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3.3 The relationship between the stock and the market..................................17

3.3.1 Covariance.........................................................................17

3.3.2 Correlation Coefficient........................................................18

3.3.3 Beta ..................................................................................18

3.3.4 Covariance Matrix...............................................................18

3.4 Portfolios Risk and Return..........................................................................20

3.4.1 Portfolio Variance...............................................................20

3.5 Plotting the efficient frontier.......................................................................20

4.0 INTERPRETATION OF RESULTS.......................................................................21

4.1 Average Weekly Return..............................................................................21

4.2 Average Annual Return...............................................................................23

4.3 Variance..................................................................................................... 25

4.4 Standard Deviation.....................................................................................26

4.5 Correlation of Coefficient Matrix.................................................................28

4.5.1 Covariance.........................................................................28

4.5.2 Correlation ........................................................................29

4.6 Beta............................................................................................................ 30

4.7 Portfolio Standard Deviation (When Short Selling was disallowed).............31

4.8 Efficient Frontier (When Short Selling was allowed)...................................33

4.9 Portfolio Standard Deviation (When Short Selling was allowed).................35

4.10 Efficient Frontier (When Short Selling was allowed).................................38

5.0 CONCLUSION................................................................................................. 39

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1.0 INTRODUCTION

The objective of this working paper is to construct an efficient portfolio that consists of 15

actively trading stocks listed on Bursa Saham Malaysia or formerly known as Kuala Lumpur

Stock Exchange (KLSE). In general, total risks include systematic risks and unsystematic

risks. Unsystematic risk is risk that can be eliminated through diversification because thiskind of risk is unique only to a specific firm. On the other hand, systematic risk is risk that

cannot be eliminated through diversification because it has market-wide effect and affect

the entire market.

Unsystematic risk can be eliminated by investing our capital in a group of assets. A portfolio

which consists of a group of assets can be used as a way to eliminate the unsystematic risk.

The range of return of a portfolio is in between the lowest possible stock return of an

individual stock in the portfolio to the highest possible stock return of an individual stock in

the portfolio. That is, the portfolio return is the weighted average return of each individual

stock as included in the portfolio. Portfolios risk is reduced when assets in the portfolio are

negatively correlated with each other.

An efficient portfolio is a portfolio that provides the highest return for a given level of risk.

Efficient frontier is a set of efficient portfolios that offers the highest expected return for a

defined level of risk or the lowest risk for a given level of expected return. Portfolios on the

efficient frontier are those that provide the best trade off between risk and return. Therefore,

every investor should target on portfolios that lie on the efficient frontier.

Therefore, asset allocation is the key of constructing an efficient portfolio. Asset allocation is

a scheme that involves dividing ones portfolio into various asset classes to preserve capital

by protecting against negative developments while taking advantage of positive ones. In view

that the assets on hold in our portfolio are stocks, therefore, the asset allocation involves the

process of spreading our investment capital across different industries within Malaysia.

As an aforementioned, the objective of this working paper is to construct an efficient

portfolio that consists of 15 stocks listed on KLSE. More specifically, the aim of this working

paper is to determine the best allocation of individual stocks within a portfolio that yields a

maximum portfolio return with the minimum portfolio risk. In order to obtain the minimum

variance portfolio, we will need to perform portfolio optimization. To do so, we must first

apply mean-variance analysis by analyzing each individual stocks return (mean) and stand-

alone risk (standard deviation) and the relationship between the individual stock return with

the market return (beta). Lastly, we vary the weights of each individual stock within a3


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portfolio in order to construct an efficient portfolio that yields the highest return with the

lowest risks. The efficient frontier is plotted at the end in order to prove that the portfolio

optimization process is a success. The end result may also help investors to select a portfolio

that lies on the efficient frontier for investment purposes. However, the selection of efficient

portfolios on the efficient frontier depends on investors risk and return preferences.

Our group had picked 15 stocks listed on Bursa Saham Malaysia at random industries. There

are Top Glove Corporation, Sapura Resources Berhad, KSL Holdings, Lafarge Malayan

Cement, Pharmaniaga Berhad, Scomi Group Berhad, Cyber Towers Berhad, Leader Steel

Holdings, Ahmad Zaki Resources Berhad, MK Land Holdings, Freight Management, FACB

Industries Incorporation, Berjaya Group, MHC Plantation Berhad and Perstima Berhad.

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2.0 Brief Reviews of Stocks and Malaysia Economics

2.1 Top Glove Corporation Berhad

The Top Glove Corporation was establish in 1991 with only one and about three production

lines, then the Top Glove Corporation has growth continuously and bound to become the

worlds largest rubber glove manufacturer. Top Glove was cooperating with the government

agencies and ministries in order to stay ahead with the shape of product development and stay

keep to get the information of the latest development in rubber research technology. Now it

was known as the one stop Centre offering an extensive and complete high range of high

quality, high value added and cost-effective rubber gloves.

The company was first listed in bursa Malaysia and Bursa Saham Kuala Lumpuron 27 March

2001. With the short period, The Top Glove Corporation was promoted from the Second

Board to the Main Board Market of Kuala Lumpur Stock Exchange on 16 May 2002. It has

the shareholder value of RM 1.28 billion with annual turnover of about 2.31 billion as atfinancial year ended 31 August 2012. It also listed as one of the component stocks of FTSE

Bursa Malaysia (FBM) Mid 70 Index, FBM Top 100 Index and FBM EmasIndex with a

market capitalization of RM3.67 billion as at 9 April 2013.The company also has developed

an expansion of its capacity. Its manufacturing facilities have spread over Malaysia, Thailand

and China has grown from 5 to 24 presently. The Top Glove has export about to 1800

customers in over 185 countries.

2.2 Sapura Resources Berhad

With over than 3 decades, the Sapura Group has leaded the acquisition and development of

competitive technologies. It was established in Malaysia in 1975 and it was owned by

Malaysian-owned-technology-based organization. The beginning of the business started as

telecommunication infrastructure and services provider and the company has expanded and

diversified it business into four majors area which are oil and gas, secured technology,

industrial and automotive manufacturing, and knowledge and education. For the history of

Sapura Resources Berhad, the business is covered by fundamental belief in intergrade peoplewith the technology. Sapura Resource give an effort to built capacity of the home-grown

skilled man power and aggressive investment in development and research, which put the

company position to the globally competitive.

The company had produced the high quality, specialized and multi-skilled pool of technology

expertise. Nowadays, Sapura Resource had expanded its capabilities and competencies that

cover the full lifecycle of product and systems.

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2.3 KSL Holdings

KSL Groups property development has the periods performance with over than twenty year,

successfully strive itself to establish as the fastest growing property developer in building

modern style and affordable residential and commercial properties in the state of Johor

Bahru. KSL Group has involved in investment holding and provision of management services

to subsidiaries. With the companys subsidiaries proceed with the property development,

property management and property investment. The businesss scope is operate in four major

segment which are, property development which is engaged in management apartment,

property investment which engaged in investment in real properties, and investment holding

which mean the provision of management services to the subsidiaries.

In February 2002, KSL Holding Berhad had successfully listed on the main-board of Bursa

Malaysia and its group of companies has been growing rapidly and stably over these years.

However the Group also cant escape from two recession since its inception, it has

successfully maintained its profitability based on its competitive advantage of being reputable

developer, competitive pricing without compromising on safety and quality, strategic land

banks, quality control and its contemporary concept and design. The company has housing

projects in Johor Bahru consist of Taman Nusa Bestari 2, Taman Nusa Bestaru, Taman

Bestari Indah, and Taman Kempas Indah.

2.4 Lafarge Malayan CementLafarge Malayan Cement (LMC)is the leader in the Malaysian construction

materials industry. Incorporated in 1950, its first cement plant was built in Rawang in 1953.

LMC is today the parent of a group of companies in Malaysia and Singapore whose core

businesses are in the manufacturing and sale of cement, ready-mixed concrete and other

related building materials.In the Cement business, LMC currently employs more than 1,150

people and operates a nationwide network of facilities, which includes three integrated

cement plants in Langkawi, Kedah; Kanthan, Perak and Rawang, Selangor, a grinding plant

in Pasir Gudang, Johor with distribution channels by road, rail and sea. It employs about 90

people in its Aggregates business and operates five quarries in Malaysia.

A world leader in building materials, Lafargeemploys 65,000 people in 64 countries, and

posted sales of 15.8 billion in 2012. As a top-ranking player in its Cement, Aggregates and

Concrete businesses, it contributes to the construction of cities around the world, through its

innovative solutions providing them with more housing and making them more compact,

more durable, more beautiful, and better connected. With the worlds leading buildingmaterials research facility, Lafarge places innovation at the heart of its priorities in order to

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contribute to more sustainable construction and to better serve architectural creativity. Since

2010, the Lafarge Group has been part of the Dow Jones Sustainability World Index, the first

global sustainability benchmark in recognition of its sustainable development actions.

2.5 Pharmaniaga Berhad

Pharmaniaga Berhad is the largest integrated local healthcare company in Malaysia.

Pharmaniaga's principal activities in manufacturing of generic pharmaceuticals, logistics and

distribution, sales and marketing, supply of medical products & services and hospital

equipping. The essence of Pharmaniaga is the seamless amalgamation of these key

disciplines, represented by an entirely integrated group of companies, processes and people

that uphold commitment to deliver quality products and services at all times.

The concession to privatise the Government Medical Store was novated to Remedi

Pharmaceutical Sdn Bhd which started operations on 1 December 1994 with a paid up capital

of RM 20 million. In 1999, Pharmaniaga Berhad made its debut on the Second Board of the

Kuala Lumpur Stock Exchange. During 2002, the company completed the corporate

rebranding exercise where all companies within the Pharmaniaga Group were renamed to

carry the singular Pharmaniaga identity. Raza Pharmaceuticals (Bangi) and Strand

Pharmaceuticals (M) Sdn Bhd was then renamed to Pharmaniag Manufacturing Bhd and

Pharmaniaga LifeScience Sdn Bhd (Puchong). Next year, migration of Pharmaniaga from the

Second Board to the Main Board of the Bursa with increased paid up capital of RM100

million from RM50 million previously via the issuance of bonus shares to shareholders.

Pharmaniaga secured a 10 year concession agreement with the Health Ministry to supply

medical products to Government-owned hospitals beginning December 2009. The group

through its subsidiary, PT Millennium Pharmacon International Tbk (MPI), distributes and

trades pharmaceuticals, foods supplements and diagnostic products in Indonesia.

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2.6 Scomi Group

Scomi Group Bhd (Scomi), a global service provider mainly in the oil and gas industry, is a

company listed on the Main Market of Bursa Malaysia. Other public listed companies within

Scomi Group are Scomi Engineering Bhd and Scomi Energy Services Bhd (formerly known

as Scomi Marine Bhd) which are listed on Bursa Malaysia, and PT Rig Tenders which is

listed on Jakarta Stock Exchange. Scomi Engineering, a subsidiary of Scomi Group, is the

regional leader in Logistics Engineering. Committed to providing world-class services that

are second-to-none; our state-of-the-art equipment, facilities, advanced technology and

proven processes are backed by skilled and experienced industry professionals, with in-depth

knowledge both locally and internationally.

Scomis subsidiary and associate companies are involved in the following wide range of

activities worldwide. There are energy services is primarily involved in the provision of high-

performance drilling solutions and related engineering services, state of the art drilling waste

management equipment and solutions, high quality multi drilling services, a varied range of

offshore support vessels, top of the class production enhancement chemicals. Second,

transport solutions are focused on the manufacturing and design of monorail systems, buses,

special purpose vehicles, rail wagons and defence vehicle solutions. Third, energy logistics is

divided into the marine logistics business and offshore support in the oil and gas industries.

Its marine logistics business focuses on coal transportation.

Scomi Group has been spearheading expansion in the emerging markets of Brazil, India, Gulf

States and China. Through its new company Scomi International Pte. Ltd., the Group is

accelerating its continued growth as a one of three world-leading manufacturers of innovative

transportation solutions especially in monorail systems.

2.7 Cyber Towers Berhad

The principal activities of CYBERT are to carry on the business of developing and operating

an internet based automatic vehicle locating system using satellite and wireless

telecommunication solutions. CYBERT is involved in the development and operation of an

Internet-based automated vehicle locating system called Cyber Track. This system uses

global positioning system satellite, ORBCOMM satellite, and global system for mobile

communication, Internet digital mapping, and geographic information system.

According to the consolidated non-Audited financial statement for the first three cumulated

quarters of 2012, total net operating revenues increased with 268.34%, from MYR 2,7238


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thousands to MYR 10,030 thousands. Operating Results increased from MYR -36 thousands

to MYR 2,239 thousands. The results of the period reached MYR 2,241 thousands at the end

of the period against MYR -11 thousands last year. Return on equity (Net income/Total

equity) went from -0.17% to 25.48%, the Return on Asset (Net income / Total Asset) went

from -0.16% to 13.67% and the Net Profit Margin (Net Income/Net Sales) went from -0.40%

to 22.34% when compared to the same period of last year. The Debt to Equity Ratio (Total

Liabilities/Equity) was 86.35% compared to 5.93% of last year. Finally, the Current Ratio

(Current Assets/Current Liabilities) went from 11.14 to 1.21 when compared to the previous

year.

2.8 Leader Steel Holding

Leader Steel Holdings Bhd, is an investment holding company listed on the Main Board of

Bursa Malaysia. Leader Steel Sdn Bhd is principally involved in the manufacturing of MildSteel Flat and Square Bars, trading of various steel products, and processing and sale of iron

ores whilst Leader Steel Service Centre Sdn Bhd focused on the production of steel pipes.

Both are wholly owned subsidiaries of the Group. The Groups diverse range of activities can

be categorized into three main streams, i.e. Manufacturing, Trading of Steel Products and

Processing and Sale of Iron Ores. Products manufactured by the Group are wide, varying

from Flat Bar and Square Bar, Square Hollow Section, Rectangular Hollow Section,

Furniture Tube, Oval Pipe, U Channel, and Black Pipes.

Application for these products are mainly for industrial applications and used in multiple type

of industries. The products are distributed to both local and export markets. Currently

operating at both Penang and Sarawak plants, the rapid growth has resulted in additional

needs for the Group to expand its manufacturing facilities. A new plant is being planned in

Kapar, Klang and is expected to be ready for operation in the near future.

2.9 Ahmad Zaki Resources Berhad

Ahmad Zaki Resources Berhad ('AZRB') was incorporated in Malaysia under the Companies

Act, 1965 on 26 May 1997 as a public limited company under its present name. AZSB was

incorporated as a private limited company. Since then, AZSB has successfully secured

contracts from government and semi-government agencies and the private sector. These

include, amongst others, Jabatan Kerja Raya Malaysia, Majlis Amanah Rakyat, Yayasan

Islam Terengganu, Kuala Lumpur City Centre Berhad, KLIA, Majlis Perbadanan Petaling

Jaya, University of Malaya and International Islamic University of Malaysia. With the

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growth, the company upgraded its licensing status until it obtained a Class 'A' contracting

license in 1993.

Now AZSB has completed nearly 2 (two) Billion Ringgit worth of projects, consisting of

various types of buildings and civil engineering works. With the ensuing business growth and

financial performance, the group under Ahmad Zaki Resources Berhad (AZRB) was listed asa Public Limited Company on the Second Board of Kuala Lumpur Stocks Exchange in June

1999 and subsequently transfered to the Main Board on 10 September 2003. Looking to the

future, the group has ventured overseas with the securing of three projects in Chennai, India

and two in Riyadh, Saudi Arabia. Other activities of the group include Oil and Gas, Property

Development and Plantations.

2.10 MK Land Holdings

MK Land is one of the largest public listed property companies with a paid up capital of

RM1.174 billion. The company is form on 1st March 1983 by Tan Sri Datuk Haji Mustafa

Kamal and it involve in property, construction, commerce, landscaping, resort, agriculture,

manufacturing and education. On 27 August 1999, MK Land debut on the main board of the

Kuala Lumpur Stock Exchange (KLSE) with three major projects that is Taman Bunga Raya,

Damansara Damai and Bukit Merah Lake Town Resort. The Group has a diversified portfolio

of projects, which includes affordable housing, lifestyle living, commercial development,

resort, a water theme park and property investment.

The MK Land tagline is be effective, do what is right and work together. The company

is quick growth because its mission is to strive towards excellence in providing quality

services and products through teamwork for the betterment of the organization, society and

nation. Next, MK Land get the edges top ten property developers awards on 2004, 2005 and

2006 and it also has high financial stability when has sold more than 40,000 housing units

worth more than RM5 billion.

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2.11 Freight Management Holdings Berhad

Freight management holdings berhad is form on 1988 is wholly Malaysian owned

international freight service provider. The company is a big company which provided

international freight service such as sea, rail, air freight and tuge barge service, customs

brokerage and distribution container haulage and conventional trucking service. Freight

Management Holdings Bhd was listed in bursa Malaysia second Board (KLSE) on 3

February 2005 and on 19th December 2007,it has transfer to the main board. Actually, the

company is first Malaysia Company which listed in main board. Today, The Freight

Management Group has offices located in Port Klang, KLIA, Penang, Ipoh, Malacca and

Johor to cover all the important maritime and air gateways of Malaysia.

Freight management holding berhad act as intermediate agent between importers/exportersand carries. This company has strong stability when has network over 107 agents in 127

countries worldwide. The service that provided by Freight management holdings berhad is

airfreight service, railfreight service, tug and barge service, warehouse service andtransport

and custom brokerage service.

2.12 FACB Industries Incorporation

FACB Industries Incorporated Berhad (FACBII) was incorporates on 11 July 1979 inMalaysia with under name of Honco Holdings Sdn Bhd. On 18 May 1987 under name

Dreamland Holdings Berhad was listed on Bursa Malaysia. On 2 November 1991, it adopted

the name of Kanzen Berhad and the name of FACB Industries on 8 November 1997. FACBII

is a diversified business group with steel manufacturing division as its flagship operation

such as stainless and carbon steel. The Group is also involved in the trading of steel related

products and manufacturing & sales of bedding products.

Since 1990s, FACB Industries is largest integrated stainless steel welded pipes and butt-weld

fittings manufacturers in South East Asia and had exports about 70% of its stainless steel

finished products to over 60 countries by leveraging on its strong worldwide marketing

network.

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2.13 Berjaya Group

The history of Berjaya Corporation dates back to 1984 when the Chairman Tan Sri Dato' Seri

Vincent Tan Chee Yioun acquired a major controlling stake in Berjaya Industrial Berhad

originally known as Berjaya Kawat Berhad from the founders, Broken Hill Proprietary Ltd,

Australia and National Iron & Steel Mills, Singapore. In October 1988, following a majorrestructuring, Berjaya Group Berhad then known as Inter-Pacific Industrial Group Berhad

became the holding company of Berjaya Industrial Berhad. Inter-Pacific Industrial Group

Berhad formerly known as Raleigh Berhad was incorporated in 1967 as a bicycle

manufacturer. In 1969, the Company gained official listing on Bursa Malaysia Securities

Berhad Berjaya Corporation assumed the listing status of Berjaya Group Berhad on the Main

Board of Bursa Securities upon the completion of the group restructuring exercise in October

2005 and the listing of the new shares on 3 January 2006. The business includes property and

construction, holiday, hotels & resorts, education, insurance, investment holdings, food &

beverages and industry business.

2.14MHC Plantation Berhad

MHC was incorporated in the Federation of Malaya on 31 December 1960 under the

Companies Ordinances. On 15 April 1966, under the Act, MHC assumed the name of Mah

Hock Cheong Company Sdn Berhad. MHC subsequently assumed the name of MHC

Plantations Sdn Berhad on 9 July 1998 and thereafter converted to a public company under

its present name on 21 August 1998. MHC has been listed on the Main Market of Bursa

Securities since 29 November 2000. In 2005, MHC had successfully acquired a strategic 32%

stake in a plantation listed company, namely Cepatwawasan Group Berhad (CWG), based

in Sandakan. CGB is listed on the Main Market of Bursa Securities. CGB is principally an

investment holding company, whilst its subsidiary companies are principally involved in the

cultivation of oil palm, operation of quarry, milling, sales of oil palm products and power

generation and selling certified emission reduction. Presently, CWG has approximately

28,000 acres of oil palm estates in Sabah.

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2.15 Perstima Berhad

Perusahaan Sadur Timah Malaysia (PERSTIMA) Berhad is the premier producer and

supplier of high quality Tinplate for both domestic and export market. Established on 16th

August 1979 and commenced commercial production on 2nd April 1982, it's now having a

total production capacity of 200,000 MT per annum. In 2002, PERSTIMA Berhad

established PERSTIMA (VIETNAM) Co. Ltd., as the first tinplate manufacturer in Vietnam,

100% owned by PERSTIMA Berhad, located in Vietnam Singapore Industrial Park (VSIP) in

Binh Dong District, which started commercial production in October 2003. PERSTIMA

(VIETNAM), as a manufacturer of prime grade tinplate, has been equipped with a Halogen

type Continuous Electrolytic Line with a rated capacity of 100,000 MT/annum.

The Company is accredited with ISO 9002 in year 1995 and now further accredited with ISO9001:2000 in year 2001. Also in year 2005, the Company is accredited with ISO 14001. With

the ISO accreditations, our Customers are assured of our highest quality on our products and

services. To cater our products for all sections of society (especially Muslim communities

everywhere), thier obtained HALAL certification for products to ensure confidence in

consumption.

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2.16 Malaysia Economic

Since it became independent in 1957, Malaysia's economic record has been one of Asia's

best. Real gross domestic product (GDP) grew by an average of 6.5% per year from 1957 to

2005. Performance peaked in the early 1980s through the mid-1990s, as the economy

experienced sustained rapid growth averaging almost 8% annually. High levels of foreign anddomestic private investment played a significant role as the economy diversified and

modernized. Once heavily dependent on primary products such as rubber and tin, Malaysia is

a middle-income country with a multi-sector economy based on services and manufacturing.

Malaysia is one of the world's largest exporters of semiconductor components and devices,

electrical goods, solar panels, and information and communication technology (ICT)

products.

The Economy of Malaysia is a growing and relatively open state-oriented and newly

industrialized market economy where witnessed an economic boom in the 1970s, following

which it expanded to become a multi-sector economy from being a raw materials producer.

Malaysia rich natural resources ensure sound developments in agriculture, forestry and

mining.

In 2007, Malaysia was the 3rd largest economy in South East Asia and 28th largest economy

in the world by purchasing power parity with gross domestic product for 2008 of $222 billion

with a growth rate of 5% to 7% since 2007. In 2010, GDP per capita (PPP) of Malaysia

stands at US$14,700. In 2009, the nominal GDP was US$383.6 billion, and the nominal per

capita GDP was US$8,100.

Nonetheless, it is interesting to note that, the recent KLCI index was robust where as of 12

April 2012, the KLCI index closed at 1601.27, successfully breaking through the barrier of

1600. However, as of 11 May 2012, the KLCI index was closed at 1584.32, retesting the

market towards the 1600 points.

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3.0 METHODOLOGY

3.1 Stocks Return

3.1.1 Nominal Return

3.1.2 Log Nominal Return

3.1.3 Average Return

The formula for average weekly markets return ( mK ) is

260

=

m

m

KK

3.1.4 Annual Return

The formula used for determining the annual stocks return (Rm) is:

52*mm

KR =

15

1,min0

1 =P

Pralreturnno

( )rLogRalreturnLogno += 1,min


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3.2 Stand Alone Risk

In general, variance is the best used measurement to measure risks or variability. Therefore,

we will use variance to measure the stand alone risks for each stock.

3.2.1 Excess Return

The formula to calculate excess return is

)(Reii

KKturnExcess =

The excess return measures the difference between the stocks return in each interval with its

average monthly stocks return. Upon that, we calculate the variance of stocks return.

3.2.2 Variance

The formula to calculate variance is:

1

)(12

=

=

n

KK

n

t

ii

3.2.3 Standard Deviation

The formula to calculate standard deviation is:

1

)(12

=

=

n

KK

n

t

ii

The denominator of n-1 represents degree of freedom, that is, the number of values in the

final calculation of a statistic that are free to vary. The stand alone risk is the risk that is

specific to an investment asset. However, the stand alone risk or unsystematic risk can be

reduced through diversification.

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3.3 The relationship between the stock and the market

In general, the CAPM model designates a single risk factor to account for the volatility

inherent in an individual security or a portfolio of security. Beta measures the responsiveness

of the change in the price of a security to the changes in the market index. In CAMP model,

beta measures systematic risks.

3.3.1 Covariance

Covariance is a measure of how much two random variables change together. A positive

covariance means that asset returns move together. A negative covariance means returns

move inversely. One method of calculating covariance is by looking at return surprises

(deviations from expected return) in each scenario. Another method is to multiply the

correlation between the two variables by the standard deviation of each variable.

The covariance formula is:

Where:

r = nominal return

r = expected return

n = numbers of year

17

( )( )( )

1,

=

n

rrrrbaCOV

bbaa
http://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variable


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3.3.2 Correlation Coefficient

The formula to compute the correlation coefficient is:

BA

BA

BA

Covr

,

, =

The correlation coefficient has a maximum value of +1 and a minimum value of -1. A value

of +1 means the two assets move in the same direction perfectly and is called, perfect positive

correlation. A value of -1 means the two assets move in the opposite direction perfectly and is

called perfect negative correlation. A value of 0 means the movements of the two assets are

perfectly uncorrelated to each other. Combining two investments with large negative

correlation in a portfolio would create diversification because this could stabilize the rates of

return over time, reducing the standard deviation of the portfolio rates of return and hence the

risk of the portfolio.

3.3.3 Beta

Betais defined as a measure of the volatility, or systematic risk, of a security or a portfolio in

comparison to the market as a whole. This shows the relationship between the company

return and the market return.

The formula to compute the beta of a portfolio is:

m

imi

i

r

,=

i represents the beta of an investment asset i, ri,m represents the correlation coefficient of

the investment asset i with the market return, i represents the standard deviation of the

investment asset i and lastly m represents the standard deviation of the market return.

3.3.4 Covariance Matrix

However, in excel, we use covariance matrix to compute the beta of each asset. To compute

the covariance matrix in excel, we first rename the matrix of the excess return )( ii KK as

M_1.

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To compute the covariance matrix, we highlight a 16 x 16 matrix in excel and key in the

formula of:

260/)1_),1_(( MMTRANSPOSEMMULT=

Then, we press Ctrl + Shift +Enter simultaneously.

To derive the beta, we can key in the formula of:

m

mi

i

Cov

2

,

=

To do so in excel, Covi,m is the covariance of each individual asset with the market return and

the 2m is the variance of market return (KLCI).

Alternatively, the beta of an individual asset can be derived by the formula of:

$AJ$196):U196,$AJ$6:SLOPE(U6=

The U6:U196 represents the array of data of each individual stock return and the

$AJ$196:$AJ$6 represents the array of data of markets return and is fixed by pressing

F4 button.

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3.4 Portfolios Risk and Return

Investing in a portfolio of assets is ideal than investing in a single asset. As the golden rule

says: never put all your eggs in one basket and therefore we should diversify our

investments. By investing in a portfolio of assets, we can reduce unsystematic risks.

3.4.1 Portfolio Variance

First of all, we arrange our data in a systematic manner. Secondly, we arrange the weight of

each individual asset in a 15 x 1 matrix column and renamed as W_1. Thirdly, we rename the

covariance matrix as had previously computed as COV_M.

The formula to compute portfolio variance is:

)1_),_),1_((( WMCOVWTRANSPOSEMMULTMMULT=

And press CTRL + SHIFT + ENTER simultaneously. The portfolio standard deviation is

equivalent to the portfolio variance to the power of 0.5.

3.5 Plotting the efficient frontier

When all the data are good, we will plot the efficient frontier based on the output as derived

from the computation.

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4.0 INTERPRETATION OF RESULTS

4.1 Average Weekly Return

After the computation have been done. The results of average weekly return for 15

companies in the period of 5 years are shown as above. The purpose for the average weekly

return is to show that the probability of the percentage of average weekly return that we can

obtain from investing into those companies. The highest return average weekly stock return

goes to CYBER TOWER with average of 1.67% while the opposite which is the lowest is

goes to SCOMI with average of -0.22%. With the 15 companies listed, 13 out of the 15

companies shown positive feedback of average weekly stock return while the rest is shown as

the negative average weekly stock return. The KLCI (Kuala Lumpur Composite Index) play

the role as to measure the average weekly market return.

The data have shown that the average weekly market return is 0.16%. Thus, it will give the

general description to describe the company performance in the market by compare them

with the KLCI data. The companies give the higher average weekly stock return after

compare with the average weekly stock market return were SAPURA with 0.98%,

LAFARGE with 0.34%, P.NIAGA with 0.20%, CYBER TOWER with 1.67%, LEADER

STEEL with 0.20%, AHMAD ZAKI with 0.31%, FREIGHT with 0.31%, BERJAYA with

0.87%, MHC with 0.48%, and finally the PRESTIMA with 0.20%. CYBER TOWER was

able to outperform the market mainly because the technology sector was disseminated

throughout the economy.

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There is no sector of the modern economy that technology does not touch and that does not

rely upon the technology sector to improve quality, productivity, and/or profitability. As of

December 30, 2010, the Companys major shareholder was Ikhtiar Syahdu Sdn Bhd with a

43.94% stake in the Company. In August 2011, the Company incorporated a subsidiary

Starvista Limited. Thus, it becomes well perform in the stock market.

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4.2 Average Annual Return

The chart above describe that the average annual stock return for the 15 companies. The

average computation is done by multiple the average weekly returns with 52 weeks. The

higher average annual return recorded was CYBER TOWER with 86.99%, while the lowest

was SCOMI with -11.37%. With the market annual return was recorded as 8.08%, SAPURA,

LAFARGE, P.NIAGA, CYBER TOWER, LEADER STEEL, AHMAD ZAKI, FREIGHT,

BERJAYA, MHC, and PRESTIMA were come out with the well performed in the stock

market. On the yearly basis, the performance of CYBER TOWER and SAPURA are quite

impressive.

SAPURA was recorded as the second higher average annual return because Sapura Crest

Petroleum is involved in drilling, installation of pipelines and facilities, marine services,

operations and maintenance as well as development and operation of oil and gas fields. One

of the key components in Malaysias economy is the oil and gas; it stated about 30% from the

countrys manufacturing income and about 8% of annual gross domestic product. For the

financial year ended 31 Jan 2011, the company registered a net profit of RM231million, up

34% from its previous financial year while revenue stood at RM3.2billion. Operationally, the

group's order book stood at RM8.5billion.

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In year 2011 Sapura Crest was achieve with the risk service contract award of the Berantai

marginal oil field development by national oil company to a consortium comprising three

players Sapura. The consortium is expected to fork out someRM2.45billion to develop

Berantai, located about 150km off Terengganu on the East Coast of Peninsular Malaysia. The

annual return for SCOMI was excessive below the market annual return. The SCOMI had

failed to development it business activity to gain the return for it investors.

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4.3Variance

The chart above shows the calculated of variance for fifteen companies. The definition of

variance is measure of volatility or total risk. . Variance is a mathematical expectation of the

average squared deviations from the mean. The variance can help investors to determine the

risk that they need to take when purchasing a specific security. From this research, Cyber

Tower show highest variance with amount 0.03270. This show that the investors has highest

risk if purchase Cyber Towers security. Then, a lower variance of companies is Pharmaniaga

Berhad with amount 0.00111. This mean that a security of Pharmaniaga Berhad is lowest

risky from another company and it is safe for investors.

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4.4 Standard Deviation

The chart above shows the standard deviation of the 15 companies from different sectors.

Standard deviation is the square root of variance and thus, standard deviation is a measure of

risks as well. Cyber Tower had the highest standard deviation and the second highest was

SAPURA with 0.11591 as its result. Pharmaniaga Berhad had the lowest standard deviation

with 0.03331 means it had the lowest risk.

Stand-alone risk is measured by the standard deviation or the square root of variance of a

specific assets stock return. In portfolio management, the stand alone risk measures the

undiversified risks of an individual asset.

From the output, Cyber Tower had the highest standard deviation which means, it had the

highest stand alone risk. Although, Cyber Tower had the highest stand-alone risk, however,

investors can reduce the unsystematic risks by diversifying its investments. In fact, investors

can achieve the same level of return at a lower level of risks by varying the weights of each

asset in the portfolio because the unsystematic risk can be eliminated through diversification.

The portfolio that gives the highest return at the given level of risk is called the optimal

portfolio and shall be plotted on the efficient frontier.

SAPURA had the second highest standard deviation and we believe this is due to the

volatility in the underlying commodity price of palm oil in futures trading. PRESTIMA had

the second lowest standard deviation, because PRESTIMA is a real estate investment trust

fund so it is less risky.

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From the output, BERJAYA had the third highest standard deviation was 0.08774. MK

LAND had the fourth highest standard deviation was 0.08038. Standard deviation for

LEADER STEEL was 0.07893. Standard deviation for SCOMI was 0.07676. Standard

deviation for FACB was 0.07349. Standard deviation for AHMAD ZAKI was 0.07322.

Standard deviation for MHC was 0.05853. Standard deviation for LAFARGE was 0.05278.

Standard deviation for KSL was 0.05128. Standard deviation for FREIGHT was 0.04355.

Standard deviation for TOP Glove was 0.04253.

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4.5 Correlation of Coefficient Matrix

4.5.1 Covariance

A Covariance means measure of the degree to which return on two risky assets move in

tandem. The assets can said move together when a covariance is positive and a negative

covariance means return move inversely. A method that can use to calculating covariance is

by looking at return surprises in each scenario and multiple the correlations between two

variables by the standard deviation of each variable. On the table show that Cyber Tower has

highest covariance with amount 0.03270 and Pharmaniaga is smaller covariance with amount

0.00111.

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4.5.2 Correlation

The correlation of coefficient matrix shows the correlation of coefficient between two assets.

Similar to covariance matrix, correlation of coefficient matrix measures the relationship

between two asset s. The different between the two matrixes is that, correlation of coefficient

has its own maximum and minimum value whereas covariance doesnt. The maximum value

of correlation of coefficient is +1 and minimum value is -1. The correlation of coefficient

allows investor to measure the strength of relationship whether positive or negative betweenthe two assets. In portfolio management, investors tend to include assets that are negatively

correlated with the portfolios assets in order to reduce the total risks of the portfolio. Modern

portfolio concepts say that combining assets that are negatively correlated can result in risk

reduction in a portfolio.

From the output above, the higher positive correlation between KLCI is Scomi Group Bhd

with amount 0.6667. This means that Scomi Group Bhd will follow all changes of KLCI.

Then, the smaller correlation with the KLCI is Top Glove with amount 0.0352. Therefore, in

order to reduce the total risks of portfolio, investors should choose individual asset that is

smaller correlated with the portfolio assets such as Top Glove.

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4.6 Beta

The meaning of beta or also known as beta coefficient is measure of the volatility or

systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta

indicates how the price of a security responds to market forces. The more responsive the price

of a security is to the changes in the market, the higher that securitys beta. The beta for theoverall market is equal to 1.0. Then, a beta equal 1 mean that the securitys price will move

with the market and the security will be less volatile than the market if its beta less than 1.

While, a beta more than 1 indicates that the securitys price will be more volatile than the

market.

From the calculate of 15 companies, the companies that show beta more than one is MHC

Plantations Bhd with amount 1.2367, Ahmad Zaki Resources Bhd with amount 1.8066 and

Scomi Group Bhd with amount 2.0911. This shows that the price of three companies has

more volatile than the market. Besides that, the others companies has beta lower than one

mean they less volatile than the market. Then, they are also less responsive to changing

returns in the market and less risky. The companies that has beta lower one is Top Glove,

Sapura, KSL Holdings, Lafarge, Pharmaniaga Bhd, Cyber Tower, Leader Steel, Mk Land,

Freight Management Holding Bhd, FACB Industries Incorporate Bhd, Berjaya and Prestima.

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4.7 Portfolio Standard Deviation (When Short Selling was disallowed)

Standard Deviation (Market) Standard Deviation (Portfolio)

0.024474 0.020932

Market Return Risk Free Rate

8.08% 3.05%

Table above shows the overall performance of the portfolio which consists of the 15

companies from different sector. The optimal portfolio variance is 0.000438 and the optimalportfolio standard deviation is 0.02932. The market return as calculated earlier was 8.08%

and the risk free rate based on Treasury Bill 3 months was 3.05%. The risk premium was

5.03% which means the return in excess of the risk-free rate of return that an investment is

expected to yield that the extra risk that the investor would take. The individual assets that

included in the portfolio were Top Glove, KSL, Lafarge, Pharmaniaga, Scomi, Cyber Tower,

Ahmad Zaki, Freight, MHC, Prestima. The rest have been excluded where solver did not

give weights. This is primarily because, short selling was disallowed. Therefore, individual

assets with negative weights will be excluded.

The optimal portfolio is built by presetting the condition that, the portfolio variance must be

at minimum by varying the weights of each individual asset in the portfolio. The optimal

portfolio gave highest return for a given level of risk.

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In order to prove that, an optimal portfolio can achieve a given level of annual return at a

lower risk, we test the argument using scenario analysis. At condition A, we want the optimal

portfolio to achieve the same level of annual return as the same as the individual stock of MK

Land which is -0.00007561 or -0.00756% but at a lower level of risk. At condition B, we

want the optimal portfolio to achieve the same level of annual return as the same as the

individual stock of PharmaNiaga which 0.001952 or 0.1952% but at a lower level of risk.

As for selected individual Stock:

Stock Name Standard Deviation Annual Return

MK Land 0.080384 -0.00393

PharmaNiaga 0.033313 0.101503

In order to prove that, investing in a portfolio of assets can eliminate unsystematic risks, we

done the test using solver. In fact, individual stock that had the highest standard deviation

was MK Land with, standard deviation of 0.080384 and annual return of -0.00393.

Individual stock that had the lowest standard deviation was PharmaNiaga ,with standard

deviation of 0.033313and annual return of 0.101503.

Thus, investors should always target on the optimal portfolio that locates on the efficient

frontier because the optimal portfolio able to give highest return for a given level of risk than

individual stock.

When short selling was disallowed, investors should buy Top Glove, KSL, Lafarge,

Pharmaniaga, Scomi, Cyber Tower, Ahmad Zaki, Freight, MHC, Prestima at the weight of

18%, 4%, 3%, 30%, 1%, 3%, 10%, 9%, and 21% respectively.

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4.8 Efficient Frontier (When Short Selling was allowed)

0.002260

0.002265

0.002270

0.0022750.002280

0.002285

0.002290

0.002295

0.002300

0.002305

0.002310

0.0004380.0004380.0004380.0004380.0004380.0004380.000438

Series1

The graph above shows the efficient frontier (when short selling was disallowed). The

efficient frontier describes the relationship between the return that can be expected from a

portfolio and the riskiness of the portfolio. Investors can look the efficient frontier because it

can gives the best return that can be expected for a given level of risk or the lowest level of

risk needed to achieve a given expected rate of return. The weights of each individual stock

as included in the optimal portfolio are 18% Top Glove, 4% KSL Holding, 4% Lafarge, 30%

Pharmaniaga, 1% Scomi, 0.46% Cyber Tower, 3% Ahmad Zaki, 10% Freight Management,

9% MHC Holding and 21% Prestima. Only ten stocks were included because short selling

had been disallowed.

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All portfolios plotted on the efficient frontier are optimal portfolios that offer the highest

expected return for a defined level of risk or the lowest risk for a given level of expected

return. Investors should always target on the portfolios that locate on the efficient frontier

because the choice of investment onto the optimal portfolios depends on the risk appetite of

investors. The investors can choose to invest into optimal portfolios that locate on the upper if

they want to have more return, however, the risk too increase proportionately.

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4.9 Portfolio Standard Deviation (When Short Selling was allowed)

Short selling means to sell a certain amount of borrowed shares from a third party now and

repurchase the sold shares at a later date in order to return the borrowed shares to the third

party. Short selling attempts to make a profit from the falling in price by selling the borrowed

shares now at a higher price and intended to repurchase the same shares at a later date at alower price and return to the third party.

In our sample, we conduct short selling with the following way:

STOCK LONG(BUY) SHORT(SELL)

TOP GLOVE 18.03%

KSL 5.93%

LAFARGE 5.02%

PHARMANIAGA 29.87%

SCOMI 0.22%CYBER TOWER 0.43%

AHMAD ZAKI 2.42%

FREIGHT 10.74%

MHC 9.45%

PRESTIMA 22.84%

SAPURA -1.65%

LEADER STEEL -1.10%

MK LAND -0.33%

FACB -1.26%

BERJAYA -0.61%

When investors conduct short selling, investors will long (buy) some shares and short(sell)

some shares in order to reap a better profit by actively managing their portfolio. Investors

should hold shares that will appreciate in value in the future and sell shares now that will

depreciate in value in future. In short selling, the sold shares are expected to be repurchased

from the open market at a lower price and the spread between the selling price at initial date

(t0) with the repurchased price at later date (t1) is the profit to the investor.

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Based on the computation, we should establish a long position for Top Glove, KSL, Lafarge,

Pharmaniaga, Scomi, Cyber Tower, Ahmad Zaki, Freight, MHC and Prestima. On the other

hand, we should establish a short position for Sapura, Leader Steel, MK Land, FACB and

Berjaya.

Pharmaniaga is a blue chip stock because its business earnings on average showed anuprising trend. The continual growing in population and demand for medical products are two

power forces that keep Pharmaniaga to continue enjoying a steady and good business

opportunities. The business itself was rather profitable. For the most recent 5 years, from

2007-2011, Pharmaniaga had a compound annual growth 11%. The strong growth in sales

was mainly attributed to the effect of the Pharmaniaga in developing medical products that

should meet the varying needs of the local citizens.

Prestima had the second largest weight in the long position. The company is the premier

producer and supplier of high quality tinplate for both domestic and export market. The

company enjoyed a compound annual sales growth 17.48% from year 2007-2011. However,

the growth in revenue soon dipped from RM 853,350 000 to RM 660, 565 000 from 2011-

2007. The sharp slipped in sales revenue was mainly due to the outbreak of Global Financial

Crisis. . The European debt concerns had further ignited the bearish sentiments in a fairly

volatile market condition. Therefore, when the global economy moved towards better, we

believe that Prestima will restore its glory and will continue yielding a higher compoundannual growth in sales. Hence, we should establish a long position on Prestima in an

anticipation of a better global economy and a greater sales revenue growth for Prestima in

the near future.

Next, we should long (buy) Top Glove because it is worlds largest rubber glove

manufacturer. In view of the uncertain global economics ahead, most investors may prefer to

invest in a safer investment instrument. . Hence, Top Glove is expected to rise in value and

we should buy. Freight Management is expected to continue from the growing needs in

technologies of the local market as well as the global because technological usage of the

world has increased. Most of the international freight service such as sea, rail, air freight and

tug barge service, customs brokerage and distribution container haulage and conventional

trucking service needs the higher in there technologies. For example, the year on year global

semiconductor sales grew by 10.7% in 2011 to a record RM327.1 million. Thus, Freight is

expected to grab a share on this robust business opportunities and its stock price will

appreciate in value in the near future.

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MHC, KSL, Lafarge, Scomi, Cyber Tower and Ahmad Zaki are expected to continue

appreciate in value in view of their good historical growth. Therefore, we should buy those

stocks. In addition, we should sell Sapura, Leader Steel, MK Land, FACB and Berjaya too.

This may due to the fact that, these stocks could be being overvalued for now and were

expected to fall in value in future.

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4.10 Efficient Frontier (When Short Selling was allowed)

The table above shows the efficient frontier when short selling was allowed. The optimal

portfolios lie on the efficient frontier where these portfolios offer the highest return for a

given level of risk. From the table above, the minimum standard deviation was 0.002

however, the portfolio return was -0.957%. However, investors can increase their return by

investing in a riskier optimal portfolio. This can be done by investing into the optimal

portfolios that locate at the upper end of the curve. This is consistent to the risk and return

trade off theory, that is, higher the risks bring higher the return.

When short selling was allowed, we should buy Top Glove, KSL, Lafarge, Pharmaniaga,

Scomi, Cyber Tower, Ahmad Zaki, Freight, MHC and Prestima at the weight of 18.03%,

5.93%, 5.02%, 29.07%, 0.22%, 0.43%, 2.42%, 10.74%, 9.45% and 22.84% respectively, and

we should sell Sapura, Leader Steel, MK Land, FACB and Berjaya at the weight of -1.65%,

-1.10%, -0.33%, -1.26% and -0.61% respectively. We have done the portfolio optimization

process successfully.

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5.0 CONCLUSION

The portfolio optimization shows that investors can achieve a higher return on investment for

a given level of risk by investing their wealth in a portfolio of stocks. The optimal portfolio

gives the highest return for a given level of risk because the risk is reduced by including

individual stock that is negatively correlated with the portfolios stocks. Throughdiversification, investors can reduce unsystematic risks because these risks are unique to a

specific stock.

In this working paper, we have shown the process of conducting the portfolio optimization

process when short selling was allowed and disallowed. We have come out with two efficient

frontiers that were, efficient frontier without short selling and efficient frontier without short

selling. Investors should always invest in optimal portfolios that lie on the efficient frontier.

When short selling was disallowed, investors should buy Top Glove, KSL, Lafarge,

Pharmaniaga, Scomi, Cyber Tower, Ahmad Zaki, Freight, MHC, Prestima at the weight of

18%, 4%, 3%, 30%, 1%, 3%, 10%, 9%, and 21% respectively.When short selling was

allowed, we should buy Top Glove, KSL, Lafarge, Pharmaniaga, Scomi, Cyber Tower,

Ahmad Zaki, Freight, MHC and Prestima at the weight of 18.03%, 5.93%, 5.02%, 29.07%,

0.22%, 0.43%, 2.42%, 10.74%, 9.45% and 22.84% respectively, and we should sell Sapura,

Leader Steel, MK Land, FACB and Berjaya at the weight of -1.65%, -1.10%, -0.33%, -1.26%

and -0.61% respectively.

In short, investors should not invest in a single stock. Instead, investors should invest in a

portfolio of stocks because the optimal portfolio can reduce the stand-alone risk by including

a set of individual stocks that are negatively correlated with each other. The unsystematic

risks were reduced through diversification, leaving only systematic risk to be taken by the

investors. If an investor wishes to have more return, he or she can investment on the optimal

portfolios that are located on the upper end of the efficient frontier, however, the risks will

increase proportionately with the increase in portfolio return as well. Investors are assumed to

adopt rational behaviour and prefer more wealth at a lower level of risk.

We would like to end our conclusion by advising investors to continue actively searching for

top performing stocks in order to create an optimal portfolio of their own that gave a higher

return at a lower level of risks. In fact, investors can construct a better optimal portfolio than

the optimal portfolio as built by us by including more top performing stocks in their own

portfolio.

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Also, investors should conduct active portfolio management by actively managing its

portfolio. Investors are recommended to review their portfolio performance on periodical

basis so that the actual performance as realized will be about the same as what had being

initially expected. This can be done by actively changing the weights of each individual stock

of the portfolio or by changing the individual assets in the portfolio, in order to yield a higher

return for a given level of risk.

The principal ideology behind portfolio optimization is to develop an optimal portfolio that

gives higher return for a given level of risk. Investors are advised to follow the portfolio

optimization process as indicated in this working paper. Lastly, in view of the high volatility

in the current stock market and some possible political rallies in Malaysia, it is advised to

hold cash for now and invest only when the stock market is regaining its strength. The

European debt crisis concerns had created a lot of volatility in the stock market and investors

should conduct a close monitoring on the global economy outlook.

Report Group Ass.

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