SUBJECT:

PORTFOLIO INVESTMENT

TOPIC:

SELECTION OF OPTIMAL PORTFOLIO

INSTRUCTOR:

SIR AHMED GILANI

SUBMITEED BY:

MUHAMMAD TAQI

ROLL NO:

7229

CLASS :

MBA 5th (Evening)

SUBMISSION DATE: 26-01-2013

DEPARTMENT OF BANKING AND FINANCE

1

Dedication

I dedicate this project to

Almighty Allah, the Creator of this Universe,

And

Hazrat Muhammad (P.B.U.P), the cause of

The creation of the Universe

And

To my parents,

To the persons who love me, persons to whom

I love and for all those who pray for me.

2

ACKNOWLEDGEMENT

In the name of Allah Almighty the creature of this universe, our best and greatest well wisher, the most beneficent, Merciful and omnipotent. I hereby acknowledge that the Allah Almighty has bestowed us with the courage and ability to ponder over the already existing ocean of knowledge. Peace and Blessings upon the Holy Prophet MUHAMMAD (Peace Be Upon Him) His family and the dearest Companions, Who are the beacon of knowledge and wisdom who showed true path to their followers and are a torch of guidance for humanity till eternity.

This project is done as a semester project, as a part of course titled “Portfolio Management”. I would like to show my greatest appreciation and really thankful to my course instructor Sir Ahmed Gillani, Professor, Department of Banking And Finance, Government College University Faisalabad, for his tremendous assistance and invaluable guidance , without which the accomplishment of the task would have never been possible. I also thank him for giving this opportunity to work on this project & and providing sagacious suggestions step-to-step guidance and close supervision during the project.

This project is based largely on the selection of an optimal portfolio among five portfolios randomly selected from Karachi stock exchange of Pakistan. The Falcons is very grateful to Brokerage firm consultants Mr.Shahzad Anwar and Mr. Rizwan who provide us sufficient knowledge about different listed companies and their securities that are traded in KSE.

I am also thankful Mr Waqar Hassan coordinator of Audit Department in Sadaqat Textile Limited who assists and guide me towards completion of this project.

Have no words to express our love and gratitude to our parents and elders whose prayers enable us to achieve our goals. I find no word to express my gratitude and profound admiration to my fellows for their support to carry our self throughout the project.

Finally, yet importantly, I would like to express my heartfelt thanks to my

beloved parents for their blessings, my friends/classmates for their help and

wishes for the successful completion of this project.

3

TABLE OF CONTENT

Sr. No

Topic Page No

01 Acknowledgement02 Executive Summary 0103 Introduction 0304 Subject Introduction

What is portfolio? Portfolio Management Objective of Portfolio Management

03030303

05 Project Introduction 0406 Investment Income and Risk 0507 Expected Return Or Return on Investment

Dividend Per Share Total Return Average Return (Mean and Geometric Mean)

05050506

08 Investment Risk 0609 Types of Risk

Systematic Risk Non Systematic Risk

060606

10 Measurement of Investment Risk

Standard Deviation Variance

080808

11 Pakistan Economic Indicators (est.2011) 0912 KSE sector Study and Company Selection 1013 Oil And Gas Sector

Pakistan Petroleum Limited Expected Return and Risk

101010

14 Food Producer Sector

Unilever Pakistan Limited Expected Return and Risk

131313

15 Chemical Sector

Biafo Industries Limited Expected Return and Risk

151515

16 Pharma and Biotech Sector

Wyeth Pakistan Limited 1717

4

Expected Return and Risk 17

17 Automobile and Parts Sector

Atlas Battery Limited Expected Return and Risk

191920

18 KSE Market Capitalization (2011) 2119 Relationship Between Risk And Return 2220 Covariance

Positive Covariance Negative Covariance Zero Covariance

22222223

21 Co-efficient of Correlation

Perfect Positive Correlation Perfect Negative Correlation No Correlation Strong and Weak Correlation

2323232424

22 Graphical presentation of various Types of Correlation 2523 Portfolio Return and Risk Using Markowitz Model

Expected Rate of Return of Portfolio Portfolio Risk

262626

24 Methodology Company Name, Code, Return, Risk and Weight Variance Covariance Matrix for portfolio

Management Calculation of Portfolio Expected Return Calculation of Portfolio Risk

2727272828

25 How to Select an Optimal Portfolio? Efficient Frontier Maximum Return at Given Level of Risk Minimum Risk at Given Level of Return

30303031

26 Portfolio Strategies Passive Strategies Active Strategies

333333

27 Suggestion and Recommendation 3428 Bibliography/ Appendix 3529 Comments 36

5

Executive Summary

This report illustrates a broader as well as detailed view about a selection optimal portfolio of securities that are traded in Karachi stock exchange of Pakistan. There are 34 sectors and 651 companies are listed in KSE.

Karachi Stock Exchange 100 Index (KSE-100 Index) is a most important stock market index of Pakistan, which acts as a benchmark for comparing prices at KSE over a period of time. The primary objective of the KSE-100 index is to have a benchmark by which the stock price performance can be compared to over a period of time. In particular, the KSE 100 is designed to provide investors with a sense of how the Pakistan equity market is performing.

The KSE-100 Index was introduced in November 1991 with base value of 1,000 points. The Index comprises of 100 companies selected on the basis of sector representation and highest market capitalization, which track over 90% of the total market capitalization of the companies listed on the Exchange.

Stock Selection Rules

The selection criteria for stock inclusion in the existing KSE-100 Index is based on two main rules, namely sector rule & capitalization rule.

1. Sector Rule

Under this rule, largest market capitalization in each sector (33) of KSE excluding Open-end Mutual Fund Sector is considered for inclusion in KSE-100.

2. The Largest Capitalization Rule

The remaining index (67) places are taken up by the largest market capitalization companies in descending order.

In this project we are considering to investing in 5 companies from

different sectors, for this purpose we make four portfolios A, B, C, D and E. Each

portfolio comprises of 5 different companies from different sectors selected on

6

basis of E.P.S, company’s annual net sales, dividend payout ratio and company’s

overall financial position. Historical data from first January 2007 to 31 June 2011

reveal that the return from each asset has fluctuated over time.

The basic purpose of this project is to make an efficient portfolio investment. For this purpose I collect the data from KSE official website and annual reports of the selected companies after analyzing sectors and company individual performance. I have calculated selected companies return and risk through Ms excel and presented graphically.

7

INTRODUCTION

Subject Introduction

What is Portfolio?A portfolio refers to a collection of investment tools such as in stocks,

bonds and mutual fund. It means that we invest resources safely in different securities. The main purpose of portfolio is to diversify the risk by making portfolio investment.

Portfolio ManagementThe skill of selecting the right investment policy for the individuals in terms

of minimum risk and maximum return is called as portfolio management. Portfolio management refers to managing an individual’s investments in

the form of bonds, shares, mutual funds etc so that he earns the maximum profits within the predetermined time frame.

The management of portfolio means how to manage the different sectorial investment under the expert guidance of portfolio managers.

“Portfolio management” course objective is to help entrepreneurs and investors to understand the investments field as it is currently understood and practiced for sound investment decisions making. Following this objective, key concepts are presented to provide an appreciation of the theory and practice of investments, focusing on investment portfolio formation and management issues. This course is designed to emphasize both theoretical and analytical aspects of investment decisions and deals with modern investment theoretical concepts and instruments. Both descriptive and quantitative materials on investing are presented.

Objectives Portfolio management

To describe and to analyze the investment environment, different types of investment vehicles

8

To understand and to explain the logic of investment process and the contents of its’ each stage

To use the quantitative methods for investment decision making – to calculate risk and expected return of various investment tools and the investment portfolio

To analyze and to evaluate relevance of stocks, bonds, options for the investments

To know active and passive investment strategies and to apply them in practice.

 To minimizes the risks involved in investing and also increases the chance of making profits

Project Introduction

This project “Investment Analysis and Portfolio Management” is given by my respectful teacher Sir Ahmed Gillani. Basically this project is based on optimal portfolio selection of different securities. For this purpose I have selected five companies listed in Karachi Stock Exchange and these selected companies are belonging to different sectors. These companies are selected according to their performance on basis of expected return and their risk. These companies under their sectors are as follows:

1. Oil & Gas Sector Pakistan Petroleum Limited

2. Food Producer Sector Unilever Pakistan Limited

3. Chemical Sector Biafo Industries Limited

4. Pharmacy and Bio Technology Sector Wyeth

5. Automobile and Parts Sector Atlas Battery Limited

To understand and achieve the goal and purpose of this project first of all I have to study the all sectors in KSE and the selected company performance. In this project I have found the expected return and risk associated with the particular securities. For calculation of expected return and risk of company I must know that how much dividend against per share by company and how much fluctuation in share price. If the share price goes up then there is a capital

9

gain otherwise there is a capital loss. For the calculation of expected return I used Geometric mean and standard deviation is used for determined the risk associated a particular stock.

After that I have determined the portfolio Risk and return by using Markowitz Model and make an optimal portfolio investment.

Investment Income and Risk

A return is the ultimate objective for any investor. But a relationship between return and risk is a key concept for investment. However to compare various alternatives of investments the precise quantitative measures for both of these characteristics are needed.

Return on Investment and Expected Rate of Return

General definition of return is the benefit associated with an investment. Return on Investment that means if one invests money or resources then what return would be expected from that investment. In simple words, what profits will be generated form that investment. When we are going to invest in a risky business then we should estimate how much return on investment.

The most important factor that affects the return on investment is inflation. We know that the value of today money is more than the value of tomorrow money due to inflation. So, the return should be over and above the inflation level. If inflation rate is 10% then return should be above 10%. In most cases the investor can estimate his/ her historical return precisely.

Many investments have two components of their measurable return:

Yield (Profit or interest) A capital gain or loss

Rate of return = yield + Capital gains / Purchase price (%)

OR

10

TR (%) =

Yield +

(Price Ending-Price Beginning)

Price Beginning

(%)

By using this formula, we can calculate what return in is given period. In this formula yield means how much dividend paying per share. Dividend per share can be calculated by this formula:

Dividend Paid calculated from financing activities of Cash flow statement and No. of outstanding shares calculated from balance sheet where share capital divided by the par value of shares issued by the company.

Average Return

Average return is require when an investor want to compare the series of return. There are two methods to calculate the average return:

1. Arithmetic Mean is used to compare cross-sectional data. When there is low fluctuation of returns in historical data.

2. Geometric Mean is used to compare time series data. When there is more fluctuation of returns in different years or historical data.

11

DPS=

Dividend Paid During yearNo. of Outstanding Shares

A.M (K)=

ƩKn

Risk on Investment

Risk can be defined as a chance that the actual outcome from an investment will differ from the expected outcome. Obviously, that most investors are concerned that the actual outcome will be less than the expected outcome.

Types of Risk

Generally there are two types of Risk.

Systematic Risk

Systematic risk is a risk which is inherent in financial markets. It is also called an external risk. This type of risk is generally uncontrollable, unavoidable and undiversifiable (Purchasing power risk, interest rate risk, liquidity risk, etc.)

Suppose when we invest in diversified portfolio consisting KSE-100 index. There are some risks that index fund will be going up and down. If the economy is going up and down it affects the stock price.

Non Systematic Risk

Non systematic risk is a risk with is associated to a given stock such (Business risk, financial risk, other risks, related to investment into particular asset).Suppose if the CEO of a company resign where we have invested. Such type of risk refers to non systematic risk.

Unsystematic risk can be diversified away by holding many different assets in the portfolio, however systematic risk can’t be diversified

Total Risk= Systematic Risk+ Non Systematic Risk

12

G.M (K)=

{(1+K1)(1+K2)(1+K3)(1+K4)

(1+Kn)}

11n

Diagram of Total Risk

In the above diagram, vertical axis show risk and the horizontal axis show the No of securities. When we move from 1 security to more than the non systemic risk will be reduce until it equal to zero, while the systematic risk cannot be control.

Measurement of Investment Risk

The total risk of investments can be measured with such common absolute measures used in statistics as:

Standard deviation.

13

Co-efficient of Variance

Standard deviation

Generally, Standard deviation is used to measure the risk of investment. When two variables are flow in same direction then we used Standard Deviation for risk measurement.

For example, compare of Inflation in Pakistan & inflation in India.

Co-efficient of Variance

Co-efficient of Variance can be calculated as a potential deviation of each possible investment rate of return from the expected rate of return. When two variables are flow in opposite direction then we used co-efficient of variance for risk measurement.

For example inflation of Pakistan Vs Inflation of Japan

14

S.D=

Ʃ(K K)n

C.V=

S.DK

Pakistan Economic Indicators (Est.2011)

The investors and analysts must watch macroeconomic statistics such as the money supply, inflation, interest rates, unemployment, changes in GDP, political events and many others. Reason for this might be their belief that new information about the changes in these macroeconomic indicators will influence future asset price movements.

Inflation and its effect on Portfolio

Inflation rate is 13.7% in Pakistan during the year 2011. Inflation is the most important factor for investment. If there is high inflation rate in country it will decrease the return on investment. If there is 10% inflation then return should be 10% above.

Unemployment rate

6%

Gross Domestic Product – GDP

2.4%GDP - composition by sector

Agriculture: 21.6% 

Industry: 25.3% 

Services: 53.1%

By investing in different sectors, the investor must see the sector performance where he wants to invest. High performance and growth rate sectors can contribute more than low level growth rate sectors. It also helpful to increase the GDP, when the investors invest in right sectors.

Discount rate 13.50% ( 10-Dec-11 )

Discount rate is another factor of investment. Discount rate is a rate at which investors can borrow money from different institutions. So the investor must compare the return on investment with the current discount rate. After calculating expected return and investor found that the expected rate of return is less than the discount rate then investor should not invest in that securities.

15

Sectors Study And Company Selection

1. Oil & Gas Producer Sector:

In this sector 12 companies are listed at the Stock exchange. The sector is performing doing well because of rising demand, higher exploration and global prices. Its index fluctuated between12, 523 to 12,166 between July-March 2010-11 and market capitalization inched up from Rs. 1,042.3 million to Rs. 1,051.7 million. Pakistan based oil and gas sector have shown healthy profits due to upward movement of prices. During the year sector shows the profit after tax of Rs.104.2 billion. The sector also has the largest paid companies like OGDCL, PPL, POL, etc. and the total paid up capital of this sector is Rs.65.2 billion. Oil and Gas sector continued to be one of the major market players.

By studying this sector, I have selected Pakistan Petroleum Limited for the Portfolio Project.

Pak Petroleum Limited

Company Name: Pakistan Petroleum LimitedCompany Symbol: PKLSector: Oil and Gas SectorSector Code: 0530Include Top 25 companies in KSE: 2006,2007,2008,2009, 2010 & 2011

Pakistan Petroleum Limited (PPL) has been a frontline player in the energy sector since the mid-1950s. PPL is fall in top 25 best performing Companies in KSE (2000-2011) on the basis of comprehensive criteria which includes dividend payout, capital efficiency, profitability, free-float shares, and transparency & investors relations.

As a major supplier of natural gas, PPL today contributes around 24 percent of the country’s total natural gas supplies besides producing crude oil, Natural Gas Liquid and Liquefied Petroleum Gas.

PPL operates six producing fields across the country at Sui (Pakistan’s largest gas field), Adhi, Kandhkot, Chachar, Mazarani and Hala and holds working interest in thirteen partner-operated producing fields, including Qadirpur the country’s second largest gas field.

16

Dividend per Share and Share Price

The company Dividend per share and share price at the end of the year.

Years 2006 2007 2008 2009 2010 2011Dividend 9 11 15 13 9 12Stock price 211.85 262.45 245.99 189.54 184.12 207.07

TR(%)=yield+(Pe-Pb)/Pb  0.2907

7-

0.00556-

0.17663 0.01889 0.18982

Expected Return (G.M) & Risk (S.D)

G. Mean 5.08%Standard Deviation 16.30%Variance 3.21Range 0.467

17

Diagram

2007 2008 2009 2010 2011

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Return Expected Return

2007 2008 2009 2010 2011

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Column1total return

18

2. Food Producers Sector: The sector having 61 sugar dominated companies posted total after tax

profit of Rs.11.9 billion. The share index moved up from 12,625 to 19,824 during July-March 2010-11. Its market capitalization increased by 58.2 percent to 282.9 billion.

For the portfolio investment purpose I have selected Unilever Pakistan Limited because according to historical data and performance of this company is much better than other company in food sectors.

Unilever Pakistan Limited

Company Name: Unilever Pakistan LimitedCompany Symbol: ULEVERSector: Food Producer SectorSector Code: 3570Include Top 25 companies in KSE: 2006,2007,2008,2009, 2010 & 2011

The company had a turnover of Rs. 23.3bn (Euro 309 Mn) in 2007, and enjoys a leading position in most of its core Home and Personal Care and Foods categories, e.g. Personal Wash, Personal Care, Laundry, Beverages (Tea) and Ice Cream.

The company operates through 5 regional offices, 4 wholly owned and 6 third party manufacturing sites across Pakistan.

Dividend per Share and Share Price

Years 2006 2007 2008 2009 2010 2011Dividend 122 123 123 229 246 307Stock price 2000 2280 1808 2300 4360 5566   

TR(%)=yield+(Pe-Pb)/Pb   0.20150 -0.153070.3987

8 1.002610.3470

2

Expected Return (G.M) & Risk (S.D)

G. Mean 30.88%Standard Deviation 37.84%Variance 1.23Range 1.156

19

Diagram

2007 2008 2009 2010 2011

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

total Return Expected Return

2007 2008 2009 2010

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Return

20

3. Chemical Sector: In this sector 36 companies are listed. Net income of this sector after tax in

2010-11 stood at Rs. 32.1 billion and its share index has decreased by 2.8 percent. Its market capitalization improved by Rs.113.6 billion during the July-March 2010- 11 and stood at Rs. 392.9 billion. This sector showed good profits due to tight –demand supply situation and rising fertilizers prices.

For my portfolio investment, according to above information I have chosen Biafo Industries limited.

Biafo Industries

Company Name: Biafo Industries LimitedCompany Symbol: BIFOSector: Chemical SectorSector Code: 1350

Biafo Industries Limited having its registered office at No. 203-204, 2nd Floor, Muhammad Gulistan Khan House, 82-East, Fazal-ul-Haq Road, Blue Area, Islamabad, Pakistan would like to take this opportunity to introduce their product-Tovex Water Gel Explosive manufactured at their plant located at Hattar Industrial Estate, Khyber Pakhtunkhwa, Pakistan.

The basic reason of chosen this company for my portfolio investment is that this company has a best performance by historically (data of 2006 to 2011) and it has best opportunity in chemical sectors with its core product such as Tovex Water Gel.

Dividend per Share and Share Price

Years200

6 2007 2008 2009 2010 2011Dividend 0 1 2.5 3.5 4.5 7.45Stock price 35 42.2 36.1 38.79 56.99 61.78

TR(%)=yield+(Pe-Pb)/Pb  0.2342

9

-0.0853

10.1714

70.5852

00.2147

7

Expected Return (G.M) & Risk (S.D)

G. Mean 20.56%

Standard Deviation 21.48%

21

Variance 1.045Range 0.3001

Diagram

2007 2008 2009 2010 2011

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Total Return Expected Return

2007 2008 2009 2010 2011

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Return

Return

22

4. Pharma & Biotech Sector: The sector of 9 companies showed profit after tax of Rs. 3.2 billion in year

2010. Its share index increased from 8241 to 8327 and market capitalization increased from Rs. 30.6 billion to Rs31.4 billion in the period under review.

By studying Pharma & Biotech sector I gained a lot of information about this sector to choose the company for my portfolio investment and I selected Wyeth Pakistan Limited.

Wyeth Pakistan Limited

Company Name: Wyeth Pakistan LimitedCompany Symbol: WYETHSector: Pharmacy and Biotechnology SectorSector Code: 4570

Wyeth Pakistan Limited (the company) is a public limited company incorporated in 1949 in Pakistan. The company is listed on the Karachi and Lahore Stock exchange.The Company is engaged in manufacturing and marketing of research based ethical specialties and other pharmaceutical products. With effect from October 15, 2009 Pfizer Inc. has acquired WYETH LLC, USA. According Pfizer Inc. has become the ultimate parent (USA) of the company however, Wyeth   LLC, USA continues to be the principal shareholder of the company.

Dividend per Share and Share Price

Years 2006 2007 2008 2009 2010 2011Dividend 65 130 250 0 10 40Stock price 888.38 992.86 795.47 690.95 709.63 823.28

TR(%)=yield+(Pe-Pb)/Pb  0.26394

10.05298

8 -0.1313940.04150

80.21652

1

Expected Return (G.M) & Risk (S.D)

G. Mean 7.93%Return 14.10%Variance 1.778

23

Range 0.395

Diagram

2007 2008 2009 2010 2011

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Total Return Expected Return

2007 2008 2009 2010 2011

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Return

Return

24

5. Automobile and Parts Sector

The share index comprised of 19 listed companies with KSE decreased by 11.2 percent and market capitalization decreased by 10.5 percent during the first nine months of the 2010-11. Sales statistics shows that the demand is gradually tapering off in the large automobile sector. Increase in the price of cars, rising interest rates and risk averse policy of banks amidst growing non-performing loans in the sector have contributed to this marked slowdown. The sector posted the profit of Rs.4.2 billion in the first nine months of 2010-11.

Atlas Battery limited

Company Name: Atlas Battery LimitedCompany Symbol: ATBLSector: Automobile and Parts SectorSector Code: 3350Include Top 25 companies in KSE: 2006,2007,2008,2009, 2010 & 2011

Atlas Battery Limited pioneered the manufacture of dry charged Hard Rubber batteries in Pakistan. Now the company manufactures a complete range of Polypropylene and hard rubber batteries which caters to the needs of passenger cars of varied capacities, trucks, tractors, heavy vehicles, construction and road building equipment, as well as host of stationary and industrial applications. Motorcycle batteries have also been added to this range.

The company has always been at the vanguard of development in the automotive industry in Pakistan making great strides in the field’s research and development. The   brand has, over the years, earned a solid reputation as a product of latest Japanese technology with consistently high levels of performance and reliability.

Dividend per Share and Share Price

years 2006 2007 2008 2009 2010 2011dividend 9 11 15 13 9 12

Stock price211.8

5 262.45 245.99 189.54 184.12 207.07

TR(%)=yield+(Pe-Pb)/Pb  0.2907

7 -0.00556 -0.17663 0.018890.1898

2

25

Expected Return (G.M) & Risk (S.D)

G. Mean 5.08%Return 16.30%Variance 3.21Range 0.467

Diagram

2007 2008 2009 2010 2011-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Total Return Expected Return

26

2007 2008 2009 2010 2011-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Return

Return

Market Capitalization

27

Relationship between risk and return

The expected rate of return and the standard deviation provide investor with information about the nature of the probability distribution associated with a single asset. However, all these numbers are only the characteristics of return and risk of the particular asset. But there are two important questions while we are investing in different securities:

a. How does one asset having some specific trade-off between return and risk influence the other one with the different characteristics of return and risk in the same portfolio?

b. And what could be the influence of this relationship to the investor’s portfolio?

The answers to these questions are of great importance for the investor when forming his/ her diversified portfolio. Covariance and correlation coefficient are providing the information to answer these questions. Covariance and correlation are related and they generally measure the same phenomenon – the relationship between two variables.

CovarianceCovariance is an absolute measurement of co-movement between two

securities. Covariance represents the unbounded form of relationship between two securities.

Covariance between two assets (A&B) can be calculated by this formula:

28

The range of Covariance form “-’ to “+” infinity. Though, the covariance number doesn’t tell the investor much about the relationship between the returns on the two assets if only this pair of assets in the portfolio is analyzed. It is difficult to conclude if the relationship between returns of two assets (A and B) is strong or weak, taking into account the absolute number of the sample variance. However, what is very important using the covariance for measuring relationship between two assets – the identification of the direction of this relationship.

Positive covariance (“+”)Positive number of covariance shows that rates of return of two assets are

moving to the same direction. If the covariance of tow asset is positive then investor would be not to put both of these assets to the same portfolio, because their returns move in the same direction and the risk in portfolio will be not diversified.

Negative covariance (“-”)Negative number of covariance shows that rates of return of two assets

are moving in the contrariwise directions. If the covariance of two asset is negative then the investor would be to include both of these assets to the Portfolio, because their returns move in the contrariwise directions and the risk in Portfolio could be diversified or decreased.

Zero covariance (“0”)If the zero covariance between two assets is identified it means that there

is no relationship between the rates of return of two assets. The assets could be included in the same portfolio, but it is rare case in practice and usually covariance tends to be positive or negative.

29

Cov =

AB

CR S.D SD

AB

AB

AB

Correlation Co-efficient Correlation co-efficient tells about level of significant bounded form of

relationship between two securities. The correlation coefficient between two assets A and B can be

calculated using this formula:

The important thing is that the correlation coefficient can range only from -1 to +1.

Perfect Positive CorrelationTwo variables are perfectly positively correlated if correlation coefficient is

+1 that means that the returns of two assets have a perfect positive linear relationship to each other.

Perfect Negative CorrelationPerfectly negatively correlated if correlation coefficient is -1 that means the

asset returns have a perfect inverse linear relationship to each other.

No CorrelationWhen correlation coefficient equals 0, there is no linear relationship between

the returns on the two assets. Combining two assets with zero correlation with each other reduces the risk of the portfolio.

Strong and Weak Correlation

30

CR

=

Cov

ABS.D SD A

BAB

Significant means there is a strong relationship between two securities (A and B).

Insignificant CR means there is a weak relationship between two securities (A and B).

31

-1 -0.5

0 0.5

Significant CR Significant CR insignificant CR insignificant CR

If CR ≥ -0.5 if CR≥ +0.5Significant CR insignificant CR

If CR ≤ -0.5 if CR≤ +0.5insignificant CR Significant CR

Y

X

Perfect Negative Correlation

Graphical Presentation of Various Type of Correlation

Positive Correlation

Negative Correlation

32

Perfect Positive Correlation

Y

X

Positive Correlation

Y

X

Zero Correlation

Portfolio Return and Risk Using Markowitz Model

The author of the modern portfolio theory is Harry Markowitz who introduced the analysis of the portfolios of investments in his article “Portfolio Selection” published in the Journal of Finance in 1952. Markowitz includes portfolio formation by considering the expected rate of return and risk of Individual stocks and, critically, their interrelationship as measured by correlation. Markowitz showed how it might be possible to better of these simplistic portfolios by taking into account the correlation between the returns on these stocks.

Two important fundamental assumptions Markowitz portfolio theory:

33

Negative Correlation

Y

X

Zero Correlation

The investors are assumed to prefer higher levels of return to lower levels of return, because the higher levels of return allow the investor to spend more on consumption at the end of the investment period. Thus, given two portfolios with the same standard deviation, the investor will choose the portfolio with the higher expected return.

Investors are risk averse. It means that the investor when given to choose, he will choose the investment or investment portfolio with the smaller risk.

The Expected Rate of Return on the Portfolio

The expected return on the portfolio is the sum of expected return and weighted average of all securities. We can calculate the expected rate of return on the portfolio by this formula:

Risk of the portfolio

The most often used measure for the risk of investment is standard deviation, which shows the volatility of the securities actual return from their expected return. To calculate the risk of the portfolio first of all the relationship between the securities in the same portfolio must be taken into account. The relationship between the securities can be estimated using the covariance and coefficient of correlation.

Methodology

34

K =(p)

K W K W K W K W K W

AA BB CC EEDD

S.D=

W² SD² W² SD² 2CR W W SD SD

A A A A ABB B B B++

Company Code, Return, SD and Weight

Company NameCode

K (%)SD(%) W (%) SD² W²

Pak Petroleum Limited A= 0.051 0.163 0.05 0.02657 0.0100UniLever Pakistan limited B= 0.309 0.378 0.25 0.14048 0.0625Biafo industries limited C= 0.206 0.215 0.40 0.00301 0.1600Wyeth D= 0.079 0.141 0.10 0.01988 0.0400Atlas Battery limited E= 0.304 0.512 0.20 0.10017 0.0025

Variance Co-variance Matrix for Portfolio Management

AA AB AC AD AEBA BB BC BD BECA CB CC CD CEDA DB DC DD DEEA EB EC ED EE

Portfolio Expected Return

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Variance=N2 25   Co- variance=N(N-1) 20   Unique Variance=N(N-1)/2 10

0.230611

23.06 %

Portfolio Risk Using Markowitz Model

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K =(p)

K W K W K W K W K W

AA BB CC EEDD

S.D =

(P)

SD=0.0341

7

SD=0.1

84852

18.49 %

By Adding Additional Calculation (table 1 and 2)

Additional Calculation

Correlation of Coefficient

Table 1

Code CORRELAB -0.13198AC 0.10945AD 0.99189AE 0.79842BC 0.96501BD -0.18944BE 0.01018CD 0.04107CE 0.25752DE 0.71971

Table 2

Wa².SDa²+Wb².SDb²+Wc².SDc²+Wd².SDd²+We².SD e² 0.010573

2CR ab.Wa.Wb.SD a.SD b -0.000204

2CR ac.Wa.Wc.SD a.SD c 0.000153

2CR ad.Wa.Wd.SD a.SD d 0.000228

2CR ae.Wa.We.SD a.SD e 0.001332

2CR bc.Wb.Wc.SD b.SD c 0.015687

2CR bd.Wb.Wd.SD b.SD d -0.000505

2CR be.Wb.We.SD b.SD e 0.000197

2CR cd.Wc.Wd.SD c.SD d 0.000100

2CR ce.Wc.We.SD c.SD e 0.004530

2CR de.Wd.We.SD d.SD e 0.002078

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How to Select an Optimal Portfolio

The Markowitz portfolio theory stresses on the optimal portfolio concept by assuming that the investors try to minimize risk obsessively while looking for the highest return possible. As per this theory, investors should make rational decisions for achieving maximum returns at their acceptable level of risk.

Efficient FrontierThe efficient frontier represents the set of portfolios that will give highest

return at the each level of risk or the lowest risk for each level of return.

Markowitz portfolio theory give suggestion to an investor will choose his/ her optimal portfolio from the set of the portfolios that

(1) Offer maximum expected return for varying level of risk, and(2) Offer minimum risk for varying levels of expected return.

1. Maximum Return At Given Level of Risk

Portfolio A is best because at this point there is high return at the given level of risk.

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K

(p)

SD

(p)

30

2520

15

10

10     15      20      25       30      35      40

A

BC

2. Minimum Risk at the Given Level of Return

Point A is best portfolio because this portfolio has a low risk at the given level of return of others portfolio.

As an investor, we can select how much risk is acceptable in the portfolio by selecting any other point that lies on the efficient frontier. It will provide us the maximum returns for the amount of risk acceptable.

 For example, if we have $10,000 to invest to build our portfolio of stocks of

five companies A, B, C, D and E; then we need to decide how much money should be invested in each stock that can provide best return possible at a level of risk acceptable by us.

According to above calculation, the optimal portfolio that contains five securities (A, B, C, D, and E) is the one that gives a return higher than 23.06% at a risk 18.49%.

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K

(p)

SD

(p)

30

2520

15

10

10     15      20      25       30      35      40

A B C

Now we will illustrate this optimal portfolio regarding Securities (A, B, C, D, and E) in a diagram with the help of Markowitz efficient Frontier.

Diagram of Efficient Portfolio

At point E a portfolio consist of purely risk free assets. At point C a portfolio consist of purely market portfolio. Between Point E and B is an efficient frontier. So, the portfolio must be

between E and B.

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SD

K

(p)

(p)

12%

23.06%

10%

20%

30%

18.49%

MEF

Best Portfolio

Attainable But not Efficient

Not affordable

AffordableBut not attainable

A

B

C

E

Portfolio Management StrategiesThere are two basic approaches for portfolio management including Active

Portfolio Management Strategy and Passive Portfolio Management Strategy.

Passive Portfolio Management Strategy

Passive asset management relies on the fact that markets are efficient and it is not possible to beat the market returns regularly over time and best returns are obtained from the low cost investments kept for the long term.

Active Portfolio Management Strategy

The Active portfolio management relies on the fact that particular style of analysis or management can generate returns that can beat the market. It involves higher than average costs and it stresses on taking advantage of market inefficiencies. It is implemented by the advices of analysts and managers who analyze and evaluate market for the presence of inefficiencies.

Active Portfolio Management Strategy refers to a portfolio management strategy that involves making accurate investments for outperforming an investment benchmark index. The portfolio manager that follows the active management strategy exploits the market inefficiencies by buying undervalued securities or by short selling overvalued securities. Any of these procedures can be used alone or in combination.

Active portfolio managers may create less instability (or risk) than the benchmark index depending on the targets of the specific hedge fund or investment portfolio. The risk reduction is considered as goal of creating an investment return larger than the benchmark. They use large number of factors and strategies for constructing their portfolio.

Strategies for Active Portfolio

Quantitative measures like Dividend per share, Expected return and Risk of individual and portfolio investment.

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Invest in Sectors that are expected to deliver long-term macroeconomic trends

Buying stocks of companies that are disliked temporarily. In order to generate profits, the investors consider that some

market segments are less efficient than others.

Suggestion and Recommendation

Portfolio management is basically an approach of balancing risks and return. Investors should keep the following tips in mind while deciding about the right portfolio combine.

Investor should be clear about his/her goals of investment. The objective of the portfolio management should be clear that one wants to accumulate wealth by good returns or to hold on his investments.

Investor should know the activities of the companies and acquire knowledge about the sector where he/she is going investing in. This way investor would be able to know is the company will continue to be successful?

The performance of the portfolio is measured by the return on investment (ROI) or expected rate of return. The individuals can successfully formulate a logical money-management strategy by knowing the probability of returns received by the investment. For this purpose I used these formula:

a) Return On Investment ROI= yield+ (price ending-price beginning)/price beginning

b) Expected Rate Of Return To calculate expected return I used Geometric & Arithmetic Mean.

As an investor one should know how to handle the fluctuations of ever changing unstable market. If investors are not capable of handling the pressure of sharp decline in the values of share then investor should try to invest in more stable stocks. It means that the investor must know the risk associated to the stocks where investors want to invest. For this purpose I have used statistical method that is Standard Deviation to calculate the risk of related to particular stocks.

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The diversification of the portfolio is required to minimize the risks and maximizes the returns in the long term. So the investor should used Markowitz model to identify the risk portfolio. As well as the investor should calculate the expected return by assigning weighted to each stock.

After determined the expected rate of return and risk of portfolio, investor should used the efficient frontier to select the optimal portfolio. Optimal portfolio means that which is the best and good portfolio.

Bibliography/Appendix

i. Mr. Waqar Hassan coordinator of Audit Department in Sadaqat Textile Limited

ii. Sir Ahmed Gillani, Professor, Department of Banking and Finance, Government College University Faisalabad.

iii. Sir Ammar Abid, Professor, Department of Banking And Finance, Government College University Faisalabad

Sources and Instrumenti. www.kse.com ii. www.boi.com.pk iii. Individual company websiteiv. Individual company annual reportv. Used MS excel to calculate Return, Risk, correlation between two

companies, and other statistical & mathematical calculation/vi. MS Power Point is used to draw a various diagram and to create different

formulae.

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