Construction of efficient portfolio depends on the selection of right asset classes and right securities that will leads to optimum portfolio performance. In this report, the correlations between the average return of different sectors of Dhaka Stock Exchange have been calculated to choose the sectors with minimal correlation of return. Four major sectors with negative correlation among them has been selected and sixteen growth stocks from these sectors has been identified to construct this portfolio. Using the portfolio optimization technique, the weight of these stocks has been determined under the situation of objective functions and constraints. In case of maximizing portfolio theta while short sales are not allowed, the optimum results suggests to invest 65.20% in BATBC, 20.89% in WATACHEM, 11.35% in JMISMDL, and rest 2.57% in GEMINISEA. The theta of this portfolio in this case is 21.41%. The weights vector has been calculated while short sells are allowed and objective function is to maximize the theta of this portfolio. Moreover, the weights vectors has been determined for different objective functions such as minimizing portfolio risk and different set of constraints.

1. Efficient Portfolio
Construction

2. ii
A report on
‘Efficient Portfolio Construction’
Course Name: Portfolio Management
Course Code: F-407
Submitted To
Md. Saimum Hossain ,CFA
Lecturer
Department of Finance
University of Dhaka
Submitted By
Pantho Sarker
ID: 20-033
Section: A
BBA 20th Batch
Department of Finance
University of Dhaka
Date of Submission: March 3, 2018

3. iii
Letter of Transmittal
March 3, 2018
Md. Saimum Hossain, CFA
Lecturer
Department of Finance
University of Dhaka
Subject: Submission of the report on ‘Efficient Portfolio Construction’
Dear Sir,
I am very happy to state that the report on “Efficient Portfolio Construction” is completed and
ready for your viewing. I am glad to submit it as part of completion of the requirements for our
Portfolio Management (F-407) course with you. It is an opportunity and great pleasure for me
to use different portfolio optimization techniques in the practical aspects.
It got an experience of applying my theoretical knowledge practically in this report. The
gathered and acquired knowledge will help me to boost up my career.
I have tried my best to put up a good report with as much information as I could gather during
the time span allotted for writing this report.
Thank you for your kind support and help throughout the course. I hope you will appreciate
this sincere effort.
Sincerely,
Pantho Sarker
ID: 20-033
BBA 20th
Batch
Section : A
Department of Finance
University of Dhaka

4. iv
Acknowledgement
It is an honor for me to submit this report to my respected teacher Md. Saimum Hossain ,CFA,
Lecturer, Department of Finance, University of Dhaka. At first, I want to convey my thanks
and gratitude to him for assigning me to prepare report on Construction of Efficient Portfolio.
It would not have been possible for me to complete the report without your help.
In preparing this report, I got full co-operation from my teachers and that was a great advantage
for me. An individual can achieve no noble achievement by his/her alone trial.

5. v
Table of Contents
Executive Summary..................................................................................................................vi
Chapter 1:Introduction...............................................................................................................1
1.1 Origin of the Report .........................................................................................................1
1.2 Objective of this Report ...................................................................................................1
1.3 Methodology ....................................................................................................................1
1.4 Sources of Secondary Data ..............................................................................................1
1.5 Scope of the Study............................................................................................................1
1.6 Limitations of the Study...................................................................................................1
Chapter 2: Constructing Efficient Portfolio...............................................................................2
2.1 Selection of Asset Class and Securities: ..........................................................................2
2.2 Collection of Data: ...........................................................................................................3
2.3 Adjustment of the Monthly Closing Prices for Stock Split, Cash Dividends and Stock
Dividends: ..............................................................................................................................3
2.4 Determination of Return Series:.......................................................................................4
2.5 Calculation of Risk Free Rate: .........................................................................................4
2.6 Preparation of Co-variance Matrix:..................................................................................4
2.7 Calculation of Theta in the Case of Equal Weight:..........................................................5
2.8 Calculating Portfolio Weight by Maximizing Theta by not Allowing Short Sell:...........5
2.9 Calculating Portfolio Weight by Maximizing Theta by Allowing Short Sell..................6
2.10 Calculating Portfolio Weight by Minimizing Risk without Short Sell:.........................7
2.11 Calculating Portfolio Weight by Minimizing Risk with Short Sell:..............................8
2.12 Minimizing Risk by Allowing Short Sale for a Given Return.......................................9
Conclusion ...............................................................................................................................10
Appendix..................................................................................................................................11

6. vi
Executive Summary
Construction of efficient portfolio depends on the selection of right asset classes and right
securities that will leads to optimum portfolio performance. In this report, the correlations
between the average return of different sectors of Dhaka Stock Exchange have been calculated
to choose the sectors with minimal correlation of return. Four major sectors with negative
correlation among them has been selected and sixteen growth stocks from these sectors has
been identified to construct this portfolio. Using the portfolio optimization technique, the
weight of these stocks has been determined under the situation of objective functions and
constraints.
In case of maximizing portfolio theta while short sales are not allowed, the optimum results
suggests to invest 65.20% in BATBC, 20.89% in WATACHEM, 11.35% in JMISMDL, and
rest 2.57% in GEMINISEA. The theta of this portfolio in this case is 21.41%. The weights
vector has been calculated while short sells are allowed and objective function is to maximize
the theta of this portfolio. Moreover, the weights vectors has been determined for different
objective functions such as minimizing portfolio risk and different set of constraints.

7. 1
Chapter 1:Introduction
1.1 Origin of the Report
This report is prepared for Md. Saimum Hossain, CFA, Lecturer, Course teacher of “Portfolio
Management” Course # F-407. Our course instructor has assigned to the students of the
department of Finance, BBA 20th batch, to make report on “Efficient portfolio” This report is
prepared during the 2nd semester of 4th Year and would be submitted in the same semester.
The standard procedure for the long, formal report is followed here as part of the instruction of
the course instructor.
1.2 Objective of this Report
The primary objective of the report is to fulfill the partial requirement of this course.
The secondary objectives of this report are :
 To know the portfolio optimization technique and method
 To gather an overall idea about the sectors and asset classes
 To know how to minimize risk and maximize return by assigning optimal weights
 To gain first-hand knowledge on the topic that we have been assigned
1.3 Methodology
To prepare this report, I was mainly dependent on the secondary data from Library of Dhaka
Stock Exchange.
1.4 Sources of Secondary Data
The main sources of secondary information regarding monthly closing price , dividends , right
issue, stock splits is DSE website and Library of DSE. The data of cut of yield of T-bill has
been collected from the website of DSE.
1.5 Scope of the Study
Everything has some advantage, which helps that work to be completed thoroughly. I get some
opportunities, which help me to make a standard report. Major of them are-
 Enough Time: I had got enough time to prepare a report so that I could gather enough
information with less tension.
 Easy Topic: The topic of us was much easier because I have learnt about “Efficient
portfolio” .So I didn’t face any problem related to my topic.
 Easy access to information: I had an easy access to information. I gathered enough
information from different websites.
1.6 Limitations of the Study
Every study has some limitations. I have faced some usual restrictions during the course of my
preparation of this report. The major limitations are as follows:

8. 2
 Lack of asset class: I had to depend on only one asset class i.e. equity. As there is no
other liquid formal market for other asset classes. So the main objective of portfolio
i.e. diversification is not fully achieved.
 Lack of Adjustments: It were required to adjust the historical return series with the
findings of fundamental analysis. But, due to some limitation it is not done in this
report.
Chapter 2: Constructing Efficient Portfolio
2.1 Selection of Asset Class and Securities:
The most common asset class, stock is used here to form a portfolio. Stocks of different sectors
has been selected from the listed stocks in Dhaka Stock Exchange (DSE). The investment style
used to construct this portfolio is investment in growth stocks. I have selected 4 sectors Food
& Allied , Fuel and Power, Telecommunication, and Pharmaceuticals & Chemicals. The whole
procedures followed is summarized below.
(a) The monthly closing price of the recent five years of all the listed companies of DSE
has been used to conduct this correlation matrix.
(b) The monthly return of all the listed stocks of different stocks has been determined.
(c) The average monthly return of each sector has been calculated for all the sectors of
listed stocks in DSE.
(d) Then, the correlation matrix (Appendix I) has been developed to determine the
correlation of the average monthly return of different sectors.
(e) Sectors with the lowest correlations have been selected for picking stocks to construct
the portfolio.
From the selected sectors, sixteen growth stocks has been selected from the selected four
sectors. The following table shows the selected stocks:
Sectors Name of the
Company
Ticker P/E P/B Dividend
yield
Pharmaceutics
&
Chemicals
RECKITTBEN Reckitt
Benckiser(Bd.)Ltd
51.11 47.57 0.02
MARICO Marico
Bangladesh
Limited
24.54 19.56 0.00
PHARMAID Pharma Aids 38.20 8.74 0.01
JMISMDL JMI Syringes &
Medical Devices
Ltd.
26.30 2.58 0.02
WATACHEM Wata Chemicals
Limited
75.43 3.62 0.00

9. 3
SQURPHARMA Square
Pharmaceuticals
Ltd.
20.74 4.59 0.01
ORIONINFU Orion Infusion
Ltd.
32.44 4.45 0.03
Food & Allied
GEMINISEA Gemini Sea Food
Ltd.
76.22 27.84 0.00
BATBC British American
Tobacco
bangladesh
Company Limited
26.96 10.37 0.02
OLYMPIC Olympic
Industries Ltd.
32.34 10.10 0.02
APEXFOODS Apex Foods
Limited
80.69 1.21 0.01
AMCL(PRAN) Agricultural
Marketing
Company Ltd.
(Pran)
30.88 2.98 0.01
Fuel and Power
EASTRNLUB Eastern Lubricants
Ltd.
26.44 6.97 0.01
LINDEBD Linde Bangladesh
Limited
22.44 5.84 0.01
MJLBD MJL Bangladesh
Limited
16.24 3.28 0.04
Telecommunication GP Grameenphone 21.32 19.25 0.04
2.2 Collection of Data:
The monthly closing price of the selected stocks has been collected for last seven years. The
monthly price of 84 periods has been collected for each stock. The price data is attached to
Appendix II.
2.3 Adjustment of the Monthly Closing Prices for Stock Split, Cash
Dividends and Stock Dividends:
The adjustments for the cash dividend and stock dividend has been made on the monthly price
on which the record date falls. Price data from January 2011 to November 2011 has been had
adjusted for stock splits if stock split. The information of cash dividends, stock dividends and
stock split is shown in Appendix III. The adjusted price data is presented in Appendix IV.

10. 4
2.4 Determination of Return Series:
The return series is calculated by using the following formula Rt: ln (Rt / Rt - 1). Ln is taken
to make the return series a normal distribution. Details result of calculation of return series is
attached to Appendix V. The summarized results of the return series is as follows-
Company Name Mean
Return
Company
Name
Mean
Return
RECKITTBEN 0.0063 BATBC 0.0191
MARICO 0.0130 OLYMPIC 0.0033
PHARMAID 0.0059 JMISMDL 0.0194
APEXFOODS 0.0038 AMCL(PRAN) 0.0039
WATACHEM 0.0346 EASTRNLUB 0.0058
SQURPHARMA -0.0017 LINDEBD 0.0083
ORIONINFU -0.0057 MJLBD -0.0048
GEMINISEA 0.0131 GP 0.0083
2.5 Calculation of Risk Free Rate:
The cut of yields of 364 days T bills of Bangladesh Bank for last seven years are used here to
determine the monthly average risk free rate. The monthly average risk free rate is 0.6481%
Year
Interest Rate of
Bangladesh Bank 364
days T bill
2011 6%
2012 11%
2013 11.38%
2014 8.88%
2015 8.30%
2016 4.50%
2017 3.74%
Risk Free Rate over last 7 years 0.006481928
2.6 Preparation of Co-variance Matrix:
Co-variance matrix is prepared and used in determine the theta of this portfolio under different
constraints and objective functions. This matrix the covariance of the asset with other asset and
with the asset itself was calculated. I have also calculated the excess return of each stock.
Moreover, I have calculated excess portfolio returns. Detail computation is in Appendix VI.

11. 5
2.7 Calculation of Theta in the Case of Equal Weight:
The detailed computation of portfolio return, excess portfolio return , risk of the portfolio and
theta is done in Appendix VI. The summary result of equal weight case is as follows-
Portfolio Return 0.83%
Portfolio excess return 0.18%
Portfolio variance 0.57%
Portfolio standard deviation 7.52%
Theta 2.39%
Total Weight 1
2.8 Calculating Portfolio Weight by Maximizing Theta by not Allowing
Short Sell:
The main objective is to maximize the risk adjusted return. Therefore, the measure used for
this purpose is Theta. I want to maximize the theta without short sales. For this purpose, I have
used the solver to maximize the theta by changing the weight of in selected sixteen securities.
The total weight is set up is equal to 1, i.e. our entire fund is invested. Furthermore, I allowed
only positive number i.e. I do not allow any short sale. The objective functions and constraints
used in solver and the result in the below tables. Further details is shown in Appendix VII.
Objective Function: Max Theta
By Change cells: The Weight Vector
Constraints:
(i) Sum of the weights equal to one.
(ii) The weight vector is greater than or equal to zero
The following table shows the weights in each stocks after using solver to find out the optimum
result based on the constraints.
Company Weight Company Weight
RECKITTBEN 0.00% BATBC 65.20%
MARICO 0.00% OLYMPIC 0.00%
PHARMAID 0.00% JMISMDL 11.35%
APEXFOODS 0.00% AMCL(PRAN) 0.00%
WATACHEM 20.89% EASTRNLUB 0.00%
SQURPHARMA 0.00% LINDEBD 0.00%
ORIONINFU 0.00% MJLBD 0.00%
GEMINISEA 2.57% GP 0.00%

12. 6
Here, I have to long stock in BATBC, WATACHEM, JMISMDL, and GEMINISEA. The
summary of the expected performance using the weights mentioned above table is as follows-
Portfolio Return 2.22%
Portfolio excess return 1.57%
Portfolio variance 0.54%
Portfolio standard deviation 7.34%
Theta 21.41%
Total Weight 1
2.9 Calculating Portfolio Weight by Maximizing Theta by Allowing Short
Sell
The main objective is to maximize the risk adjusted return. Therefore, the measure used for
this purpose is Theta. We want to maximize the theta by allowing short sales. For this purpose,
I set up the solver to maximize the theta by changing the weight of in selected sixteen securities.
The total weight is set up is equal to 1, i.e. our entire fund is invested. Furthermore, short sales
are allowed. Therefore, negative value is allowed in weight vector. The objective functions and
constraints used in solver and the result in the below tables. Further details is shown in
Appendix VIII.
Objective Function: Max Theta
By Change cells: The Weight Vector
Constraints:
(i) Sum of the weights equal to one.
The following table shows the weights in each stocks after using solver to find out the optimum
result based on the constraints.
Company Weight Company Weight
RECKITTBEN -49% BATBC 121%
MARICO 22% OLYMPIC 14%
PHARMAID 33% JMISMDL 101%
APEXFOODS 32% AMCL(PRAN) -217%
WATACHEM 25% EASTRNLUB 17%
SQURPHARMA -33% LINDEBD 65%
ORIONINFU -5% MJLBD -35%
GEMINISEA -3% GP 11%

13. 7
The summary of the expected performance of this portfolio using the above optimum weights
under given constraints is as follows-
Portfolio Return 5.58%
Portfolio excess return 4.93%
Portfolio variance 1.78%
Portfolio standard deviation 13.33%
Theta 36.95%
Total Weight 1
2.10 Calculating Portfolio Weight by Minimizing Risk without Short Sell:
Now I are concern about portfolio risk. I want to minimize the portfolio risk i.e. the standard
deviation. In this case, short sales are not allowed and the main goal is to minimize the standard
deviation of portfolio return. The objective functions and constraints used in solver and the
result in the below tables. The detailed calculation is shown in the Appendix IX.
Objective Function: Minimize Portfolio Standard Deviation
By Change cells: The Weight Vector
Constraints:
(i) Sum of the weights equal to one.
(ii) The weight vector is greater than or equal to zero
The following table shows the weights in each stocks after using solver to find out the optimum
result based on the constraints.
Company Weight Company Weight
RECKITTBEN 0% BATBC 34%
MARICO 0% OLYMPIC 0%
PHARMAID 0% JMISMDL 12%
APEXFOODS 0% AMCL(PRAN) 0%
WATACHEM 4% EASTRNLUB 0%
SQURPHARMA 9% LINDEBD 21%
ORIONINFU 0% MJLBD 12%
GEMINISEA 4% GP 3%
The summary of the expected performance of this portfolio using the above optimum weights
under given constraints is as follows-
Portfolio Return 1.22%
Portfolio excess return 0.57%
Portfolio variance 0.35%

14. 8
Portfolio standard deviation 5.89%
Theta 9.72%
Total Weight 1
2.11 Calculating Portfolio Weight by Minimizing Risk with Short Sell:
Now I am concerned about the portfolio risk. I want to minimize the portfolio risk i.e. the
standard deviation. In this case, short sales are allowed and the main goal is to minimize the
standard deviation of portfolio return. The objective functions and constraints used in solver
and the result in the below tables. The detailed calculation is shown in the Appendix X.
Objective Function: Minimize Portfolio Standard Deviation
By Change cells: The Weight Vector
Constraints:
(i) Sum of the weights equal to one.
The following table shows the weights in each stocks after using solver to find out the optimum
result based on the constraints.
Company Weight Company Weight
RECKITTBEN -5% BATBC 37%
MARICO 7% OLYMPIC 2%
PHARMAID -1% JMISMDL 27%
APEXFOODS 8% AMCL(PRAN) -39%
WATACHEM 4% EASTRNLUB 1%
SQURPHARMA 6% LINDEBD 30%
ORIONINFU 3% MJLBD 12%
GEMINISEA 3% GP 4%
The summary of the expected performance of this portfolio using the above optimum weights
under given constraints is as follows-
Portfolio Return 1.54%
Portfolio excess return 0.89%
Portfolio variance 0.31%
Portfolio standard deviation 5.60%
Theta 15.87%
Total Weight 1.00

15. 9
2.12 Minimizing Risk by Allowing Short Sale for a Given Return
In this case, the main goal is to minimize the risk of the portfolio return while another additional
constraint is that the rate of portfolio return is given. I have to achieve this given return by
changing weight vector while the key goal is to minimize the risk of the portfolio return.
Moreover, short sales is allowed in this case. The objective functions and constraints used in
solver and the result in the below tables. The detailed calculation is shown in the Appendix XI.
Objective Function: Minimize Portfolio Standard Deviation
By Change cells: The Weight Vector
Constraints:
(i) Sum of the weights equal to one.
(ii) The weight vector is greater than or equal to zero
(iii) Portfolio return will be equal to 15%
The following table shows the weights in each stocks after using solver to find out the optimum
result based on the constraints.
Company Weight Company Weight
RECKITTBEN -152% BATBC 318%
MARICO 59% OLYMPIC 42%
PHARMAID 111% JMISMDL 274%
APEXFOODS 89% AMCL(PRAN) -630%
WATACHEM 74% EASTRNLUB 56%
SQURPHARMA -122% LINDEBD 148%
ORIONINFU -31% MJLBD -143%
GEMINISEA -17% GP 26%
The summary of the expected performance of this portfolio using the above optimum weights
under given constraints is as follows-
Portfolio Return 15%
Portfolio excess return 14%
Portfolio variance 16%
Portfolio standard deviation 41%
Theta 35%
Total Weight 1

16. 10
Conclusion
The portfolio constructed here in this case provides without short sales provides optimum theta
of 21.41%. This is the risk adjusted return of this portfolio under the constraints of without
short sales. As short sell is not is not allowed in our country, it is not possible to optimize the
risk adjusted return with short sales. It possible to minimize the risk of the portfolio. In this
case, if short sell is not allowed the theta of this portfolio will be 9.72% while the risk will be
5.89%. This portfolio construction will be more accurate if I adjust the historical data of return
series with information gathered from fundamental analysis of these stocks.

17. 11
Appendix
Appendix I: Correlation among the return of the stocks of different sectors

18. 12
Appendix II: Monthly Closing Price

19. 13

20. 14

21. 15
Appendix III: Information of Cash Dividends , Stock Dividends, and Stock Splits
Cash Dividend

22. 16

23. 17

24. 18
Stock Dividends:

25. 19

26. 20

27. 21
Stock Split:

28. 22
Appendix IV: Adjusted Monthly Closing Prices

29. 23

30. 24

31. 25
Appendix V: Return Series

32. 26

33. 27

34. 28
Appendix VI: Co-variance matrix and portfolio performance while equal weight in each
stocks

35. 29
Appendix VII: Maximizing Theta not allowing Short Sells
Appendix VIII: Maximizing Theta Allowing Short Sells

36. 30
Appendix IX: Minimizing risk (Standard Deviation) by not allowing short sells

37. 31
Appendix X: Minimizing risk (Standard Deviation) by allowing short sells

38. 32

39. 33
Appendix XI: Minimizing risk (Standard Deviation) by not allowing short sells for a given
return

40. 34
Appendix XII: Minimizing risk (Standard Deviation) by allowing short sells for a given
return