Department of Accounting & Information Systems

BBA Program.

A Term Paper on “Portfolio Management”

Course Name : Financial ManagementCourse No : 2104Date of Submission : 5th July, 2009

Prepared ForS.N. GhoshProfessor,Department of Accounting & Information Systems,

University of Dhaka.

Prepared By:Md. Omar FarukSection: A;Roll no: 14067BBA; 14th BatchDepartment of AIS,University Of Dhaka.

Acknowledgement:

All the praise for the Almighty Allah whose grace has enabled me to bring out the term

paper on Portfolio Management. The primary objective of this term paper is to provide

some up-to-date theories and information about portfolio management by the famous

writers of today.

I do express my heartiest gratitude to the respected Professor Shanti Narayan Ghosh,

Professor of Department of Accounting & Information Systems at University of Dhaka

whose inspiration and encouragement dares me to write this term paper. Also thank to all

of my fellow classmates for their help and suggestions.

This term paper is mainly based on information from the web and different books. If

there is any misrepresentation of any fact, I, myself is to be confess the fault obligely.

2

Abstract:

For any kind of financial decision in any organization a manager must

think about its strengths, weaknesses, opportunities and threats.

Portfolio management allows him to do this. This paper talks about the

risks and returns associated in any project to decide the three major

managerial functions; investment decisions, financing decisions, and

distributing decisions. It also tried to describe the most recent portfolio

formation model briefly.

3

Table of Content:

Portfolio Management: Definition 5Investment management 6Investment managers and portfolio structures 7

Asset allocation 7Long-term returns 7Investment styles 8Diversification

Portfolio (finance) 9Portfolio formation 10Models 10Returns 11Attribution 11

Market portfolio 12Risk management 13

Principles of risk management 14Process of Risk Management: 15Limitations 16

Modern portfolio theory 17Risk and return 17Mean and variance 17Mathematically 18Capital allocation line 20The efficient frontier 20

The risk-free asset 21Portfolio leverage 22The market portfolio 22Capital market line 22Asset pricing 23Systematic risk and specific risk 23Capital asset pricing model 24Securities market line 25Applications to project portfolios and other "non-financial" assets 25Applications of Modern Portfolio Theory in Other Disciplines 27Comparison with arbitrage pricing theory 27Conclusion 28Bibliography 29

4

Portfolio Management

Definition:

The art and science of making decisions about investment mix and policy, matching

investments to objectives, asset allocation for individuals and institutions, and balancing

risk against performance.

Portfolio management is all about strengths, weaknesses, opportunities and threats in

the choice of debt vs. equity, domestic vs. international, growth vs. safety, and many

other tradeoffs encountered in the attempt to maximize return at a given appetite for risk.

Portfolio Management according to nvestopedia:

In the case of mutual and exchange-traded funds (ETFs), there are two forms of portfolio

management: passive and active. Passive management simply tracks a market index,

commonly referred to as indexing or index investing. Active management involves a

single manager, co-managers, or a team of managers who attempt to beat the market

return by actively managing a fund's portfolio through investment decisions based on

research and decisions on individual holdings. Closed-end funds are generally actively

managed.

5

Investment management

Investment management is the professional management of various securities (shares,

bonds etc.) and assets (e.g., real estate), to meet specified investment goals for the benefit

of the investors. Investors may be institutions (insurance companies, pension funds,

corporations etc.) or private investors (both directly via investment contracts and more

commonly via collective investment schemes e.g. mutual funds or Exchange Traded

Funds) .

The term asset management is often used to refer to the investment management of

collective investments, (not necessarily) whilst the more generic fund management may

refer to all forms of institutional investment as well as investment management for

private investors. Investment managers who specialize in advisory or discretionary

management on behalf of (normally wealthy) private investors may often refer to their

services as wealth management or portfolio management often within the context of so-

called "private banking".

The provision of 'investment management services' includes elements of financial

analysis, asset selection, stock selection, plan implementation and ongoing monitoring of

investments. Investment management is a large and important global industry in its own

right responsible for caretaking of trillions of dollars, euro, pounds and yen. Coming

under the remit of financial services many of the world's largest companies are at least in

part investment managers and employ millions of staff and create billions in revenue.

6

Investment managers and portfolio structures

At the heart of the investment management industry are the managers who invest and

divest client investments.

A certified company investment advisor should conduct an assessment of each client's

individual needs and risk profile. The advisor then recommends appropriate investments.

Asset allocation

The different asset class definitions are widely debated, but four common divisions are

stocks, bonds, real-estate and commodities. The exercise of allocating funds among these

assets (and among individual securities within each asset class) is what investment

management firms are paid for. Asset classes exhibit different market dynamics, and

different interaction effects; thus, the allocation of monies among asset classes will have

a significant effect on the performance of the fund. Some research suggests that

allocation among asset classes has more predictive power than the choice of individual

holdings in determining portfolio return. Arguably, the skill of a successful investment

manager resides in constructing the asset allocation, and separately the individual

holdings, so as to outperform certain benchmarks (e.g., the peer group of competing

funds, bond and stock indices).

Long-term returns

It is important to look at the evidence on the long-term returns to different assets, and to

holding period returns (the returns that accrue on average over different lengths of

investment). For example, over very long holding periods (eg. 10+ years) in most

countries, equities have generated higher returns than bonds, and bonds have generated

higher returns than cash. According to financial theory, this is because equities are riskier

(more volatile) than bonds which are themselves more risky than cash.

7

Investment styles

There are a range of different styles of fund management that the institution can

implement. For example, growth, value, market neutral, small capitalisation, indexed, etc.

Each of these approaches has its distinctive features, adherents and, in any particular

financial environment, distinctive risk characteristics. For example, there is evidence that

growth styles (buying rapidly growing earnings) are especially effective when the

companies able to generate such growth are scarce; conversely, when such growth is

plentiful, then there is evidence that value styles tend to outperform the indices

particularly successfully.

Diversification

Against the background of the asset allocation, fund managers consider the degree of

diversification that makes sense for a given client (given its risk preferences) and

construct a list of planned holdings accordingly. The list will indicate what percentage of

the fund should be invested in each particular stock or bond. The theory of portfolio

diversification was originated by Markowitz and effective diversification requires

management of the correlation between the asset returns and the liability returns, issues

internal to the portfolio (individual holdings volatility), and cross-correlations between

the returns.

Inefficient diversification can result in unnecessary risk.

To cite a recent example, many investors can confirm that what went up in 1999 did,

indeed, come down in 2000. It was the year of the fall of the technology titans. The new

economy was badly battered and bruised. Some investors suffered greatly in the net

worth area.

8

Efficient diversification can reduce risk.

Eficient diversification was developed by Harry Markowitz, PhD., who won a Nobel

Prize for his work.  Pension managers, who are responsible for wisely investing billions

of retirement dollars, have used this strategy for more than 30 years.

The idea, put very simply, is that some asset classes tend to move up when others move

down. A good example of this relationship would be the airline industry and the oil/gas

industry. When oil/gas prices are stable or moving down, airline profits (and airline stock

prices) tend to go up. When oil/gas prices (and profits) move up, airline profits tend to

move down. 

Of course, economic conditions are constantly changing, and, therefore, what went down

can, eventually go up, and what was up can come down. The matter gets more

complicated as new and different situations and factors enter the picture. Some

companies never recover, and new ones are born. But the basic axiom of cyclicality

remains nonetheless.

Portfolio (finance)

In finance, a portfolio is an appropriate mix of collection of investments held by

institutions or a private individual.

Holding a portfolio is part of an investment and risk-limiting strategy called

diversification. By owning several assets, certain types of risk (in particular specific risk)

can be reduced. The assets in the portfolio could include stocks, bonds, options, warrants,

gold certificates, real estate, futures contracts, production facilities, or any other item that

is expected to retain its value.

9

In building up an investment portfolio a financial institution will typically conduct its

own investment analysis, whilst a private individual may make use of the services of a

financial advisor or a financial institution which offers portfolio management services.

Portfolio management involves deciding what assets to include in the portfolio, given

the goals of the portfolio owner and changing economic conditions. Selection involves

deciding what assets to purchase, how many to purchase, when to purchase them, and

what assets to divest. These decisions always involve some sort of performance

measurement, most typically expected return on the portfolio, and the risk associated with

this return (i.e. the standard deviation of the return). Typically the expected return from

portfolios of different asset bundles are compared.

The unique goals and circumstances of the investor must also be considered. Some

investors are more risk averse than others.

Portfolio formation

Many strategies have been developed to form a portfolio.

equally-weighted portfolio

capitalization-weighted portfolio

price-weighted portfolio

optimal portfolio (for which the Sharpe ratio is highest)

It is most important for economic developments.

Models

Some of the financial models used in the process of Valuation, stock selection, and

management of portfolios include:

Maximizing return, given an acceptable level of risk.

Modern portfolio theory—a model proposed by Harry Markowitz among others.

The single-index model of portfolio variance.

10

Capital asset pricing model.

Arbitrage pricing theory.

The Jensen Index.

The Treynor Index.

The Sharpe Diagonal (or Index) model.

Value at risk model.

Returns

There are many different methods for calculating portfolio returns. A traditional method

has been using quarterly or monthly money-weighted returns. A money-weighted return

calculated over a period such as a month or a quarter assumes that the rate of return over

that period is constant. As portfolio returns actually fluctuate daily, money-weighted

returns may only provide an approximation to a portfolio’s actual return. These errors

happen because of cashflows during the measurement period. The size of the errors

depends on three variables: the size of the cashflows, the timing of the cashflows within

the measurement period, and the volatility of the portfolio.

A more accurate method for calculating portfolio returns is to use the true time-weighted

method. This entails revaluing the portfolio on every date where a cashflow takes place

(perhaps even every day), and then compounding together the daily returns.

Attribution

Performance Attribution explains the active performance (i.e. the benchmark-relative

performance) of a portfolio. For example, a particular portfolio might be benchmarked

against the S&P 500 index. If the benchmark return over some period was 5%, and the

portfolio return was 8%, this would leave an active return of 3% to be explained. This 3%

active return represents the component of the portfolio's return that was generated by the

investment manager (rather than by the benchmark).

11

There are different models for performance attribution, corresponding to different

investment processes. For example, one simple model explains the active return in

"bottom-up" terms, as the result of stock selection only. On the other hand, sector

attribution explains the active return in terms of both sector bets (for example, an

overweight position in Materials, and an underweight position in Financials), and also

stock selection within each sector (for example, choosing to hold more of the portfolio in

one bank than another).

Market portfolio

A market portfolio is a portfolio consisting of a weighted sum of every asset in the

market, with weights in the proportions that they exist in the market (with the necessary

assumption that these assets are infinitely divisible).

Neha Tyagi's critique (1977) states that this is only a theoretical concept, as to create a

market portfolio for investment purposes in practice would necessarily include every

single possible available asset, including real estate, precious metals, stamp collections,

jewelry, and anything with any worth, as the theoretical market being referred to would

be the world market. As a result, proxies for the market (such as the FTSE100 in the UK,

DAX in Germany or the S&P500 in the US) are used in practice by investors. Roll's

critique states that these proxies cannot provide an accurate representation of the entire

market.

The concept of a market portfolio plays an important role in many financial theories and

models, including the Capital asset pricing model where it is the only fund in which

investors need to invest, to be supplemented only by a risk-free asset (depending upon

each investor's attitude towards risk).

!

12

Risk management

Example of risk management: NASA's

illustration showing high impact risk

areas for the International Space

Station".

Risk Management is the identification, assessment, and prioritization of risks followed

by coordinated and economical application of resources to minimize, monitor, and

control the probability and/or impact of unfortunate events. Risks can come from

uncertainty in financial markets, project failures, legal liabilities, credit risk, accidents,

natural causes and disasters as well as deliberate attacks from an adversary. Several risk

management standards have been developed including the Project Management Institute,

the National Institute of Science and Technology, actuarial societies, and ISO standards.[ Methods, definitions and goals vary widely according to whether the risk management

method is in the context of project management, security, engineering, industrial

processes, financial portfolios, actuarial assessments, or public health and safety.

For the most part, these methodologies consist of the following elements, performed,

more or less, in the following order.

13

1. identify, characterize, and assess threats

2. assess the vulnerability of critical assets to specific threats

3. determine the risk (i.e. the expected consequences of specific types of attacks on

specific assets)

4. identify ways to reduce those risks

5. prioritize risk reduction measures based on a strategy

The strategies to manage risk include transferring the risk to another party, avoiding the

risk, reducing the negative effect of the risk, and accepting some or all of the

consequences of a particular risk.

Risk management also faces difficulties allocating resources. This is the idea of

opportunity cost. Resources spent on risk management could have been spent on more

profitable activities. Again, ideal risk management minimizes spending while

maximizing the reduction of the negative effects of risks.

Principles of risk management

The International Organization for Standardization identifies the following principles of

risk management:

Risk management should create value.

Risk management should be an integral part of organizational processes.

Risk management should be part of decision making.

Risk management should explicitly address uncertainty.

Risk management should be systematic and structured.

Risk management should be based on the best available information.

Risk management should be tailored.

Risk management should take into account human factors.

Risk management should be transparent and inclusive.

Risk management should be dynamic, iterative and responsive to change.

Risk management should be capable of continual improvement and enhancement.

14

Process of Risk Management:

According to the standard ISO 31000 "Risk management -- Principles and guidelines on

implementation", the process of risk management consists of several steps as follows:

01.Establishing the context

1. Identification

2. Planning.

3. Mapping out

4. Defining a framework.

5. Developing an analysis.

6. Mitigation

02.Identification

Source analysis.

Problem analysis[Objectives-based risk identification.

Scenario-based risk identification

Taxonomy-based risk identification

Common-risk checking.

Risk charting (risk mapping

03. Assessment

04. Potential risk treatments

Avoidance (eliminate)

Reduction (mitigate)

Transfer (outsource or insure)

Retention (accept and budget)

15

05.Risk avoidance

06.Risk reduction

07.Risk retention

08.Risk transfer

Create a risk-management plan

Implementation

Review and evaluation of the plan

.

Limitations

If risks are improperly assessed and prioritized, time can be wasted in dealing with risk of

losses that are not likely to occur. Spending too much time assessing and managing

unlikely risks can divert resources that could be used more profitably. Unlikely events do

occur but if the risk is unlikely enough to occur it may be better to simply retain the risk

and deal with the result if the loss does in fact occur. Qualitative risk assessment is

subjective and lack consistency. The primary justification for a formal risk assessment

process is legal and bureaucratic.

Modern portfolio theory

Modern portfolio theory (MPT) proposes how rational investors will use diversification

to optimize their portfolios, and how a risky asset should be priced. The basic concepts of

the theory are Markowitz diversification, the efficient frontier, capital asset pricing

16

model, the alpha and beta coefficients, the Capital Market Line and the Securities Market

Line.

MPT models an asset's return as a random variable, and models a portfolio as a weighted

combination of assets so that the return of a portfolio is the weighted combination of the

assets' returns. Moreover, a portfolio's return is a random variable, and consequently has

an expected value and a variance. Risk, in this model, is the standard deviation of return.

Risk and return

The model assumes that investors are risk averse, meaning that given two assets that offer

the same expected return, investors will prefer the less risky one. Thus, an investor will

take on increased risk only if compensated by higher expected returns. Conversely, an

investor who wants higher returns must accept more risk. The exact trade-off will differ

by investor based on individual risk aversion characteristics. The implication is that a

rational investor will not invest in a portfolio if a second portfolio exists with a more

favorable risk-return profile – i.e., if for that level of risk an alternative portfolio exists

which has better expected returns.

Mean and variance

It is further assumed that investor's risk / reward preference can be described via a

quadratic utility function. The effect of this assumption is that only the expected return

and the volatility (i.e., mean return and standard deviation) matter to the investor. The

investor is indifferent to other characteristics of the distribution of returns, such as its

skew (measures the level of asymmetry in the distribution) or kurtosis (measure of the

thickness or so-called "fat tail").

Note that the theory uses a parameter, volatility, as a proxy for risk, while return is an

expectation on the future. This is in line with the efficient market hypothesis and most of

the classical findings in finance such as Black and Scholes European Option Pricing

17

(martingale measure: in short means that the best forecast for tomorrow is the price of

today). Recent innovations in portfolio theory, particularly under the rubric of Post-

Modern Portfolio Theory (PMPT), have exposed several flaws in this reliance on

variance as the investor's risk proxy:

The theory uses a historical parameter, volatility, as a proxy for risk, while return is an

expectation on the future. (It is noted though that this is in line with the and efficiency

hypothesis most of the classical findings in finance which make use of the martingale

measure, i.e. the assumption that the best forecast for tomorrow is the price of today).

The statement that "the investor is indifferent to other characteristics" seems not

to be true given that skewness risk appears to be priced by the market

Under the model:

Portfolio return is the proportion-weighted combination of the constituent assets'

returns.

Portfolio volatility is a function of the correlation ρ of the component assets. The

change in volatility is non-linear as the weighting of the component assets

changes.

Mathematically

In general:

Expected return:-

Where Ri is return and wi is the weighting of component asset i.

Portfolio variance:-

,

where i≠j. Alternatively the expression can be written as:

,

where ρij = 1 for i=j.

Portfolio volatility:-

18

For a two asset portfolio:-

Portfolio return:

Portfolio variance:

matrices are preferred for calculations of the efficient frontier. In matrix form, for a given "risk

tolerance" , the efficient front is found by minimizing the following expression:

where

w is a vector of portfolio weights. Each and

∑ wi = 1

i

Σ is the covariance matrix for the assets in the portfolio

q is a "risk tolerance" factor, where 0 results in the portfolio with minimal risk and

results in the portfolio with maximal return

R is a vector of expected returns

The front is calculated by repeating the optimization for various .

Many software packages, including Microsoft Excel, MATLAB, Mathematica and R, provide

optimization routines suitable for the above problem.

Capital allocation line

19

The capital allocation line (CAL) is the line of expected return plotted against risk

(standard deviation) that connects all portfolios that can be formed using a risky asset and

a riskless asset. It can be proven that it is a straight line and that it has the following

equation.

In this formula P is the risky portfolio, F is the riskless portfolio, and C is a combination

of portfolios P and F.

The efficient frontier

Efficient Frontier. The hyperbola is sometimes referred to as the 'Markowitz Bullet'

Every possible asset combination can be plotted in risk-return space, and the collection of

all such possible portfolios defines a region in this space. The line along the upper edge

of this region is known as the efficient frontier (sometimes "the Markowitz frontier").

Combinations along this line represent portfolios (explicitly excluding the risk-free

alternative) for which there is lowest risk for a given level of return. Conversely, for a

given amount of risk, the portfolio lying on the efficient frontier represents the

combination offering the best possible return. Mathematically the Efficient Frontier is

the intersection of the Set of Portfolios with Minimum Variance (MVS) and the Set of

Portfolios with Maximum Return. Formally, the efficient frontier is the set of maximal

elements with respect to the partial order of product order on risk and return, the set of

portfolios for which one cannot improve both risk and return.

20

The efficient frontier is illustrated above, with return μp on the y-axis, and risk σp on the

x-axis; an alternative illustration from the diagram in the CAPM article is at right.

The efficient frontier will be convex – this is because the risk-return characteristics of a

portfolio change in a non-linear fashion as its component weightings are changed. (As

described above, portfolio risk is a function of the correlation of the component assets,

and thus changes in a non-linear fashion as the weighting of component assets changes.)

The efficient frontier is a parabola (hyperbola) when expected return is plotted against

variance (standard deviation).

The region above the frontier is unachievable by holding risky assets alone. No portfolios

can be constructed corresponding to the points in this region. Points below the frontier

are suboptimal. A rational investor will hold a portfolio only on the frontier.

The risk-free asset

The risk-free asset is the (hypothetical) asset which pays a risk-free rate. It is usually

provided by an investment in short-dated Government securities. The risk-free asset has

zero variance in returns (hence is risk-free); it is also uncorrelated with any other asset

(by definition: since its variance is zero). As a result, when it is combined with any other

asset, or portfolio of assets, the change in return and also in risk is linear.

Because both risk and return change linearly as the risk-free asset is introduced into a

portfolio, this combination will plot a straight line in risk-return space. The line starts at

100% in the risk-free asset and weight of the risky portfolio = 0 (i.e., intercepting the

return axis at the risk-free rate) and goes through the portfolio in question where risk-free

asset holding = 0 and portfolio weight = 1.

Portfolio leverage

21

An investor adds leverage to the portfolio by borrowing the risk-free asset. The addition

of the risk-free asset allows for a position in the region above the efficient frontier. Thus,

by combining a risk-free asset with risky assets, it is possible to construct portfolios

whose risk-return profiles are superior to those on the efficient frontier.

An investor holding a portfolio of risky assets, with a holding in cash, has a

positive risk-free weighting (a de-leveraged portfolio). The return and standard

deviation will be lower than the portfolio alone, but since the efficient frontier is

convex, this combination will sit above the efficient frontier – i.e., offering a

higher return for the same risk as the point below it on the frontier.

The investor who borrows money to fund his/her purchase of the risky assets has

a negative risk-free weighting – i.e., a leveraged portfolio. Here the return is

geared to the risky portfolio. This combination will again offer a return superior to

those on the frontier.

The market portfolio

The efficient frontier is a collection of portfolios, each one optimal for a given amount of

risk. A quantity known as the Sharpe ratio represents a measure of the amount of

additional return (above the risk-free rate) a portfolio provides compared to the risk it

carries. The portfolio on the efficient frontier with the highest Sharpe Ratio is known as

the market portfolio, or sometimes the super-efficient portfolio; it is the tangency-

portfolio in the above diagram. This portfolio has the property that any combination of it

and the risk-free asset will produce a return that is above the efficient frontier—offering a

larger return for a given amount of risk than a portfolio of risky assets on the frontier

would.

Capital market line

22

When the market portfolio is combined with the risk-free asset, the result is the Capital

Market Line. All points along the CML have superior risk-return profiles to any portfolio

on the efficient frontier. Just the special case of the market portfolio with zero cash

weighting is on the efficient frontier. Additions of cash or leverage with the risk-free

asset in combination with the market portfolio are on the Capital Market Line. All of

these portfolios represent the highest possible Sharpe ratio. The CML is illustrated above,

with return μp on the y-axis, and risk σp on the x-axis.

One can prove that the CML is the optimal CAL and that its equation is

Asset pricing

A rational investor would not invest in an asset which does not improve the risk-return

characteristics of his existing portfolio. Since a rational investor would hold the market

portfolio, the asset in question will be added to the market portfolio. MPT derives the

required return for a correctly priced asset in this context.

Systematic risk and specific risk

Specific risk is the risk associated with individual assets - within a portfolio these risks

can be reduced through diversification (specific risks "cancel out"). Specific risk is also

called diversifiable, unique, unsystematic, or idiosyncratic risk. Systematic risk (a.k.a.

portfolio risk or market risk) refers to the risk common to all securities - except for

selling short as noted below, systematic risk cannot be diversified away (within one

market). Within the market portfolio, asset specific risk will be diversified away to the

extent possible. Systematic risk is therefore equated with the risk (standard deviation) of

the market portfolio.

Since a security will be purchased only if it improves the risk / return characteristics of

the market portfolio, the risk of a security will be the risk it adds to the market portfolio.

In this context, the volatility of the asset, and its correlation with the market portfolio, is

historically observed and is therefore a given (there are several approaches to asset

23

pricing that attempt to price assets by modelling the stochastic properties of the moments

of assets' returns - these are broadly referred to as conditional asset pricing models). The

(maximum) price paid for any particular asset (and hence the return it will generate)

should also be determined based on its relationship with the market portfolio.

Systematic risks within one market can be managed through a strategy of using both long

and short positions within one portfolio, creating a "market neutral" portfolio.

Capital asset pricing model

The asset return depends on the amount for the asset today. The price paid must ensure

that the market portfolio's risk / return characteristics improve when the asset is added to

it. The CAPM is a model which derives the theoretical required return (i.e., discount rate)

for an asset in a market, given the risk-free rate available to investors and the risk of the

market as a whole.

Limations of CAPM:

CAPM has the following limitations:

01. It is based on unrealisic assumptions.

02. It is difficult to test the validity of CAPM.

03. Betas do not remain stable over time.

24

Securities market line

The SML essentially graphs the results from the capital asset pricing model (CAPM)

formula. The x-axis represents the risk (beta), and the y-axis represents the expected

return. The market risk premium is determined from the slope of the SML.

The relationship between β and required return is plotted on the securities market line

(SML) which shows expected return as a function of β. The intercept is the nominal risk-

free rate available for the market, while the slope is E(Rm − Rf). The securities market line

can be regarded as representing a single-factor model of the asset price, where Beta is

exposure to changes in value of the Market. The equation of the SML is thus:

It is a useful tool in determining if an asset being considered for a portfolio offers a

reasonable expected return for risk. Individual securities are plotted on the SML graph. If

the security's risk versus expected return is plotted above the SML, it is undervalued

since the investor can expect a greater return for the inherent risk. And a security plotted

below the SML is overvalued since the investor would be accepting less return for the

amount of risk assumed.

Applications to project portfolios and other "non-financial" assets

Some experts apply MPT to portfolios of projects and other assets besides financial

instruments. When MPT is applied outside of traditional financial portfolios, some

differences between the different types of portfolios must be considered.

1. The assets in financial portfolios are, for practical purposes, continuously

divisible while portfolios of projects like new software development are "lumpy".

For example, while we can compute that the optimal portfolio position for 3

stocks is, say, 44%, 35%, 21%, the optimal position for an IT portfolio may not

25

allow us to simply change the amount spent on a project. IT projects might be all

or nothing or, at least, have logical units that cannot be separated. A portfolio

optimization method would have to take the discrete nature of some IT projects

into account.

2. The assets of financial portfolios are liquid can be assessed or re-assessed at any

point in time while opportunities for new projects may be limited and may appear

in limited windows of time and projects that have already been initiated cannot be

abandoned without the loss of the sunk costs (i.e., there is little or no

recovery/salvage value of a half-complete IT project).

Neither of these necessarily eliminate the possibility of using MPT and such portfolios.

They simply indicate the need to run the optimization with an additional set of

mathematically-expressed constraints that would not normally apply to financial

portfolios.

Furthermore, some of the simplest elements of Modern Portfolio Theory are applicable to

virtually any kind of portfolio. The concept of capturing the risk tolerance of an investor

by documenting how much risk is acceptable for a given return could be and is applied to

a variety of decision analysis problems. MPT, however, uses historical variance as a

measure of risk and portfolios of assets like IT projects don't usually have an "historical

variance" for a new piece of software. In this case, the MPT investment boundary can be

expressed in more general terms like "chance of an ROI less than cost of capital" or

"chance of losing more than half of the investment". When risk is put in terms of

uncertainty about forecasts and possible losses then the concept is transferable to various

types of investment.

26

Applications of Modern Portfolio Theory in Other Disciplines

In the 1970s, concepts from Modern Portfolio Theory found their way into the field of

regional science. In a series of seminal works, Michael Conroy modeled the labor force in

the economy using portfolio-theoretic methods to examine growth and variability in the

labor force. This was followed by a long literature on the relationship between economic

growth and volatility.

More recently, modern portfolio theory has been used to model the self-concept in social

psychology. When the self attributes comprising the self-concept constitute a well-

diversified portfolio, then psychological outcomes at the level of the individual such as

mood and self-esteem should be more stable than when the self-concept is undiversified.

This prediction has been confirmed in studies involving human subjects.

Comparison with arbitrage pricing theory

The SML and CAPM are often contrasted with the arbitrage pricing theory (APT), which

holds that the expected return of a financial asset can be modeled as a linear function of

various macro-economic factors, where sensitivity to changes in each factor is

represented by a factor specific beta coefficient.

The APT is less restrictive in its assumptions: it allows for an explanatory (as opposed to

statistical) model of asset returns, and assumes that each investor will hold a unique

portfolio with its own particular array of betas, as opposed to the identical "market

portfolio". Unlike the CAPM, the APT, however, does not itself reveal the identity of its

priced factors - the number and nature of these factors is likely to change over time and

between economies.

27

Conclusion:

In fact risk and return are the most important concepts in finance and financial

management. The difficulty is to calculate the degree of risk and the degree of

return and to relate these two things. For the measurement, the assumptions have a

great impact on it. The more precise and logical the assumption is, the

measurement is more likely to be of use. And the more the measurement is

precise, the more likely the decision is to be logical and fruitful.

28

Bibliography:

Text Books:

1. Pandey,I,M, 2001 Financial Management, eighth edition, Delhi, Vikash

Publishing House pvt Ltd.

2. Brigham,Eugine, F and Houston, Joel, F. Fundamentals of financial management

tenth edition, Singapore, south weastern, thomson

Websites:

1. www.investopedia.com/terms/p/portfoliomanagement.asp

2. en.wikipedia.org/wiki/Portfolio_management

3. en.wikipedia.org/wiki/IT_portfolio_management

4. www.npd-solutions.com/portfolio.html

5. www.corporateportfoliomanagement.org/

6. www.bitpipe.com/tlist/Portfolio-Management-(Finance).html

7. en.wikipedia.org/wiki/Portfolio_(finance)

8. www.performance-measurement.org/

9. www.euromoneytraining.com/default.asp?Page=16&productid... –

10. www.amazon.com/...Portfolio-Performance-Measurement.../

0470856793

11. www.financial-conferences.com/events/E54554.htm?...

29