VIEW WITH IMAGES AND CHARTS
Portfolio Construction Using Ten Securities
We were assigned to make a report on portfolio construction. For this purpose we collected data from DSE. We know, portfolio is the combination of securities of an individual. The goals of investment vary with man to man, institutions to institutions based on their financial conditions, economic stability, and risk tolerance, need of income stream, age, and job status. Regardless of the ultimate goal, all face the same set of challenges that extend beyond just the choice of what asset classes to invest in. Here our main objective is to find out optimum portfolio convergence with individual and institutions investment policy objectives. By portfolio approach I mean evaluating individual securities in relation to their contribution to the investment characteristics of the whole portfolio. Here we have taken 10 companies that are listed in Dhaka stock exchange from different industries. We want to maximize the theta and want to minimize risk. We use solver function through excel worksheet to find out portfolio weight to be complied with given eight situation. These are, 1. Maximizing Theta allowing short sell 2. Maximizing Theta by not allowing short sell 3. Minimizing Risk (Standard Deviation) by allowing short sell 4. Minimizing Risk (Standard Deviation) by not allowing short sell 5. Minimizing Risk (Standard Deviation) by allowing short sell for a given return 6. Minimizing Risk (Standard Deviation) by not allowing short sell for a given return 7. Maximizing Return by allowing short sell for a given risk 8. Maximizing return by not allowing short sell for a given risk
Objectives of the Report To construct an efficient portfolio- is the main objective of making this report which (1) minimizes risk without short sell; (2) minimizes risk with short sell; (3) minimizes risk without short sell with a given return; (4) minimizes risk with short sell with a given return; (5) maximizes Theta without short sell and (6) maximizes Theta with short sell (7) maximizes return at given risk without short sell (8) maximizes return at given risk with short sell. Methodology
The methodologies taken to construct my portfolio are as follows: 1.
Asset class selection
2.
Individual asset selection.
3.
Closing price collection of the selected stocks for year 2006-2010
4.
Dividend adjustment
5.
Monthly return and average monthly return calculation for each stock
6.
Risk free rate of return calculation
7.
excess return calculation
8.
Weighting each stocks & Excess Portfolio Return Calculation
9.
Variance-covariance matrix preparation and calculation of portfolio variance, standard deviation and theta
10.
Using solver function to find out the efficient portfolio in different situation
About DSE Dhaka Stock Exchange (DSE) is the main stock exchange of the two operating stock exchange in our country. Being incorporated as “East Pakistan Stock Exchange” in 1954 with the authorized capital of Rs. 300000 divided into 150 shares, “Dhaka Stock Exchange” is now operating with 250 listed companies (as of 12September 2011) with a combined market capitalization of tk. 2836 billion. It is formed and managed under Company Act 1994, Security and Exchange Commission Act 1993, Security and Exchange Commission Regulation 1994, and Security Exchange (Inside Trading) regulation 1994. Dhaka Stock Exchange (DSE) operates with Equity Stocks, Debt Securities and Mutual Funds. There are four categories of equity stocks; “A” category stocks consisting of 197 issues, “B” category stocks consisting of 8 issues, “N” category stocks consisting of 4 issues and “Z” category stocks consisting of 15 issues. There are also issues of 29 mutual fund and 3 corporate bonds. DSE has three types of calculated index, ALL SHARES PRICE INDEX (DSI), DSE - 20 INDEX (DS20), DSE GENERAL INDEX (DGEN). DSE GENERAL INDEX is calculated for A, B & N categories only and Z category companies are kept out of computation of top 10 gainers list. Gradual Development of Dhaka Stock Exchange (DSE): In 1976 trading restarted in Bangladesh after being discontinued for 5 years due to liberation war in 1971. On 16 September 1986 DSE was started. The formula for calculating DSE all share price index was changed according to IFC
on 1 November 1993. The automated trading was initiated in 10 August 1998 and started on 1 January 2001.
Central Depository System (CDS) was initiated in 24 January 2004.
As of November 16, 2009, the benchmark index of the Dhaka Stock Exchange (DSE) crossed 4000 points for the first time, setting another new high at 4148 points. In 2010, the index crossed 8500 points and finally crashed in the first quarter of 2011. Optimum Portfolio Market portfolio is combination of all securities that trade in the market. Among all the securities choosing two or more securities for individual investment is called optimum investment portfolio. We can also refer optimum investment portfolio as efficient portfolio that offer higher return in a given risk level or lower risk at a given Return level. A Graph is Shown Below where we can see a curve called as opportunity set. The point Minimum Variance Portfolio is a portfolio with lowest risk. Above part of Minimum Variance Portfolio is Called Efficient Frontier. Rf is the risk free rate. A line starting from the origin at risk free rate tends upward by touching the efficient frontier is known as CML (Capital market line) The point of tangency is known as optimum or efficient portfolio.
Rf
Minimum variance portfolio
Standard deviation б
There are many factors that work behind the determination of portfolio. Such as economic condition, inside information, the investors objective and constraints, risk tolerance etc. Here we have tried to create a portfolio on the basis of the Market Price Data and the Dividend adjustments. We have collected last 5 years data from DSE. Selection of Industry: We select our industries based on following analysis:
Banking, NBFI And Insurance Industry:
Banking corporations, Non-Bank Financial Institutions (NBFI), and insurance companies are the major players of the both stock exchanges in our country. They contribute largely to the change of all kinds of indices in both DSE &CSE. Banks, NBFIs and Insurance Companies are holding the largest portion of market capitalization. We have identified that Banks, NBFIs and Insurance Companies are greater in number in the calculation of DSE-20 Index. It indicates the sensitivity of changing index to the change of the player of this industry. Textile Industry: Our textile industry has high potentiality. We know that Bangladesh earns the largest portion of foreign currency from Ready Made Garments (RMG). Recently this potentiality has increased radically due to the global financial crisis. As income of the people of developed countries has fallen in remarkable number, their living standard also has fallen. And now they are trying to saving money by saving costs. As a result, the demand for Bangladeshi textile based low priced cloths is increasing worldwide. Specially, the demand has increased largely in the market of U.S.A. So, we can easily conclude by saying that “Textile Industry is now one of the potential industries in our country�. Pharmaceuticals Industry: The growth of pharmaceuticals industry is mentionable in our country. Competition in this industry is increasing day after day. Moreover, government recently has reduced import duty of raw materials of this industry by 5%. Export of the product of this industry is also increasing gradually. Cement Industry: Cement industry is also potential for two main reasons. I.
Infrastructure development
II.
Availability of raw material
Real estate development projects have been increased largely in recent period. As a result the construction of infrastructure has also increased. And cement is the key material of infrastructure development. Finally, the demand of cement has increased in a greater number. Besides, china has withdrawn the barrier of supplying fly ash to us. This increased the availability of raw material and also increased the attractiveness of the industry. Engineering industry: Growth of engineering industry occurred simultaneously with the growth of Real estate industry, cement industry and power industry. Attractiveness of this industry has increased as the demand of the product of this industry has increased. Power industry: Government is heavily emphasizing on the development of power sector. Govt. is calling for more and more private investment in the generation of power, making contract with the foreign investors to make the industry leading one and also taking proper care of the industry. As a result the potentiality of the industry is bright.
Selection of Company: We select our company based on following criteria •
Listed in DSE
•
Listed on or before January 1, 2006
•
‘A ’category Stock
Within these criteria we found total 158 companies from where we pick 25 companies based on the two criteria: •
Below or close to industry P/E
•
Low P/BV
Industry
Industry P/E
Bank
12.58
Cement
21.96
Engineering
32.85
Financial Institutions
25.17
Fuel & Power
22.06
Insurance
25.47
Pharmaceuticals 23.22
Textile
19.04
Company Dhaka Bank Eastern Bank Islami Bank National Bank NCC Bank Prime Bank Southeast Bank Confidence Cement Heidelberg Cement BD Lamps BD Thai Singer BD IDLC Prime Finance Uttara Finance Summit Power Eastern Insurance Green Delta Insurance Pragati Insurance BEXIMCO Pharma Renata Ltd. Square Pharma CMC Kamal Metro Spinning Square Textile
Company P/E 8.94 12.41 7.88 9.53 12.34 11.2 10.88 22.03 17.88 31.07 26.35 27.90 35.7 23.18 14.11 21 23.27 23.73
Company P/BV 1.79 1.48 1.74 1.65 1.62 1.58 1.34 2.12 3.60 1.19 1.37 2.04 3.24 3.074 2.58 3.06 2.22 2.39
26.8 17.48 23.89 18.34 26.49 17.4 19.01
1.92 1.21 0.71 3.14 1.68 2.39 3.11
For these 25 Companies we calculate their return and construct a correlation matrix. The construction of correlation matrix is shown below:
After constructing the correlation matrix we choose 7 companies which have lowest correlation with others as our group’s common companies for efficient portfolio construction. These Seven Companies are: •
Islami Bank
•
National Bank Limited
•
BD Thai
•
Pragati Ins.
•
BeximcoPharma
•
CMC Kamal
•
Metro Spin
Then we choose three different companies for each of our group member. So everyone have 10 companies in his/her portfolio. My portfolio’s Companies are given below: Selected companies: 1.Eastern Bank Ltd. 2.National Bank Ltd. 3.Islamic Bank Ltd. 4.Heidelberg Cement 5.Pragati Insurance Ltd. 6.Beximco Pharma. 7.Reneta 8.Metro Spin 9.CMC Kamal 10.BD Thai
Category A A A A A
Industry Bank Bank Bank Cement Insurance
A A A A A
Pharmaceuticals Pharmaceuticals Textile Textile Engineering
Adjustment of Price: We used monthly closing price of each companies from January2006 to December 2010.Some companies have split their share recently. We multiplied the price with split ratio and assumed the situation to be pre split situation. All the companies have paid dividend throughout the year. We adjusted the dividend with price assuming the market to be perfect. As per perfect market theory price will increase by the amount of dividend at declaration date and reduce by the amount of dividend at record date. As there was no information available about the record date we assumed declaration date and record date are at the same month and adjusted the price in the month of declaration date. When declaration date is within last seven days of the month I assumed the record date is in next month and adjusted the price in the next month.
We also adjust the right share and split with the closing price of the share. The formula for right share adjustment is : Previous month: (price t-1 + issue price)/ 1+% share Record date month: (price t * 1+%share) – issue price*%no of share Split are adjusted by multiplying the closing price by 10 to get the adjusted price.
Then we calculated return of each companies from february 2006 to december 2010. We used the formula to calculate the monthly return, R = LN(Pt/Pt-1)
Figure: return calculation Then we calculated mean return by adding return of 59 months and dividing by 59. I calculated mean return for each company. Thus we got 10 mean returns.
Risk free rate: We take the last 5 years monthly treasury bills interest rates as the risk free rate because this types govt.bills are generally risk free. This five years rates then we averaged to get a average risk free rate for last 5 years.
Figure: risk free return calculation Excess Return:
Then we calculated Excess return by subtracting risk free return from Mean return. The equation is, Excess Return = Rm聞-Rf
Figure: excess return calculation Variance Covariance Matrix: Then I calculated Variance and covariance of each company using VAR and COVAR function.
Figure: covariance determination Here we put equal weight on each security, which is 10%. That means we invest 10% of my asset on every securities irrespectively. Excess Portfolio Return: Then Calculated Excess portfolio returns by multiplying each excess return with respective weight and adding all.
Figure: portfolio returns calculation Portfolio Variance: Then I calculated the portfolio variance σp² using the theory of matrix .We know in variance we need to multiply individual variance covariance with weight square. So, my multiplication was like followingσp² = [W1,W2,W3,W4,…………..,W10]×
σ1²,σ12,σ13,………………,σ110 σ12,σ2², σ23,…………………,σ210 σ13, σ23, σ3²,………………,σ310 . . . .
. . . .
. .
. .
σ110, σ210 σ310,………….., σ10²
×
W1 W2 W3 W4 W5 W6 W7 W8 W9 W10
Portfolio Standard Deviation: We know portfolio standard deviation σp is the square root of standard deviation. That’s why we calculated the square root of the portfolio standard deviation.
Figure: standard deviation calculation Theta Calculation: Next we calculated the theta. We knowƟ = (Rmʹ –Rf)/ σp Excess Return = Rmʹ –Rf So, Ɵ = Excess Return / σp
Figure 1: THETA CALCULATION Use of solver function:
Maximizing Theta by not allowing short sell
In this situation we maximized theta by not allowing short sell. In this situations the constrains are1. ∑Wi = 1 2. Wi >= 0
Figure 2: MAXIMIZING THETA BY NOT ALLOWING SHORT SELL
Here my findings are-
So, we don’t need to invest in EBL, Heidelberg, Beximco Pharma. Here my theta will be 74%.
Fig: Weights in case of Maximizing Theta by not allowing short sell
Maximizing Theta allowing short sell
Allowing short sell means the investor can sell certain security of others in an expectation that the price will go down in near future, and then the investor will buy back the security and return to the real owner. In first situation I allowed short sale. The only constraint was1.∑Wi = 1
Figure: maximizing theta by allowing short sell
My findings is we have to short sell
In EBL (36%), Beximco Pharma by (12)%
We should invest all of my investment in other securities. At this option I will get maximum theta of 82%.
Fig: Weights in case of Maximizing Theta by allowing short sell Minimizing Risk (Standard Deviation) by not allowing short sell
Then I tried to find the weights in which risk will be minimum. I have not allowed short sell. Constraints are1. ∑Wi = 1 2. Wi >= 0
Figure: minimizing standard deviation by not allowing short sell
Here my findings are-
I don’t need to invest in EBL.
Thus my standard deviation will be minimum.
Fig: Weights in case of Minimizing Risk by not allowing short sell Minimizing Risk (Standard Deviation) by allowing short sell Then we allowed short sell to get the weight at minimum risk. The only constraint is ∑Wi = 1
Figure: minimizing standard deviation by allowing short sell Here we should allow short sell in case of EBL at minimum level of standard deviation 5.57%.
Fig: Weights in case of Minimizing Risk by allowing short sell Minimizing Risk (Standard Deviation) by not allowing short sell for a given return
Then we considered a situation in which we can earn a monthly return of 8% and my risk will be minimum. We have also not allowed short sell. My constraints are1.
∑Wi = 1
2. Wi >= 0 3. Monthly return=5%
Figure: minimizing the risk by not allowing short sells at given return
Fig: Weights in case of Minimizing Risk by not allowing short sell at given return Here we found that to get 5% return I have no need invest in EBL,Islami Bank, Heidelberg, Beximco Pharma. All my investment should be in other companies. Minimizing Risk (Standard Deviation) by allowing short sell for a given return Then we considered a situation in which I can earn a monthly return of 3.5% and my risk will be minimum. We have also allowed short sell. My constraints are: 1.
∑Wi = 1
2. Monthly payment=5%
Fig: Minimizing Risk (Standard Deviation) by allowing short sell for a given return
Here, we assume that the portfolio return is 5% (monthly). We can see that if short sale is allowed then, to minimize risk with 5% return we have to invest as above mentioned proportion to each company. We can see that the solver brings the result of short selling Beximco Pharma and Eastern Bank Limited and maximum investment can be made to National Bankk Limited (30%).
Maximizing return by not allowing short sell for a given risk
Here, we assume that the portfolio standard deviation is 6.6% (monthly). We can see that if short sale is not allowed then, to maimize return with 6.6% standard deviation, we have to invest as above mentioned proportion to each company. We can see that the solver brings the result of short selling Beximco Pharma,Heidelberg,EBL and maximum investment can be made to National Bnak Limited (33%).
Maximizing return by allowing short sell for a given risk:
Here, we assume that the portfolio standard deviation is 6.6% (monthly). We can see that if short sale is not allowed
then, to maimize return with 6.6% standard dviation, we have to invest as above mentioned proportion to each company. We can see that the solver brings the result of not investing or zero investment in Heidelberg and negative investment in EBL and Beximco Pharma and only 4% in BD Thai and maximum investment can be made to National Bnak Limited (48%).
Conclusion From above calculation we have shown that by allocating different weights to different securities the investor can maximize his return. He can also keep his risk at desire level as well as he can achieve expected return. Here we have show that if short selling is possible the theta and return can be maximized than if short selling is not allowed. But there is also disadvantage of short selling that is when market falls, short selling mechanism creates pressure to price fall which is not expected for share market. That’s why in Bangladesh short sell is not allowed. Bibliography: Investment analysis and portfoilio manage ment by Reilly and K. Brwon http://www.bdstock.com/
http://www.stockbangladesh.com/ www.google.com www.wikipedia.org www.dsebd.org www.yahoo.com