Assign Ment 1 Investmemt

8/6/2019 Assign Ment 1 Investmemt

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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:
http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficienthttp://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient


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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.

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Assign Ment 1 Investmemt