MARKOWITZ PORTFOLIO THEORY ON DSE ENLISTED COMPANIES

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SPRING 2014

FIN 435: INVESTMENT THEORY

TERM PROJECT

SECTION: 01

COURSE INSTRUCTOR:

MR. M. MORSHED

SENIOR LECTURER, SCHOOL OF BUSINESS

NORTH SOUTH UNIVERSITY

SUBMITTED BY

NAME ID#

ZAHIN SARWAR 111-0021-030

MD. SAJEDUL HAQUE 112-0359-030

FAYSOL MD. AL-KOVI 111-0393-030

SHEIKH FUAD AHMED 101-0078-030

MD. SIRAJUM MUNIR 091-0138-030

DATE OF SUBMISSION: APRIL 27, 2014.

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LETTER OF TRANSMITTAL

April 27, 2014.

Mr. M. Morshed,

Senior Lecturer, School of Business

North South University

Bashundhara Residential Area, Dhaka-1100

Subject: Submission of Term Paper.

Dear Sir,

We have tried to prepare the project with due sincerity and we would like to thank you for giving

us the opportunity to have the chance to work on this. Despite some limitations we have tried our

best to address the major and in depth issues in making this project accurate and reliable.

If you have any further enquiry concerning any additional information we would be very pleased

to explain that.

Sincerely yours,

ZahinSarwar

Md. Sajedul Haque

Faysol Md. Al-Kovi

Sheikh Fuad Ahmed

Md. Sirajum Munir

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ACKNOWLEDGEMENT

Preparing this report has been a great task for all of us. Since the beginning of our work we have

come through many confusions and dead-ends, but still, we managed at the end. First of all, we

would like to thank almighty Allah for giving us patience and strength in order to complete this

project successfully.

We would like to extend our gratitude to our faculty Mr. M. Morshed for his immense support.

We are grateful to him for guiding us and helping us to finish this project.

Finally, we would like to thank each other for the wonderful cooperation we had shared among

ourselves as group members. Our dedication and strong teamwork has resulted in the successful

completion of this project. We learned extensively on real world implementation of Markwoitz

Portfolio Theory. This project has helped us to gain some knowledge and has exposed some

interesting answers.

Group Members of this Project

April 27, 2014

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OBJECTIVES

The objective of this report is to:

Recording the daily prices of Square Pharmaceuticals Ltd, Olympic Industry

Ltd, Heidelberg Cement Ltd, IDLC, Singer Bangladesh Ltd and DSE all shares

price index and calculating their daily returns based on closing price for the year

of 2003-2012.

Calculating the arithmetic mean return and standard deviation of these five

stocks and DSE all shares price index.

Calculating the correlation coefficient and covariance of theses five stocks with

each other and also with the market index.

Calculating the portfolio risk and return by using different combinations of the

five stocks and drawing an efficient frontier of the portfolios.

Calculating the beta of each stock and comparing the calculated beta with the

beta available on market data.

Calculating the required rate of return of each stock based on Capital Asset

Pricing Model (CAPM).

This evaluation will be very helpful for the potential investors to have vast knowledge about the

portfolios and it will help them to decide in which company they should invest. Investment

decisions are critical decisions and need thorough analysis. When making investments, investors

look for dividend paid by a company and the capital gain. That is why the objective of any

company is to maximize shareholder’s wealth. So throughout all the report, starting from

collecting of the data up to drawing the conclusion on the financial situation of these stocks gives

the knowledge and understanding of ‘how it works’ in real finance world.

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METHODOLOGY

Primary Data

No primary data was required to prepare this report because all of the relevant information was

available in secondary data sources.

Secondary Data

The report is prepared by using secondary data only and the sources of the data were Daily

Trading Information from 2003 to 2012, annual reports and relevant websites.

Key Information reflected in the overviews of the companies was obtained from the official

websites of the companies as well as the latest annual report of the companies.

Microsoft Excel 2007 spread sheet was used for calculation as well as creating diagrams.

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LIMITATIONS

There were quite a few limitations while doing this project. Here are some of the general limitations:

Access of information:

One of the biggest limitations was the absence of a standard format of information. Specifically, some of the market data were missing. For example, 2004 market data were missing. Therefore, we failed to calculate the market return for 2004.

Stock selection factors:

We selected the stocks solely based on the performance of the company. Even though past performance is worthwhile to evaluate investments, but it will not guarantee the future. Therefore beside the performance of the company, we need to focus on other the macro economic factors related to our investment.

Fundamental Analysis:

We selected our companies after doing the fundamental analysis only. We have chosen our stocks based on certain key ratios. However, if we could do the technical analysis as well as calculate the intrinsic value of the company, it will be more appropriate for evaluating the value of stocks.

Our personal flaws:

As the report is huge and time were very short, there may be some mistakes in our calculation. This may give rise to wrong understanding of actual performance of the portfolio.

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EXECUTIVE SUMMARY

This report focuses on implementing Markowitz Portfolio Theory by using IDLC, Square,

Olympic, Heidelberg Cement and Singer BD stocks which are currently enlisted in Dhaka Stock

Exchange. This report begins with selection of 5 stocks as well as the reasons behind selecting

those stocks and followed by a brief overview of selected companies.

Arithmetic mean, geometric mean, and standard deviations of five stocks as well as the market

are determined based on past 10 years daily returns. The correlations and co variances among

five stocks are also determined next. Then 10 portfolios were chosen and each portfolio consists

of two stocks. Risk and returns of those ten portfolios were calculated using Markowitz Portfolio

theory and risk-return trade off for those 10 portfolios are shown. Then efficient frontier was

constructed by plotting the risk and returns of efficient portfolios.

Finally, we calculated betas of those five stocks and compared with the betas already available in

the market. Then we calculated the required rate of returns of five stocks by using Capital Asset

Pricing Model and concluded the report.

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TABLE OF CONTENTS

Instructions 10

Overview of company 11

Fundamental analysis of the company 13

Theoretical background: Markowitz portfolio theory 16

Portfolio construction 17

Beta calculation 24

Required rate of return 25

Conclusion 26

Reference 27

Appendix 28

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INTRODUCTIONThe objective of stock selection criteria is to: (1) Maximize the total return on investment for the

targeted holding period. (2) Minimize the risk. & (3) Maintain an appropriate degree of portfolio

diversification. One of the simplest ways to diversify a portfolio is to buy a stock in each of the

sectors that are widely referred to as broad sectors within the stock market. These different

sectors stocks rise or fall at different times within stock market advances and declines. In order

to create our diversified portfolio, we have picked five different sectors stocks from the

Pharmaceuticals and Chemical industry, Food and Allied industry, Financial Institution, Cement

industry and Engineering industry. We have chosen these sectors stocks to create our portfolio

because these industries have been experiencing robust growth over the last few years. A local

industry support policy and effective regulatory framework are the key reasons of success of

these industries. The consumption has steadily been rising and it is expected that these

companies will enjoy a good growth of margin over the next couple of years. Moreover, these

industries are achieving self sufficiency and have been expanding locally and internationally.

Many investors choose stocks based solely on performance. Even though, past performance will

not guarantee the future, but it is still worthwhile to evaluate investments based on their ability to

deliver consistent returns with minimal risk. Before selecting the stocks, we have gone through

the fundamental analysis where we have calculated some key ratios of these companies.

According to the Lanka Bangla Securities analysis (2013), Food & allied sector was the best

performing sector in 2013 as it gave more than 90% return. Second highest major gaining sector

was Pharmaceuticals with a rise of almost 40%, Square Pharmaceuticals gained 57.9%.The

engineering sector rally was mostly dominated by the Olympic Industries with 124.5% gain in

the market capitalization. Among engineering sector stocks, Singer Bangladesh posted 42.3%

return. Since, the banking sector is incurring loss of capitalization; therefore we have chosen to

invest in financial institution sector instead of banking sector to minimize the risk. Moreover,

these companies have consistent net profit over the last few years and huge amount of paid-up

capital in the stock market. These companies have had steady dividends over the past couple of

years and it is expected that it will continue to do so in the future.

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OVERVIEW OF COMPANYIDLC Finance Limited

IDLC is one of the largest Non-Bank Financing Institute in Bangladesh. they offers a wide range

of products and solutions comprising loans, deposit and capital market products and services to

corporate, consumer and SME clients. IDLC also operates two wholly-owned subsidiaries in the

capital markets through IDLC Investments Limited (providing merchant banking services) and

IDLC Securities Limited (providing brokerage services). Currently IDLC has 26 branches. IDLC

is listed on both Dhaka and Chittagong stock exchanges. The Company’s market capitalization

stood at Taka 10,119 million as on31 December 2013. IDLC was initially established in

Bangladesh in 1985 through the collaboration of International Finance Corporation (IFC) of the

World Bank, German Investment and Development Company (DEG), Kookmin Bank and

Korean Development Leasing Corporation of South Korea, the Aga Khan Fund for Economic

Development, the City Bank Limited, IPDC of Bangladesh Limited, and Sadharan Bima

Corporation. Initial foreign shareholding of 49% was gradually withdrawn and the last foreign

shareholding was bought out by local sponsors in 2009.

Square Pharmaceuticals Limited

Square Pharmaceuticals Limited is the largest pharmaceutical company in Bangladesh and it has

been continuously in the 1st position among all national and multinational companies since 1985.

It was established in 1958 and converted into a public limited company in 1991. The sales

turnover of SPL was more than Taka 11.46 Billion (US$ 163.71 million) with about 16.43%

market share (April 2009– March 2010) having a growth rate of about 16.72%.Square

Pharmaceuticals Limited has extended its range of services towards the global market. It

pioneered exports of medicines from Bangladesh in 1987 and has been exporting antibiotics and

other pharmaceutical products.

Olympic Industry Limited

Olympic Industries Limited is one of the longest running and most reputed manufacturing-based

companies in Bangladesh. Olympic Industries Limited has very diversified product line. It has

various consumer goods including biscuits, confectioneries, batteries, and ball pens as well as

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Pharmaceuticals, Power, and Information Technology. Olympic Industries Limited is currently

the market leader in the biscuit market and second in position in the battery market in

Bangladesh. Olympic Industries Limited is a public listed company and is trading on the Dhaka

Stock Exchange and Chittagong Stock Exchange. Olympic Industries Limited also involved in

some CSR activity like Olympic scholarship program and Energy plus football tournament.

Heidelberg Cement Bangladesh Limited

Heidelberg Cement Bangladesh Limited is a member of Heidelberg cement group, Germany.

This company came into Bangladesh in 1998. They have two reputed brand in the cement market

“Ruby Cement” and “Scan Cement”. Initially they started with a floating terminal in Chittagong.

Then they gradually have their own manufacturing facility. Now they have more than one

manufacturing facility in Bangladesh. 39 percent of their total share is to the general public and

other institutions.

Singer Bangladesh Limited

Singer Bangladesh is one of the oldest companies in Bangladesh. It was listed in Dhaka stock

exchange in 1983. During that time only 20 percent of its share was offered in the market. Now

its share is also traded in Chittagong stock exchange. Singer Bangladesh has a very diversified

product line. Initially it started as a sewing machine producer. But now it has many different type

of product. Its diversified product line include color televisions, fans, washing machines, irons,

microwave ovens, rice cookers, audio products, air conditioners, motorcycles, instant power

supply, DVD players, room heaters, kitchen appliances, net book, laptop, desktop computers,

generators, blue ray DVD players, LCD/LED TV and 3D television.

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FUNDAMENTAL ANALYSIS OF THE COMPANIES

IDLC Finance Limited

Market Capital in BDT 10859.063 mnPaid up Capital in BDT 2011.0 mn

Reserve & Surplus in BDT 3348.1 mnNet Profit After Tax in

BDT 361.71 mnBasic EPS in BDT 2.25Current P/E Ratio 12.67

Share Percentage Sponsor- 63.82% Institution- 14.54% Public-21.64%

YearNet Asset Value Per

Share Year End P/E% Dividend

Yield2012 37.93 20.74 N/A2011 40.21 34.28 N/A2010 61.5 34.67 0.752009 797.7 27.13 0.272008 644.52 14.86 0.66

Square Pharmaceuticals Ltd

Market Capital in BDT 135875.592 mnPaid up Capital in BDT 4820 mn

Reserve & Surplus in BDT 15514.8 mnNet Profit After Tax in BDT 4104.82 mn

Basic EPS in BDT 8.52Current P/E Ratio 24.53

Share Percentage Sponsor- 54.21% Institution- 27.18% Public-8.96%

Year Net Asset Value Per Share Year End P/E% Dividend

Yield2012 72.2 24.31 1.05

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2011 81.375 26.6 0.922010 857.52 28.13 0.982009 905.05 23.44 1.362008 N/A 35.9 0.97

Olympic Industry Ltd

Market Capital in BDT 28762.520 mnPaid up Capital in BDT 1175.0 mn

Reserve & Surplus in BDT 556.3 mnNet Profit After Tax in BDT 615.36 mn

Basic EPS in BDT 3.45Current P/E Ratio 46.7

Share Percentage Sponsor- 31.49% Institution- 30.31% Public-27.45% Foreign-10.75%

YearNet Asset Value Per

Share Year End P/E% Dividend

Yield2012 14.91 21.38 0.792011 14.23 38.82 0.532010 15 33.08 0.552009 183.15 11.32 1.592008 177.38 16.82 4.06

Heidelberg Cement Bangladesh Ltd.

Market Capital in BDT 33625.286 mnPaid up Capital in BDT 565 mnReserve & Surplus in

BDT 5735.0 mnNet Profit After Tax in

BDT 1474.08 mnBasic EPS in BDT 26.09Current P/E Ratio 23.48

Share Percentage Sponsor- 60.66%Institution-

20.58% Public-18.76%

Year Net Asset Value Per Year End P/E % Dividend

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Share Yield2012 111.49 11.58 1.892011 93.13 19.28 1.762010 84.18 20.7 1.182009 703.05 14.29 1.772008 585.46 11.58 2.72

Singer Bangladesh Ltd.

Market Capital in BDT 10882.028 mnPaid up Capital in BDT 491.0 mn

Reserve & Surplus in BDT 2048.7 mnNet Profit After Tax in BDT 343.87 mn

Basic EPS in BDT 7.01Current P/E Ratio 28.32

Share Percentage Sponsor- 75% Public-25%

Year Net Asset Value Per Share Year End P/E% Dividend

Yield2012 64.67 16.43 7.622011 55.99 28.23 1.042010 139.96 82.14 8.372009 481.68 24.42 3.222008 278.81 29.06 1.51

MARKET YIELD

Company   Last Price Dividend Yield   Payout Ratio   Declaration(C)

IDLC 52.7 0.949 % 12.019 % 5 %

SINGERBD 219.9 4.548 % 128.370 % 100 %

SQURPHARMA 278.7 0.897 % 22.462 % 25 %

HEIDELBCEM 612.7 6.202 % 166.302 % 380 %

OLYMPIC 244.7 0.409 % 12.739 % 10 %

THEORETICAL BACKGROUND OF MARKOWITZ PORTFOLIO THEORY

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Prior to 1950, people considered that they can reduce the risk by adding more and more

securities in a portfolio without any systematic manner. This was known as the insurance

principle. This theory tells us that each security is unique and by adding more securities the risk

of one security will be canceled out by other security. So by adding more security the risk of a

portfolio is reduced.

In 1950 Markowitz came with an idea that adding more security will reduce risk but it have to be

in a systematic manner. He told that risk in not only subject to weighted average risk of each

security but also subject to weighted co-movement of securities. The co-movement is the co-

variance of securities. Co-variance tells us the degree at which two variables are moving

together. Negative co-variance tells us that variables are moving in the opposite direction at the

same time. And positive co-variance tells us that two variables are moving in the same direction

at the same time. So when we are going to add any securities to the portfolio we should add

securities with negative or zero co-variance. If we add securities with positive co-variance that

will not reduce any risk of a portfolio. However to calculate the risk of a portfolio we have to

take the weighted average risk and the weighted average co-variance of the securities. And

weight of each security in a portfolio should be the market weight. The number of co-variance

one have to calculate for “n” number of securities is n(n-1). And this is a major problem for the

Markowitz theory, for a large portfolio investor has to calculate a large number of variances and

co-variances.

PORTFOLIO CONSTRUCTIONThe following steps are taken to construct two stocks portfolio from the selected five stocks of

Dhaka Stock Exchange.

Calculating Daily Returns

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We have calculated daily returns of each stock from the daily trading information from the year

2003 to 2012 (10 years).

Calculating Arithmetic Mean, Geometric Mean and Standard Deviation

Arithmetic mean is the average of all returns of a single stock and it is the expected next period

return of that particular stock. Geometric mean refers to the compounding growth rate of daily

return over the last 10 years of a particular stock. Standard Deviation refers to risk or fluctuation

of returns in last 10 years. Higher the value of standard deviation higher risk is associated with

the stock. We have calculated arithmetic mean, geometric mean and standard deviation of each

stock based on 10 years daily return. Microsoft Office Excel 2007 formulas were used for

calculation.

Stock & Market

Arithmetic Mean

Geometric Mean

Standard Deviation

IDLC 0.0047% -0.1271% 4.0991%

Square 0.0264% -0.0667% 3.1221%

Olympic -0.1540% -0.2728% 4.9012%

Heidelberg -0.0555% -0.1014% 3.2025%

Singer 0.0127% -0.0903% 3.4966%

Market 0.0477% 0.0360% 1.5379%

Among the selected stocks Singer is expected to produce highest daily return and Olympic is

expected to produce lowest daily return. Olympic is also the most risky stock and Square

pharmaceuticals is the least risky stock among the chosen stocks.

Determining Correlation & Covariance

Correlation is the relationship (positive, negative or no relationship) in between two random

variables and covariance refers to the measure of how much two random variable will change

together.

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We have calculated the correlations and co variances among the stocks based on 10 years daily

return. The correlation indicates the relationship of movement in between two random stocks and

covariance indicates the degree of change.

Correlations Matrix

  IDLC Square Olympic Heidelberg Singer

IDLC 1.0000 -0.0104 -0.0194 0.0323 0.0122

Square -0.0104 1.0000 -0.0100 -0.0462 -0.0331

Olympic -0.0194 -0.0100 1.0000 -0.0251 0.0318

Heidelberg 0.0323 -0.0462 -0.0251 1.0000 -0.0050

Singer 0.0122 -0.0331 0.0318 -0.0050 1.0000

Table of Co variances

  IDLC Square Olympic Heidelberg Singer

IDLC 0.001680 -0.000013 -0.000039 0.000042 0.000018

Square -0.000013 0.000975 -0.000015 -0.000046 -0.000036

Olympic -0.000039 -0.000015 0.002402 -0.000039 0.000055

Heidelberg 0.000042 -0.000046 -0.000039 0.001026 -0.000006

Singer 0.000018 -0.000036 0.000055 -0.000006 0.001223

By analyzing different correlations and co-variances among different stocks, we found that most

of the stocks have negative relationship with other stocks. So, our portfolio risks will be reduced

due to negative correlations and co-variances.

Determining Weight

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We have constructed our set of portfolios by using two stocks in each portfolio. The weight of

each stock was determined by the percentage of its market weight to total market cap of two

stocks.

Portfolios Stocks Weights

Portfolio 1IDLC 7.24%Square 92.76%

Portfolio 2IDLC 27.64%Olympic 72.36%

Portfolio 3IDLC 23.95%Heidelberg 76.05%

Portfolio 4Square 73.50%Olympic 26.50%

Portfolio 5Square 71.21%Heidelberg 28.79%

Portfolio 6Olympic 45.18%Heidelberg 54.82%

Portfolio 7Singer 51.71%IDLC 48.29%

Portfolio 8Singer 7.72%Square 92.28%

Portfolio 9Singer 29.03%Olympic 70.97%

Portfolio 10Singer 25.21%Heidelberg 74.79%

Risk & Returns of Selected Stocks

The expected risk & return (daily basis) are shown in table below. Expected return is the

arithmetic mean of past 10 years daily return and risk is the standard deviation of the returns.

Stock Return Risk

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IDLC 0.0047% 4.0991%

Square Pharma 0.0264% 3.1221%

Olympic -0.1540% 4.9012%

Heidelberg -0.0555% 3.2025%

Singer BD 0.0127% 3.4966%

Identifying Correlations & Co variances of the desired portfolios

The correlation and covariance in between the stocks of each portfolio is shown in the following

table.

Portfolio Correlation Covariance

IDLC & Olympic -0.0194 -0.000039

Olympic & Singer 0.0318 0.000055

Olympic & Heidelberg -0.0251 -0.000039

IDLC & Heidelberg 0.0323 0.000042

Heidelberg & Singer -0.0050 -0.000006

Square & Olympic -0.0100 -0.000015

Square & Heidelberg -0.0462 -0.000046

IDLC & Singer 0.0122 0.000018

IDLC & Square -0.0104 -0.000013

Square & Singer -0.0331 -0.000036

Most of the portfolios’ stocks in the above table consist of negative correlation as well as

negative covariance. So, the portfolio risk is supposed to be reduced due to negative relationship

in between the movement of returns of the stocks.

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Determining Risk & Return of the Portfolios

We have calculated the daily expected risk and returns of each portfolio by using Markowitz

Model. Markowitz formulas are used to calculate expected risk & return of each portfolio.

Portfolio Return Risk

IDLC & Olympic-0.1101% 3.7020%

Olympic & Singer-0.1056% 3.6544%

Olympic & Heidelberg-0.1000% 2.7911%

IDLC & Heidelberg-0.0411% 2.6553%

Heidelberg & Singer-0.0383% 2.5481%

Square & Olympic-0.0214% 2.6255%

Square & Heidelberg0.0028% 2.3672%

IDLC & Singer0.0089% 2.6973%

IDLC & Square0.0248% 2.9080%

Square & Singer0.0253% 3.0028%

Constructing Efficient Frontier

Risk & Return Trade off Diagram

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We have constructed a scattered diagram by using risk of each portfolio as horizontal axis

variable and return of each portfolio as vertical axis variable. The diagram gives us the risk and

return trade of all portfolios. The diagram is created by Microsoft Excel 2007.

2.2000% 2.4000% 2.6000% 2.8000% 3.0000% 3.2000% 3.4000% 3.6000% 3.8000%

-0.1200%

-0.1000%

-0.0800%

-0.0600%

-0.0400%

-0.0200%

0.0000%

0.0200%

0.0400%

-0.1101%

-0.1056%

-0.1000%

-0.0411%-0.0383%

-0.0214%

0.0028%0.0089%

0.0248% 0.0253%

Risk Return Trade off of all Portfolios

Risk

Ret

urn

(%)

The diagram above shows the risk and return trade off of all portfolios. However, there are only

four portfolios that belong to the efficient frontier.

Efficient Portfolios

Efficient Portfolios Return Risk

Square & Heidelberg 0.0028%

2.3672%

IDLC & Singer 0.0089%

2.6973%

IDLC & Square 0.0248%

2.9080%

Square & Singer 0.0253%

3.0028%

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Efficient Frontier

We have constructed a scattered diagram by using risk of each efficient portfolio as horizontal

axis variable and return of each efficient portfolio. The diagram gives us the Efficient Frontier.

The diagram is created by Microsoft Excel 2007.

2.3000% 2.4000% 2.5000% 2.6000% 2.7000% 2.8000% 2.9000% 3.0000% 3.1000%0.0000%

0.0050%

0.0100%

0.0150%

0.0200%

0.0250%

0.0300%

0.0028%

0.0089%

0.0248%

0.0253%

Efficient Frontier

Risk

Ret

urn

(%)

Now we have an efficient frontier consisting of four portfolios. Only these four portfolios of ten

portfolios produce the optimal risk and return trade off and other portfolios produce lower

returns at assumed risk.

An investor may choose any of those 4 portfolios according to his or her risk and return

preference. In other words, an investor will match their Indifference Curve with this Efficient

Frontier to make an investment decision.

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BETA CALCULATIONWe have calculated Beta (β) of each stock by regression analysis in Microsoft Excel 2007. In the

regression analysis we have considered Daily Market Returns of past 10 years as horizontal axis

variables and Daily Stock Returns of past 10 years as vertical axis variables. To compare our

betas with betas calculated by experts, we have taken betas from www.stockbangladesh.com

website.

Stocks Beta calculated by us Beta calculated by experts

IDLC -0.01449923 1.04009418

Square -0.01015178 0.61093204

Olympic 0.04118967 1.16839486

Heidelberg 0.01927099 0.88888641

Singer 0.07260845 0.96598688

Reason for different Betas for same stock:

1. Calculation of Beta depends on variables. We have taken daily returns to calculate the

Beta. However, the expert may have used weekly, monthly or yearly return to calculate

beta. So, there must be difference in variables that led to different betas.

2. We have considered the returns from the year 2003 to the year 2012. Expert’s time

period may be different and that can be a reason for different betas.

3. Different Betas can be resulted from different Index which is compared with the

stock’s returns. In our analysis we used total market index, but experts’ may have used

DSEX or the industry wise Index.

4. Beta of each stock changes with the financial performance of the company. So, Beta

value may have changed due to recent financial performance.

5. Measure of β in this model is subject to error. In our beta calculation error is not

corrected.

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REQUIRED RATE OF RETURNWe have used Capital Asset Pricing Model to calculate the required rate of return of the investors

for the five stocks. We are assuming 3% or risk free rate of return and 7% of market return.

Stock Market Return

Risk Free Return

Beta calculated by us

Beta calculated by experts

Required Rate of return based on our beta

Required Rate of return based on expert’s beta

IDLC 7% 3% -0.0145 1.040094178 2.9420% 7.1604%

Square 7% 3% -0.0102 0.610932042 2.9594% 5.4437%

Olympic 7% 3% 0.0412 1.16839486 3.1648% 7.6736%

Heidelberg

7% 3% -0.0193 0.888886414 2.9229% 6.5555%

Singer 7% 3% 0.072608 0.965986879 3.2904% 6.8639%

Required rate of return of each stock is subject to that particular stock’s beta. Higher beta

produce higher required rate of return because the stock consists of higher systematic risk. In our

chosen stocks, Olympic has the highest rate of return and Square pharmaceutical has the lowest

rate of return. Difference in beta is the reason for different required rate of return.

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CONCLUSION

The portfolios were constructed with proper diversification but, most of the portfolios failed

serve as efficient portfolios for investors. Constructing portfolios according to Markowitz model

has helped to reduce the risk of a portfolio but it also reduced the returns of some portfolios.

Hence, most of the portfolios are inefficient for the investors. However, investors can satisfy

their investment objective by investing in four efficient portfolios that provide optimal risk-

return combination.

Due to economic slowdown systematic has risen significantly and returns of most of the stocks

are affected with fluctuation of the market. However, Markowitz Model does not consider the

systematic risk. Capital Asset Pricing Model can be very useful to design portfolios because the

model considers the systematic risk associated with the stocks’ returns.

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REFERENCEDhaka Stock Exchange. (n.d.). Retrieved April 24, 2014, from Dhaka Stock Exchange:

http://www.dsebd.org/

Heidelberg Cement Industries. (n.d.). Retrieved April 17, 2014, from Heidelberg Cements:

www.heidelbergcementbd.com

IDLC Finance Limited. (n.d.). Retrieved April 15, 2014, from IDLC: http://idlc.com/

Olympic Industtries. (n.d.). Retrieved April 14, 2014, from

www.olympicbd.com/index.php/about-company

Sectoral beta. (n.d.). Retrieved April 25, 2014, from Stockbangladesh.com:

http://www.stockbangladesh.com/resources/sector_beta/

Singer Bangladesh Limited. (n.d.). Retrieved April 16, 2014, from Singer: www.singerbd.com

Square Pharmaceutical Limited. (n.d.). Retrieved April 20, 2014, from Square Pharmaceutical

Limited: www.squarepharma.com.bd

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Appendix

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Calculation Formulas

We have calculated different values with the help of Microsoft Excel 2007 work sheet.

1. Daily Return: Ending price−Beginning price

Beginning price×100 %

2. Arithmetic Mean (average return): “=AVERAGE (returns)”

3. Geometric Mean of returns: “=(PRODUCT(1+retrurns)^(1/COUNT(Returns)))-1”

4. Standard Deviation: “=STDEV (returns)”

5. Correlation x,y : =CORR(Returns of X, Returns of Y)

6. Covariancex,y: Correlationx,y×Sigmax×Sigmay

7. Calculation of Beta: Regression Analysis in excel. Taking Market return at horizontal axis and

Stock Return at vertical axis.

8. Portfoliox,y Weights:

Weightx = Market CAP X

Market CAP X+Market CAPY

Weighty = Market CAPY

Market CAP X+Market CAPY

9. Return of the Portfoliox,y = Wx×Returnx + Wy×Returny

Risk of the Portfoliox,y =

√Weight (x)2 × Risk (x)2+Weight ( y )2× Risk ( y )2+2× Weight (x)×Weight ( y )× Covariance(x , y )

10. Required Rate of Return: Risk Free Return +β×(Market Return-Risk Return)

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Sector Index

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Fundamental Chart

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