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Risk and return analysis
The traditional approach of portfolio building has some basic
assumptions. An investor wants higher returns at the lower risk.
But the rule of the game is that more risk, more return. So whilemaking a portfolio the investor must judge the risk taking
capability and the returns desired.
Diversification
The asset mix is determined and risk return relationship is
analyzed the next step is to diversify the portfolio. The main
advantage of diversification is that the unsystematic risk isminimized
1.3 Approaches of Portfolio Management
In general, the value of utilizing a portfolio management approach
to managing your investments is as follows:
Improved Resource Allocation:Too often today, lowvalue projects, or projects in trouble, squeeze scarce
resources and do not allow more valuable projects to be
executed. One critical step is for all departments to prioritize
their own work. However, that is only part of the process.
True portfolio management on an organization-wide basis
requires prioritization of work across all of the departments.In addition to more effectively allocating labor, non-labor
resources can be managed in the portfolio as well.
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This includes equipment, software, outsourced work, etc.
Just because you outsource a project, for instance, and do
not use your own labor, does not mean it should not be a
part of the portfolio. The same prioritization process shouldtake place with all of the resources proposed for the
portfolio.
Improved Scrutiny of Work:Everyone has petprojects that they want to get done. In some departments,
managers make funding decisions for their own work and
they are not open to challenge and review. Portfolio
management requires work to be approved by all the key
stakeholders. The proposed work is open to more scrutiny
since managers know that when work is approved in one
area, it removes funding for potential work in other areas. As
stewards of the department's money, the Executive will now
have a responsibility to approve and execute the work that is
absolutely the highest priority and the highest value.
More Openness of the Authorization Process:Utilizing a portfolio management process removes any
clouds of secrecy on how work gets funded. The Business
Planning Process allows everyone to propose work and
ensures that people know the process that was followed to
ultimately authorize work.
Less Ambiguity in Work Authorization: Theportfolio management planning process provides criteria for
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evaluating work more consistently. This makes it easier to
compare work on an apples-to-apples basis and do a better
job in ensuring that the authorized work is valuable, aligned
and balanced.
Improved Alignment of the Work: In addition tomaking sure that only high priority work is approved,
portfolio management also results in the work being aligned.
All portfolio management decisions are made within the
overall context of the department's strategy and goals. In
the IT department, portfolio management provides a process
for better translating business strategy into technology
decisions.
Improved Balance of Work: In financial portfoliomanagement, you make sure that your resources are
balanced appropriately between various financial
instruments such as stocks, bonds, real estate, etc. Business
portfolio management also looks to achieve a proper balance
of work.
Example: When you first evaluate your portfolio of work, you
may find that your projects are focused too heavily on cost
cutting, and not enough on increasing revenue. You might also
find that you cannot complete your strategic projects because you
are spending too many resources supporting your old legacy
systems. Portfolio management provides the perspective to
categorize where you are spending resources and gives you away to adjust the balance within the portfolio as needed.
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Changed Focus from Cost to Investment: Youdon't focus on the "cost" side of your financial portfolio
although, in fact, all of your assets were acquired at a cost.
Example: You may have purchased XYZ company stock for
$10,000. However, when you discuss your financial portfolio, you
don't focus on the $10,000 you do not have anymore. You
invested the money and now have stock in return so you focus on
the stock that you now own. You might also talk about your
investment of $10,000 to purchase the stock, but your interest is
in its current value and whether it has generated a positive ornegative benefit! Likewise, in your business portfolio, you are
spending money to receive benefits in return. Portfolio
management focuses on the benefit value of the products and
services produced rather than just on their cost.
This switch in focus is especially important in the Information
Technology (IT) area, where many executives still think of value in
terms of the accumulated cost of computers, monitors and
printers. Using the portfolio management model, you show thevalue of all expenditures in your portfolio. These expenditures
include not just the computing hardware and software, but also
the value associated with all project and support work. If the
value is there relative to the cost, the work should be authorized.
If the value is not there relative to the cost, the work should be
eliminated, cut back or backlogged. However, the basic discussion
should be focused on value delivered not just on the cost of the
products and services.
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portfolio management dashboard should be created and
shared. The business value of portfolio projects should also
be measured and shared.
Increased Focus on When to Stop a Project: Thisis equivalent to selling a part of your financial portfolio
because the investment no longer meets your overall goals.
It may no longer be profitable, or you may need to change
your portfolio mix for the purposes of overall balance. In
either case, you need to sell the investment. Likewise, when
you are managing a portfolio of work, you are also managing
the underlying portfolio of assets that the work represents.
In the IT Division, for instance, the assets include business
application systems, software, hardware,
telecommunications, etc. As you look at your portfolio, you
may recognize the need to "sell" assets. While the asset may
not literally be sold, you may decide to retire or eliminate
the asset.
Example: A number of years ago you may have converted to newdatabase software and now you realize that only a couple of the
old databases remain in use. It may make sense to proactively
migrate the remaining old databases to the new software. This
simplifies the technical environment and may also result in
eliminating a software maintenance contract. This is equivalent to
selling an asset that is no longer useful within the portfolio.
2.1 Definition of Risk
1. Uncertainty of future outcomes
2. Probability of an adverse outcome
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2.2 Risk Aversion
The assumption that most investors will choose the least
risky alternative, all else being equal and that they will not
accept additional risk unless they are compensated in the
form of higher return
Given a choice between two assets with equal rates of
return, most investors will select the asset with the lower
level of risk.
2.3 Evidence That Investors are Risk
Averse
Many investors purchase insurance for: Life, Automobile,
Health, and Disability Income. The purchaser trades known
costs for unknown risk of loss
Yield on bonds increases with risk classifications from AAA to
AA to A.
2.4 Not all investors are risk averse
Risk preference may have to do with amount of money involved -
risking small amounts, but insuring large losses.
3.1 Expected rate of return
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Risk is uncertainty that an investment will earn its expected
rate of return
Probability is the likelihood of an outcome
3.2 Expected rate of return Formula
)E(RReturnExpected i=
=
n
i 1
Return(PossibleReturn)ofyProbabilit(
)R(P....)) (R(P)) (R[ (P nn2211 +++
))(RP(1
ii
n
i
=
3.3 Return and Risk of a Portfolio
Often investors have a combination of different stocks. Such
combinations of stocks are called a portfolio.
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One of the main reasons why we would like to hold a
combination of different stocks is to reduce the risk-return
tradeoff by exploiting the situation where correlations
between the returns of different stocks is less than one. To
see how it might reduce the tradeoff, let us first look at the
expected return and standard deviation of the returns on a
portfolio of two stocks.
3.4 Expected return of a portfolio
Consider a portfolio of the stock A stock B. You have a fixed
amount of money to invest. Let Xa
be the proportion of the
money you invest in stock A, and X
bbe the proportion of
money you invest in stock B. Let E(R
A) and E(R
B) be the
expected returns stock A and stock B.
Expected return of this portfolio is computed as
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Expected return:
whereRp is the return on the portfolio,Ri is the return on asset i and wiis the weighting of component asset i (that is, the share of asset i in the
portfolio).
Portfolio return variance:
where ij is the correlation coefficient between the returns on assets iandj. Alternatively the expression can be written as:
,Where ij = 1 fori=j.
Portfolio return volatility (standard deviation):
For a two asset portfolio:
Portfolio return:
Portfolio variance:
For a three asset portfolio:
Portfolio return:
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Portfolio variance:
3.6 Portfolio Measuring the Risk of
Expected Rates of Return
1)
=Variance
2n
1i
Return)Expected-Return(Possibley)Probabilit( =
2) Standard Deviation is the
square root of the variance
2
iii
1
)]E(R)[RP( =
n
i
=
n
i 1
2
iii )]E(R-[RP
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3) Coefficient of variation (CV) a measure of relative variability
that
Indicates risk per unit of return
Standard Deviation of Returns
Expected Rate of Returns
E(R)
i=
3.7 Portfolio Standard Deviations
Formula
ji
ijij
ij
2
i
i
port
n
1i
n
1i
ijj
n
1i
i
2
i
2
iport
rCovwhere
j,andiassetsforreturnofratesebetween thcovariancetheCov
iassetforreturnofratesofvariancethe
portfolioin thevalueofproportionby thedeterminedareweights
whereportfolio,in theassetsindividualtheofweightstheW
portfoliotheofdeviationstandardthe
:where
Covwww
=
=
=
=
=
+= = = =
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)()( PortfolioVarPortfolioSD =
3.12 The relationship between the
return and SD of a portfolio of two
stocks
To see how a portfolio may reduce the return-risk tradeoff, it
is constructive to plot the expected return against thestandard deviation of portfolio for different weights.
Use the excel file return and SD of portfolio to plot the
relationship between standard deviation and return of the
portfolio of stock A and stock B for different weights.
3.13 Relationship between standard
deviation and expected return of the
portfolio of stock A and B.
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relationship. If Covariance is positive, two
random variables are positively correlated.
If it is negative, then the two random
variables are negatively correlated. Let RA
and RB be the returns for stock A and stockB. We use Cov(RA,RB) or AB to denote the
covariance.
related to each other.
More specifically, it
shows the strength of
linear relationship. If
the correlation is +1,two random variables
have perfect positive
linear relationship. If
it is 1, the two
random variables
have perfect negative
linear relationship. As
it becomes close tozero, the linearity in
the relationship
weakens.
Let RA1 RA2, RAn be the possible values of
Company As stock, and RB1, RB2, RBn be
the possible values of company Bs stock.Then Covariance between the returns of
stock A and stock B is defined as
Correlation between
the returns of the
stock A and stock B iswritten asAB, and
this is defined as
=
=n
i
BBi
AAiiBA
RRRRRRCov
1
))((Pr),()()(
),(
BA
BA
AB
RSDRSD
RRCov
=
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So relationship of covariance & correlation is very vital role for
portfolio theory.
4.3 Correlation Coefficient
It can vary only in the range +1 to -1. A value of +1 would
indicate perfect positive correlation. This means that returns
for the two assets move together in a completely linear
manner. A value of 1 would indicate perfect correlation.
This means that the returns for two assets have the samepercentage movement, but in opposite directions
The correlation coefficient is obtained by standardizing
(dividing) the covariance by the product of the individual
standard deviations
Correlation coefficient varies from -1 to +1
jt
iti
ij
Rofdeviationstandardthe
Rofdeviationstandardthe
returnsoftcoefficienncorrelatiother
:where
Cov
r
=
=
=
=
j
ji
ij
ij
5.0 Measures of Historical Rates of
Return
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5.1 Arithmetic Mean
yieldsperiodholding
annualofsumtheHPY
:where
HPY/AM
=
= n
5.2 Geometric Mean
6.1 Define
Markowitz
PortfolioTheory
Quantifies risk.
Derives the
expected rate of
return for a portfolio of assets and an expected risk
measure.
[ ]
( ) ( ) ( )n
n
HPRHPRHPR
:followsasreturnsperiodholdingannualtheofproductthe
:where
1HPRGM
21
1
=
=
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The efficient frontier represents that set of portfolios with the
maximum rate of return for every given level of risk, or the
minimum risk for every level of return
Frontier will be portfolios of investments rather thanindividual securities
Exceptions being the asset with the highest return and
the asset with the lowest risk
7.2 Efficient Frontier for Alternative
Portfolios with no Risk- Free AssetAs shown in this graph, every possible combination of the risky assets,
without including any holdings of the risk-free asset, can be plotted in
risk-expected return space, and the collection of all such possible
portfolios defines a region in this space. The left boundary of this region
is a hyperbola, and the upper edge of this region is the efficient frontier
in the absence of a risk-free asset (sometimes called "the Markowitz
bullet"). Combinations along this upper edge represent portfolios
(including no holdings of the risk-free asset) for which there is lowest
risk for a given level of expected return. Equivalently, a portfolio lying on
the efficient frontier represents the combination offering the best
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possibleexpected return for given risk level.
Efficient Frontier: The hyperbola is sometimes referred to
as the 'Markowitz Bullet', and is the efficient frontier if no risk-
free asset is available. With a risk-free asset, the straight line is
the efficient frontier.
Graph: Efficient Portfolio
7.3 Efficient Frontier and Investor
Utility
An individual investors utility curve specifies the trade-offs
he is willing to make between expected return and risk
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The slope of the efficient frontier curve decreases steadily as
you move upward
These two interactions will determine the particular portfolio
selected by an individual investor The optimal portfolio has the highest utility for a given
investor
It lies at the point of tangency between the efficient frontier
and the utility curve with the highest possible utility
7.4 Selecting an Optimal Risky Portfolio
A line created from the risk-reward graph, comprised of
optimal portfolios.
The optimal portfolios plotted along the curve have the
highest expected return possible for the given amount of
risk.
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Second phase began in the year 1930. The phase was of
professionalism. After coming up of the Securities Act, the
investment industry began the process of upgrading its ethics,
establishing standard practices and generating a good public
image. As a result the investments market became safer place toinvest and the people in different income group started investing.
Investors began to analyze the security before investing. During
this period the research work ofBenjamin Graham and David L.
Dood was widely publicized and publicly acclaimed. They
published a book Security Analysis in 1934, which was highly
sought after. There research work was considered first work in the
field of security analysis and acted as the base for further study.
They are considered as pioneers of security analysis as adiscipline
Third phase was known as the scientific phase. The foundation of
modern portfolio theory was laid by Markowitz. His pioneering
work on portfolio management was described in his article in the
Journal of Finance in the year 1952 and subsequent books
published later on.
The work of Markowitz was extended by the William Sharpe,
John Linter andJan Mossin through the development of the
Capital Asset Pricing Model (CAPM).
If we talk of the present the last two phases of Professionalismand Scientific Analysis are currently advancing simultaneously
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with investment in various financial instruments becoming safer,
with proper knowledge to each and every investor
8 .2 Conclusions
Thus on the whole it can be concluded that there is no conclusive
evidence which suggest that performance of mutual fund scheme
portfolio is superior to others. But it is for sure performance of the
most of the funds in better.
Above this view point we can say that, this deeper understanding
of portfolio theory should lead to reflect back on our earlierdiscussion of global investing. Because many foreign stock and
bond investments provide superior rates of return compared with
U.S securities and have low with portfolios of U.S stocks and
bonds, including these foreign securities in portfolio will help to
reduce the overall risk of portfolio while possibly increasing rate
of return.
Many implementations of portfolio management start directly with
trying to identify and prioritize the work of the portfolio, mostlikely because that is obviously where you will find the greatest
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William F. Sharpe / Gordon J. Alexander /
Jeffery V. Bailey (2004). Investments
(6
th
edition)
Web Address http://www.Portfolio Theroy.com.
http://www.Portfolio Management.com.