hedge Fundkelmstrom
Crowd-sourcing opens a fire hose of ideas.
Diversity of ideas will result in a diversified hedge fund portfolio.
Quantopian has unique access to tens of thousands of quants which allows for idea generation at an unprecedented scale.
Quantopian provides a platform for you to build, test, and execute trading algorithms. Live trading algorithms can become part of our crowd-sourced hedge fund where top quant talent is matched with outside investor capital.
https://www.quantopian.com/home
5_Saurabh-Agarwal-Sarita v.pdf a study on portfolio management & financial se...vaghasiyadixa1
This research report about portfolio management & financial sector including all the requirements of making research report as per University required.
How Investment Analysis & Portfolio Management greatly focuses on portfolio c...QUESTJOURNAL
Abstract: Portfolio Construction is a capstone elective that draws on previously studied investment principles, theories and techniques. Its enable synthesize that acquired financial theories and knowledge in the context of portfolio construction and asset allocation. It focuses on gaps in theory and how they can be managed in practice.
The activities of large, internationally active financial institutions have grown increasingly
Complex and diverse in recent years.This increasing complexity has necessarily been accompanied by a process of innovation in how these institutions measure and monitor their exposure to different kinds of risk. One set of risk management techniques that has attracted a great deal of attention over the past several years, both among practitioners and regulators, is "stress testing", which can be loosely defined as the examination of the potential effects on a firm’s financial condition of a set of specified changes in risk factors, corresponding to exceptional but plausible events. A concept of security analysis and portfolio management services has been very famous and old among various institutions. This report represents practices application of portfolio management techniques in the portfolio section. Portfolio management is an integrated and exhaustive of fundamental and technical methods which are used for calculation of annul return and earnings per share for the portfolio. Modern portfolio theory suggests that the traditional approach to portfolio analysis, selection and management may yield less than optimum results. Hence a more scientific approach is required, based on estimates of risk and return of the portfolio and the attitudes of the investor toward a risk-return trade-off stemming from the analysis of the individual Securities.
Writekraft Research and Publications LLP was initially formed, informally, in 2006 by a group of scholars to help fellow students. Gradually, with several dissertations, thesis and assignments receiving acclaim and a good grade, Writekraft was officially founded in 2011 . Since its establishment, Writekraft Research & Publications LLP is Guiding and Mentoring PhD Scholars.
Our Mission
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Writekraft endeavours to be the leading global research and publications company that will fulfil all research needs of our clients. We will achieve this vision through:
Analyzing every customer’s aims, objectives and purpose of research
Using advanced and latest tools and technique of research and analysis
Coordinating and including their own ideas and knowledge
Providing the desired inferences and results of the research
In the past decade, we have successfully assisted students from various universities in India and globally. We at Writekraft Research & Publications LLP head office in Kanpur, India are most trusted and professional Research, Writing, Guidance and Publication Service Provider for PhD. Our services meet all your PhD Admissions, Thesis Preparation and Research Paper Publication needs with highest regards for the quality you prefer.
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We have PhD experts from reputed institutions/ organizations like Indian Institute of Technology (IIT), Indian Institute of Management (IIM) and many more apex education institutions in India. Our works are tailored and drafted as per your requirements and are totally unique.
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We started this Academic Writing Help in the year 2011.Writekraft Research & Publication: www.writekraft.com 1000s of students have graduated across the globe from our in-depth research.
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Writekraft Research and Publications LLP was initially formed, informally, in 2006 by a group of scholars to help fellow students. Gradually, with several dissertations, thesis and assignments receiving acclaim and a good grade, Writekraft was officially founded in 2011 . Since its establishment, Writekraft Research & Publications LLP is Guiding and Mentoring PhD Scholars.
Our Mission
“To provide breakthrough research works to our clients through Perseverant efforts towards creativity and innovation”.
Vision
Writekraft endeavours to be the leading global research and publications company that will fulfil all research needs of our clients. We will achieve this vision through:
Analyzing every customer’s aims, objectives and purpose of research
Using advanced and latest tools and technique of research and analysis
Coordinating and including their own ideas and knowledge
Providing the desired inferences and results of the research
In the past decade, we have successfully assisted students from various universities in India and globally. We at Writekraft Research & Publications LLP head office in Kanpur, India are most trusted and professional Research, Writing, Guidance and Publication Service Provider for PhD. Our services meet all your PhD Admissions, Thesis Preparation and Research Paper Publication needs with highest regards for the quality you prefer.
Our Achievements
NATIONAL AWARD FOR BEST RESEARCH PROJECT (By Hon. President APJ Abdul Kalam)
GOLD MEDAL FOR RESEARCH ON DISABILITY (By Disabled’s Club of India)
NOMINATED FOR BEST MSME AWARDS 2017
5 STAR RATING ON GOOGLE
We have PhD experts from reputed institutions/ organizations like Indian Institute of Technology (IIT), Indian Institute of Management (IIM) and many more apex education institutions in India. Our works are tailored and drafted as per your requirements and are totally unique.
From past years our core advisory members, research team assisted research scholars from various universities from all corners of world.
EVALUATING PERCEPTION OF INVESTORS TOWARDS MUTUAL FUNDS & PERFORMANCE OF THE ...Nishant Kumar
This study has investigated into the perception of the investors in Indian markets towards Mutual Funds and has evaluated the returns of the top Mutual Fund performers in India over period of last 3 years – January 1, 2016 to December 31, 2018. It has helped us to conclude on how different schemes attract investors of different age groups and how the impact of different characteristics are known by investors.
This study looks specifically into open-ended equity schemes. Returns have been calculated using daily closing values of NAV of the selected schemes. BSE-Sensex has been chosen as the market portfolio as a comparison basis here. Based on Sharpe, Treynor, and Jensen’s measure the historical performance of the selected schemes are evaluated, whose results will be useful for investors for taking better investment decisions.
A Study on Portfolio Analysis on Selected Securities with Reference to Angel Oneijtsrd
Portfolio analysis refers to analyzing the risk and return of each security in the portfolio.it is finding the balance between maximizing returns and minimizing risk by diversifying investment fund in different investment avenues or sectors. The term portfolio refers to any collection of financial assets such as stocks, bonds and cash. Portfolios may be held individual investors and or managed by financial professionals, hedge funds, banks and other financial institutions. It is a generally accepted principle that a portfolio is designed according to the investor’s risk tolerance, time frame and investment objectives. The monetary value of each asset may influence the risk reward ratio of the portfolio and is referred to as the asset allocation of the portfolio. When determining a proper asset allocation, one aims at maximizing the expected return and minimizing the risk. R Venkateswarlu | Dr. P. Viswanath "A Study on Portfolio Analysis on Selected Securities with Reference to Angel One" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-6 , October 2022, URL: https://www.ijtsrd.com/papers/ijtsrd51940.pdf Paper URL: https://www.ijtsrd.com/other-scientific-research-area/other/51940/a-study-on-portfolio-analysis-on-selected-securities-with-reference-to-angel-one/r-venkateswarlu
A Study on Portfolio Analysis on Selected Securities with Reference to Angel One
Term paper
1. PRESENTED BY
SAIED MAHMUD ZUBAYER
PGDCM, 1ST BATCH
ID-2015-01-06
“Efficient portfolio construction”
June 8, 2016
1
2. EXECUTIVE SUMMARY
Most investment portfolios are designed to meet a specific
future financial need—either a single goal or a multifaceted
set of objectives. To best meet that need, the investor must
establish a disciplined method of portfolio construction that
balances the potential risks and returns of various types of
investments.
This paper reviews my analysis into the investment decisions
involved in constructing a diversified portfolio. The term
“Construction of efficient portfolio” in common practice refers
to selection of securities and their continuous shifting in a
way that the holder gets maximum returns at the minimum
possible risk. A portfolio manager by the virtue of his
knowledge, background and experience helps his clients to
make investment in profitable avenues.
2
June 8, 2016
3. EXECUTIVE SUMMARY
This paper discusses how to create a diversified portfolio by focusing on
eight major steps:
Calculating Portfolio Weight by Maximizing Theta without allowing short
sell
Calculating Portfolio Weight by Maximizing Theta with allowing short sell
Calculating Portfolio Weight by Minimizing Risk without allowing short
sell
Calculating Portfolio Weight by Minimizing Risk with allowing short sell
Calculating Portfolio Weight by Maximizing Portfolio Return for a given
Risk without allowing short sell
Calculating Portfolio Weight by Maximizing Portfolio Return for a given
Risk with allowing short sell
Calculating Portfolio Weight by Minimizing Risk for a given return without
allowing short sell
Calculating Portfolio Weight by Minimizing Risk for a given return without
allowing short sell
3
June 8, 2016
4. INTRODUCTION:
Security analyzing and selection of portfolios and managing them in the
right manner helps in improving the investor’s awareness about the
trends and changes that exist in the market and helps the investors as a
very attractive avenue for investment. In these investments, generally
both rationale and emotional responses are involved. So, investing in
financial securities is considered to be one of the attractive areas for
investing and saving while it is also acknowledged to be one of the most
risky areas for investment. Creation of an optimum portfolio helps to
reduce risk, without sacrificing returns. Portfolio management deals with
the analysis of individual securities as well as with the theory and
practice of optimally combining securities into good portfolios. An
investor who understands the fundamental principles and analytical
aspects of portfolio management has a better chance of earning higher
returns.
It is widely accepted that investors should aim to maximize the level of
return for a given level of risk. Alternatively they aim at minimizing the
risk for a given level of return. This is done by constructing a portfolio of
assets which as a whole is subject to the investor’s risk appetite.
4
June 8, 2016
5. INTRODUCTION:
In this paper, 10 stocks from different sectors are taken for study.
The risk and return of all the stocks are studied individually.
Based on the study top five stocks are selected for forming
optimum portfolio. The final step in the process is to determine
the number of shares of each stock to be purchased. This method
helps us to carefully select the stocks and also the proportion of
investment to be made in each stock, thereby yielding higher
returns.
The study will start by providing an overview of efficient portfolio
construction to apply excel solver and its most important
elements, namely risk, return and diversification. Secondly, the
study will identify and discuss various alternative investments in
securities that are believed to hold the potential for better
diversification and move investors closer to attaining a true
market portfolio. Lastly, the study will attempt to prove the
hypothesis that these investments do hold the potential of
improving the diversification of existing portfolios.
5
June 8, 2016
6. OBJECTIVES OF THE STUDY:
The main objective of this project is to find the
optimum portfolio from the selected companies in
different sectors. At the end of the analysis a portfolio
of 10 stocks with maximum return for a given risk is
constructed which shows how much proportion of
money is to be invested in each security wholly taken
from different sectors.
These sectors are generally consistently performing
as these kinds of sectors are depended by the public
in a large extent. Main objective is to maximize the
value of theta which is the portfolio excess return for
each unit of portfolio risk.
6
June 8, 2016
7. OBJECTIVES OF THE STUDY:
Main objective is to maximize the value of theta which is the portfolio
excess return for each unit of portfolio risk.
7
June 8, 2016
8. OBJECTIVES OF THE STUDY:
Objective of the study are as under:
Maximize Theta:
When short sale is allowed
When short sale is not allowed
Minimize Risk:-
When short sale is allowed
When short sale is not allowed
Maximize portfolio return for a given risk:
When short sale is allowed
When short sale is not allowed
Minimize risk for a given return:
When short sale is allowed
When short sale is not allowed
8
June 8, 2016
9. BACKGROUND OF THE STUDY
This report entitled “Construction of Efficient Portfolio” is
prepared for the fulfillment of the course title Financial
Modeling, Course No. 304. Everybody earns and spends
money. But to optimize this earning & spending and to
accommodate the future uncertainties, inflation etc., there
needs to be proper planning & management of wealth.
Investment decision is one of major part of this management
of wealth. Because, sometimes may have enough money in
hand and sometimes not. If excess money is invested in a
proper manner, then it can encounter the problem during
deficit. Portfolio management is an important management
process of wealth, which maximizes the return for desirable
risk level. In portfolio management, emphasis is given on
the investment in the capital market. For this reason, study
on security market is so essential. Evaluating efficient
portfolio that maximize the return & minimize the risk
compare to other portfolio is very much important.
9
June 8, 2016
10. SCOPE OF THE STUDY:
I have prepared the assignment as a part of the
Course Study of Financial Modeling, Course
Code-D304. To achieve the objective it is
needed to collect the price of the different
companies. For achieving the objectives, the
study will be focused on different steps for
maximizing return on portfolio based on the
shares listed in Dhaka Stock Exchange Limited
considering the price, volume, P/E, EPS, Price
to book value ratio and other criteria of different
companies.
10
June 8, 2016
11. METHODOLOGY:
To attain the objective, I have collected the required data &
information for preparing the report. Those data & information
were collected from various sources & then analyzed. The
following are the sources of data and information:
Collection of data & information:
Secondary data & information:
Observation & collection of data from DSE
Conversation with the executives & officers of Dhaka stock
exchange Ltd.
Collection of Annual Report of Listed companies from DSE library
Monthly review of Dhaka Stock Exchange Ltd
Several kind of academic Test-Book.
Different publications regarding stock exchange function
Price index
Dividend information
Right Information
11
June 8, 2016
12. LIMITATION OF THE STUDY
Some limitations that I have faced want to mention from report
preparation point of view.
Shortcoming of practical experience to comprehend the conceptual
framework of this type of report.
My sample for analysis includes only four year's data i.e. from July 2011
to June 2015, so, it may affect the result of the analysis.
This study was limited only to the 10 companies. As a result it has a
narrow outlook of overall industry.
The study is based on the secondary data collected from the published
annual report of the companies and website of DSE like www.dsebd.org.
So limitation of the secondary data will remain with the study.
Every person has its own thinking and believes so in this research work
may include personal bias during the research work.
Analytical tools, which are used in the study, may have their own
limitations, which may apply to this study too.
It was very difficult to incorporate all the data in the report due to the
limitation from the organization and thus certain information is not
incorporated.
12
June 8, 2016
13. CONSTRUCTION OF THE EFFICIENT PORTFOLIO:
Efficient portfolios may contain any number of asset combinations.
We examine efficient asset allocation by using excel solver.
The make-up of any portfolio is subject to decisions being made on
one of three levels namely:
The capital allocation decision – which refers to the choice
investors need to make between investing in a risk-free asset and
a risky asset portfolio.
The asset allocation decision – which describes the distribution of
risky investments across different asset classes. (Construction of
the optimal risky asset portfolio).
Security selection decision – which describes the choice of
particular securities held within each asset class
13
June 8, 2016
14. SECTOR SELECTION:
All data are collected from the based on trading
of Dhaka Stock Exchange Limited. There are 22
sectors in Dhaka Stock Exchange Limited.
Here, I selected the following Sectors based on
the previous positive performance in DSE:
Fuel and Power
Pharmaceuticals and Chemicals
Bank
Engineering
Food and Allied
14
June 8, 2016
15. SELECTION CRITERIA:
Here sector and shares are selected based on
the following issues:
Price Earning Ratio for the last Five years
Price to Book value ratio for the last five
years
Market Capitalization
Listed before January 01, 2011
Listed in Dhaka Stock Exchange Limited
Relative higher lower P/E ratio of the
companies with comparing market average.
15
June 8, 2016
16. ASSET SELECTION:
Asset Selection:
Fuel and Power
DESCO
TITASGAS
Pharmaceuticals and Chemicals
The Ibn Sina
Square Pharma
Beximco Pharma
Bank
The City Bank
Eastern Bank
Engineering
BSRM Steel
Singer BD
Food and Allied
Olympic BD
16
June 8, 2016
21. CALCULATING CORRELATION MATRIX
The correlation coefficient is a simple statistic that describes
the variability of asset returns relative to other assets for the
purpose of asset allocation. Determining how the asset
classes correlate is an important step in the process of
optimizing the allocation of assets. Without this normalized
form of the covariance, it would be very difficult to evaluate
the relative variability of asset returns.
Asset allocation accounts for over 90% of success as an
investor. Assessing how assets complement one another is
a crucial step in the process of asset allocation.
Correlation describes on a scale of -1 to +1 the relative
movement of two securities' prices or one security relative to
an index, with +1 being perfectly positively correlated, -1
being perfectly negatively correlated and 0 indicating no
correlation. The correlation coefficient, R, which is the
normalized form of the covariance, is a measure of relative
variation.
21
June 8, 2016
22. Perfect positive correlation is like moving in lock step.
Perfectly positively correlated securities do not
complement each other and therefore provide no
diversification.
Perfectly negatively correlated securities' prices move in
the opposite direction from each other by the exact same
amount. For example, if stock A and stock B are perfectly
negatively correlated, stock B will decline by 10% when
stock A rises 10% and stock A will decline by 15% when
stock B rises 15%. Perfectly negatively correlated
investments would provide 100% diversification, as they
would form a portfolio with zero variance, which translates
to zero risk. Unfortunately, in the real world such
investments don't exist, but there are a few assets that
tend to be negatively correlated to most other asset
classes. These assets provide excellent diversification.
CALCULATING CORRELATION MATRIX
22
June 8, 2016
39. PORTFOLIO CONSTRUCTION:
Objectives:
Maximize the Theta
Ө= Rp-Rf/σp
Here,
Ө=Theta, Rp= Portfolio Return, Rf= Risk free return,
σp = Standard Deviation of Portfolio return
The Main objective in a portfolio construction is to
maximize the value of Theta (Ө) which is the portfolio
excess return for each unit of portfolio risk.
39
June 8, 2016
40. CONSTRUCTION THE FUNCTION
When short sell is allowed: Various
constraints may preclude a particular investor
from choosing portfolios on the efficient frontier,
however. Short sale restrictions are only one
possible constraint. Short sale is a usual
regulated type of market transaction. It involves
selling assets that are borrowed in expectation
of a fall in the assets’ price. When and if the
price declines, the investor buys an equivalent
number of assets at the new lower price and
returns to the lender the assets that were
borrowed.
40
June 8, 2016
41. CONSTRUCTION THE FUNCTION
When short sell is allowed:
Return: the general formula of expected return for n assets is:
where:
n= the number of securities;
Wi = the proportion of the funds invested in security i;
rirp= the return on ith security and portfolio p; and
E()=the expectation of the variable in the parentheses.
The return computation is nothing more than finding the weighted
average return of the securities included in the portfolio.
1
( )
n
P i i
i
E r w E r
1
n
i
i
w
= 1.0;
41
June 8, 2016
42. CONSTRUCTION THE FUNCTION
n= the number of securities;
wi=the proportion of the funds invested in
security i;
rirp= the return on ith security and portfolio p;
and
E()=The expectation of the variable in the
parentheses.
1
( )
n
P i i
i
E r w E r
wi >= 0
42
June 8, 2016
43. CONSTRUCTION THE FUNCTION
The variance of a single security is the expected value of the sum of the
squared deviations from the mean, and the standard deviation is the
square root of the variance. The variance of a portfolio combination of
securities is equal to the weighted average covariance of the returns on
its individual securities:
2
1 1
Var Cov ,
n n
p p i j i j
i j
r w w r r
43
June 8, 2016
45. CONSTRUCTION THE FUNCTION
The assumption of no short selling, investors could sell the lowest-return
asset B (here, we assume that ). If the number of short sales is
unrestricted, then by a continuous short selling of B and reinvesting in A
the investor could generate an infinite expected return. The efficient
frontier of unconstraint portfolio is shown in above Figure. The upper
bound of the highest-return portfolio would no longer be A but infinity
(shown by the arrow on the top of the efficient frontier). Likewise the
investor could short sell the highest-return security A and reinvest the
proceeds into the lowest-yield security, thereby generating a return less
than the return on the lowest-return assets. Given no restriction on the
amount of short selling, an infinitely negative return can be achieved,
thereby removing the lower bound of B on the efficient frontier. Hence,
short selling generally will increase the range of alternative investments
from the minimum-variance portfolio to plus or minus infinity.
Relaxing the assumption of no short selling in this development of the
efficient frontier involves a modification of the analysis of the efficient
frontier of constraint (not allowed short sales). Next section, we
introduce the mathematical analysis of the efficient frontier with/without
short selling constraints by excel solver.
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47. EFFICIENT PORTFOLIOS IN EXCEL USING THE
SOLVER
The solver is an Excel Add‐In created by Frontline Systems
(www.solver.com) that can be used to solve general optimization
problems that may be subject to certain kinds of constraints. In
this note we show how it can be used to find portfolios that
minimize risk subject to certain constraints.
The solver add‐in must be activated before it can be used within
Excel. In Excel 2007, you activate addins by clicking on the office
button and then clicking on the Excel Options box at the bottom of
the menu.
This opens the Excel options dialogue box. Click Add‐Ins, which
displays the available Add‐Ins for Excel. Make sure the Solver
Add‐In is an Active Application Add‐In.
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53. CALCULATING PORTFOLIO WEIGHT BY MAXIMIZING PORTFOLIO
RETURN FOR A GIVEN RISK WITHOUT ALLOWING SHORT SELL
HERE, WE ASSUME THAT THE RISK RATE IS 8%
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54. CALCULATING PORTFOLIO WEIGHT BY MAXIMIZING PORTFOLIO
RETURN FOR A GIVEN RISK WITH ALLOWING SHORT SELL
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57. CONCLUSION
The objective of portfolio management is to create and maintain efficient
portfolios. Efficient portfolios are portfolios which yield the greatest
return for any given level of risk. Portfolio is collection of different
securities and assets by which we can satisfy the basic objective
“Maximize yield minimize risk”. Further we have to remember some
important investing rules which are related to the trading and set by the
concerned regulator.
Asset allocation accounts for over 90% of success as an investor, which
is why to need a means to allocate capital efficiently across a specific
set of assets. The Capital Allocation Line explains the basic procedure
for the allocation of capital and modern portfolio theory explains how to
identify the optimal allocation using mean-variance criteria to identify
what's known as the Efficient Frontier, a concept that was first described
by Harry Markowitz in 1952.
Portfolio diversification is the means by which investors minimize or
eliminate their exposure to company-specific risk, minimize or reduce
systematic risk and moderate the short-term effects of individual asset
class performance on portfolio value. In a well-conceived portfolio, this
can be accomplished at a minimal cost in terms of expected return.
Such a portfolio would be considered to be a well-diversified.
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58. REFERENCES
Efficient Portfolio Construction by Mahmood
Osman Imam, Professor of Finance, DU
Website of the different listed Companies
www.dsebd.org
Annual Report of different listed Companies
Research and Information Department of
DSE
Corporate Finance by Stephen A. Ross
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