No. 3/2012
29
OPTIMAL PORTFOLIO SELECTION IN EX ANTE
STOCK PRICE BUBBLE AND FURTHERMORE
BUBBLE BURST SCENARIO FROM DHAKA STOCK
EXCHANGE WITH RELEVANCE TO SHARPE’S
SINGLE INDEX MODEL
Javed Bin Kamal
Dhaka University
House-20, Road-7, Block-B, Banasree, Rampura, Dhaka-1219, Bangladesh
b_bubble@live.com
Abstract: The paper aims at constructing an optimal portfolio by applying Sharpe’s single
index model of capital asset pricing in different scenarios, one is ex ante stock price
bubble scenario and stock price bubble and bubble burst is second scenario. Here we
considered beginning of year 2010 as rise of stock price bubble in Dhaka Stock Exchange.
Hence period from 2005 -2009 is considered as ex ante stock price bubble period. Using
DSI (All share price index in Dhaka Stock Exchange) as market index and considering
daily indices for the March 2005 to December 2009 period, the proposed method
formulates a unique cut off point (cut off rate of return) and selects stocks having excess
of their expected return over risk-free rate of return surpassing this cut-off point. Here,
risk free rate considered to be 8.5% per annum (Treasury bill rate in 2009). Percentage
of an investment in each of the selected stocks is then decided on the basis of respective
weights assigned to each stock depending on respective ‘β’ value, stock movement
variance representing unsystematic risk, return on stock and risk free return vis-à-vis
the cut off rate of return. Interestingly, most of the stocks selected turned out to be bank
stocks. Again we went for single index model applied to same stocks those made
to the optimum portfolio in ex ante stock price bubble scenario considering data
for the period of January 2010 to June 2012. We found that all stocks failed to make
the pass Single Index Model criteria i.e. excess return over beta must be higher than
the risk free rate. Here for the period of 2010 to 2012, the risk free rate considered to be
11.5 % per annum (Treasury bill rate during 2012).
Keywords: Sharpe’s single index model, Sharpe ratio, optimal portfolio, cut-off rate
JEL Classification: G11, G12
Introduction
A fundamental question in finance is how the risk of an investment should affect its
expected return. The Capital Asset Pricing Model (CAPM) provided the first coherent
framework for answering this question (Perold, 2004).
Financial Assets and Investing
30
From individual to group, the main purpose of investment is to earn risk adjusted return.
The principle of diversification seeks to place all the eggs in different baskets and hence
to keep entire investment in a single asset would be unwise and risky. This gives rise
to the idea of portfolio.
Portfolio management has been a topic in focus over the years. The art of successful
portfolio management does not only depend on rational investment decision but also
on different biases. Despite of that in order to construct and allocate assets to the different
asset classes is done with care and prudence.
There is a process of portfolio management. At first the securities are selected
and portfolio is created. After that the portfolio must be managed and optimum return is
attained. Portfolio management means construct portfolios with suitable allocation
of assets in order to reach investor's return objectives, while valuing the investor's
constraints in term of risk and asset allocation.
Portfolio managers employ modern portfolio theory as more traditional methods
or financial analysis to achieve optimum results. In this paper, we exhibit managing
portfolios using Sharpe single index model in pre stock price bubble and post stock price
bubble burst scenario.
Portfolio management becomes profitable particularly during stock price bubble and often
gains profit. But when the bubble bursts, the portfolio managers will fall in a bit uneasy
situation.
According to Mohammad A. Ashraf and Mohammad S. I. Noor (2010) a stock market
bubble is a type of economic bubble taking place in a market when market participants
drive the stock price above a value in relation to system of valuation. A bubble occurs
when speculators note the fast increase in value and decide to buy in anticipation
of further rises, rather than because shares are undervalued. Thus many companies
become grossly overvalued. When the bubble bursts the share prices fall dramatically and
numerous general investors as well as business organizations face serious financial loss
and ultimate economic hardship.
Modern portfolio theory (MPT) or portfolio theory was first introduced by Harry
Markowitz in his paper which is popularly known as "Portfolio Selection." Explaining
the concept of diversification, Markowitz proposed that investors should focus
on selecting portfolios based on their overall risk-reward characteristics. In other words;
investors should select portfolios and not individual securities.
Markowitz (1952) identified the optimal rule for allocating one’s wealth across risky
assets in a static setting. That in turn led to the later development of model of portfolio
allocation. The model considers only two factors which are the expected return
and variance, and assumes investors are risk averse. The idea behind the model is that
No. 3/2012
31
an investor cannot increase its expected return without increasing the risk of the portfolio.
Sharpe (1964) and Lintner (1965) have built on Markowitz (1952) model adding more
assumptions to the model. One of the assumptions behind the CAPM is that investors
agree on the expected rates of the return and the risks that they bear. That means
the distribution of the future returns is known to the investors. CAPM also assumes
borrowing and lending at a risk-free rate regardless of the amount borrowed or lent.
Having market portfolio consisting of all risky assets, one can form a minimum variance
frontier where portfolios are formed that minimize variance for a specific level
of expected return.
Together with William Sharpe and Merton Miller, Harry Markowitz was awarded
the Nobel Prize for their research in 1990. In the research, Markowitz demonstrated
that the portfolio risk came from the covariances of the assets that made up the portfolio.
The marginal contribution of a security to the portfolio return variance is therefore
measured by the covariance between the security's return and the portfolio's return rather
than by the variance of the security itself. Markowitz thus established that the risk
of a portfolio is lower than the average of the risks of each asset taken individually and
gave quantitative evidence of the contribution of diversification.
Literature review
In deriving the CAPM, Sharpe, Lintner and Mossin assumed expected utility (EU)
maximization in the face of risk aversion. Legendary article of Markowitz (1952) then
gives rise to MPT. To avoid problems such as difficulty in input data, educating portfolio
managers and time-cost consideration, using single index model and generating mean
variance structure have become famous (Elton, Gruber and Padberg,1976 and 2003).
Sharpe has received a Nobel Prize in 1990 for the model which empirical evidence is less
than poor. Fama and French (2004) argue the reason could be many simplifying
assumptions. To better understanding these assumptions we should break down the model
and see its segmented portions.
Many academics have applied single index model on real world data and have tried
to construct optimal portfolio. Debasish Dutt (1998) found that all the stocks selected are
bank stocks. He used Sharpe single index model in order to optimize a portfolio of 31
companies from BSE (Bombay Stock Exchange) for the period October 1, 2001 to April
30, 2003 and used BSE 100 as market index.
Later on Asmita Chitnis (2010) optimized two portfolios using single index model,
compared them, and he found out that portfolios tend to spread risk over many securities
and thus help to reduce the overall risk involved. “The greater the portfolio’s Sharpe’s
ratio, the better is its performance.”
Financial Assets and Investing
32
A bubble in stock price may occur due to behavioural finance responses of individuals.
Werner de Bondt found that behavioural finance has already proved to be a productive,
pragmatic, and intuitive approach to asset pricing research. With its requirements
for realism in assumptions, behavioural finance also brings discipline to market
modelling.
According to Barley Rosser (200) a speculative bubble exists when the price
of something does not equal its market fundamentals for some period of time for reasons
other than random shock.
The latest situation of the extremely inflated asset prices during early 2010 and up to 2011
has been indicated as bubble (Rahman, 2010) because DSE (Dhaka Stock Exchange) had
risen by 125 percent over the period from March 2009 and February 2010.
Objectives of the study
The study has the following objectives:
− To construct an optimal portfolio in different market scenarios.
− To test and analyse single index model by Sharpe – an intelligent tool to select
profitable stock in different market scenario for investors.
− To allocate investment in different stocks considering risk-return criteria.
− Selection of stocks in optimal portfolio both in ex ante bubble and bubble burst
scenario.
Rationale of the study
The rational of the study is to apply theoretical framework of portfolio management
on a real world scenario and to form a well-balanced optimized and diversified portfolio
of stocks.
Sharpe’s single index model
Markowitz’s efficient portfolio combines securities with a correlation of negative one
in order to reduce risk in the portfolio to gain optimum return. In order to study N-security
portfolio using Markowitz model, the inputs required are:
− expected returns,
− variances of returns,
− − /2 covariance’s.
As a result, Markowitz’s model requires + 3 /2 separate pieces of information
for identification of efficient portfolio. Hence the model is complex in nature. William
Sharpe contributed to Markowitz’s work and found out a more simplified model, where he
considered the fact that relationship between securities occurs only through their
individual relationships with some index or indices.
No. 3/2012
33
As a result of which the covariance data requirement reduced from − /2
under Markowitz model to only N measures of each security as it relates to the index.
Overall, the Sharpe model requires 3 + 2 separate pieces of information as against
+ 3 /2 for Markowitz.
Sharpe’s Model of Portfolio Optimization
William Sharpe (1963) studied Markowitz's research and worked on simplifying
the calculations in order to develop a practical use of the model.
The single index model assumes co-movement between stocks is due to movement
in the index. The basic formula underlying the single index model is:
= + (1)
Where is return on the i-th stock, is component of security i’s that is independent
of market performance, is coefficient that measures expected change in given
a change in and is rate of return on market index.
The term in the formula above is usually broken down into two elements which is
the expected value of and which is the random element of 	 .
Construction of optimal portfolios – methodology
The first step towards construction of an optimum portfolio using Sharpe’s single index
model is to select securities on the basis of following criteria:
− The return on the investment is greater than the risk free return.
− The beta value for that security is positive.
For each security selected in the portfolio, expected return is then calculated using
equation (1). After selecting these securities to the portfolio, next step is to construct
an optimal portfolio.
The construction of an optimal portfolio is simplified if a single number measures
the desirability of including a security in the optimal portfolio. For Sharpe’s single model,
such a number exists. In this case, the desirability of any security is directly related to its
excess return-to-beta ratio given by:
− / 	 (2)
Where is expected return of stock i, is risk-free rate of return and is beta of stock
i.
Excess return-to-beta ratio is calculated for each security in the portfolio and securities are
ranked in descending order of magnitude according to their excess return-to-beta ratio.
Further, the number of stocks selected in the optimum portfolio depends on a unique cut
Financial Assets and Investing
34
off rate ∗
such that all stocks with excess return-to-beta ratios greater than this unique cut
off ∗
are included and all stocks with lower ratios excluded.
To determine ∗
it is necessary to calculate its value as if different numbers of securities
were in the optimum portfolio. For a portfolio of i stocks, is given by:
=
	 ∑ /
!" ∑#
#$% /
										 (3)
Where & ' market variance, &	
variance of a security’s movement that is not associated
with the movement of the market index; this is the unsystematic risk of stock.
Over establishing the cut off rate ∗
, investor knows which securities are qualified
for the optimum portfolio and hence the optimum portfolio is constructed using qualified
securities.
Once an optimum portfolio is constructed, next step is to calculate the percentage invested
in each security in the optimum portfolio. The percentage invested in i-th security is
denoted by ( and is calculated using the expression:
	( 	=
)#
∑ )#
	 (4)
* = #
	
+
# ,
	− ∗
	-	 (5)
Where ∗
is cut off rate, * is variable of weight, is expected return of stock i, is
risk-free rate of return, is beta of stock i and & . is unsystematic risk of stock i.
For further discussion read Edwin J. Elton, Martin J. Gruber, and Manfred W. Padberg.
(1976) “Simple Criteria for Optimal Portfolio Selection, Dec., The Journal of Finance,
Volume 31, Issue 5, 1341-1357.
Thus, the above expression determines the relative investment in each security.
Constructing an optimal portfolio – analysis
Ex Ante Stock Price Bubble Scenario
DSI has been taken as the market indexes for the period from March 31, 2005
to December 31, 2009 obtained from Dhaka stock exchange library. Risk free return has
been taken to be the Treasury bill rate at 8.5% p. a. Monthly prices were taken from
Dhaka stock exchange.
Throughout and ex post Bubble Burst Scenario
Daily index and monthly price figures for the period march January 2010 to June 2012
have been obtained from Dhaka stock exchange library. Risk free return has been taken
to be the Treasury bill rate 11.5% % p.a.
No. 3/2012
35
Stock Choice
Tab. 1 Portfolio
Sector Stock
Pharmaceuticals
− Beximco Pharma
− Square Pharma
Power and fuels
− PGCB
− Summit Power
− Jamuna oil
− Titas gas
Bank
− Prime Bank
− South East bank
− National Bank
− The city Bank
Cement
− Lafarge Surma
− Heidelberg Cement
NBFI
− IDLC
− PLFSL
Insurance
− Green Delta
− National life Insurance
Source: Author`s selection
As the criteria for selection mentioned in Tab. 1 ignores stocks with negative , stocks
with negative returns have been ignored as well. The Sharpe model will automatically
exclude such stocks as its ranking is based on excess returns over .
Appendix 1 shows that almost all stocks have expected returns higher than the risk free
rate of return. For determining which of these stocks will be included in the optimal
portfolio, it is necessary to rank the stocks from highest to lowest based on excess return
to beta ratio.
Appendix 2 shows that in the case of no short sales, it can be seen the cut off rate ∗
is
C13 or 8.62 and only the top ten securities make it to the optimal portfolio. Whereas in the
case of short sales allowed situation, c is 8.52.
Once the composition of the optimal portfolio is known, the next step is to calculate
the percentage to be invested in each security (see Appendix 3).
Besides during and after the bubble burst no stock made an optimal portfolio due to not
surpassing the Single index model criteria (see Appendix 4).
In ex ante stock price bubble scenario, most of the stocks selected are banks and financial
institutions stocks when no short sales allowed. Besides in short sales allowed situation,
Financial Assets and Investing
36
there is it can be found dominance of stocks of banks, insurance, cement and non-banking
financial institutions (see Graph 1 and Graph 2).
Graph 1 Investment weight in asset (no short sales)
Souce: Author`s construction
Graph 2 Investment weight in asset (short sales allowed)
Souce: Author`s construction
0
0.05
0.1
0.15
0.2
0.25
Prim
e
bank
City
bank
South
eastbank
H
eidelberg
cem
ent
Nationalbank
Ltd.Nationallife
IDLC
Sum
m
itpow
erG
reen
DeltaBex
pharm
a
Stocks
Weight
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Prim
e
bankCity
bank
South
eastbank
Heidelberg
cem
ent
Nationalbank
Ltd.
Nationallife
IDLC
Sum
m
itpow
er
G
reen
Delta
Bex
pharm
aJam
una
oil
Square
pharm
a
Lafrage
surm
aTitas
gas
Stocks
Weight
No. 3/2012
37
Furthermore, during and after the bubble burst no stock took part on an optimal portfolio.
This is because of that the most stocks were as risky as market and market return was
negative after bubble burst.
Hence it has been seen based on random choice of stocks in Dhaka Stock Exchange that
we applied single index model which helped us to achieve a well rationalized
and diversified portfolio.
Banks have performed well in last five years and most stock have positive and higher
beta. The beta, variance of the stocks changes, so the market data should be analysed
continually. The optimum portfolio and proportions may change time to time and hence
proper market research and expert opinion is helpful in portfolio management.
Conclusion
Constructing a portfolio rather than a stand-alone stock may benefit an investor through
diversification and utilization of different risk return combination. Stocks are selected
if their expected return is mostly strong enough and beta is positive one.
The purpose of the article has been effective due to its success to reveal the single index
model application in different scenarios. The cut off point changes hence new security
may be included in the optimal portfolio based on risk return criteria.
Many empirical studies criticize the CAPM (Fama and French, 2004) whether it is
from empirical failing or theoretical perspectives. Despite that CAPM is widely used
and taught in MBA courses. Haim Levy, Enrico G. De Giorgi and Thorsten Hens (2011)
tested co-existence of expected utility theory of Markowitz, Sharpe and Prospect Theory
of Kahneman and Tversky (1979).
CAPM might be useful for investing companies, it does not have any benefits
for individual investors who do not intend to borrow and lend and are willing to invest
their funds in a limited number of shares (Savabi, Shahrestani and Bidabad, 2012). They
presented a mathematical model for this group of investors to invest their funds
in a limited number of shares and to minimize their unsystematic risk, which the market
does not reward.
The financial literature has been always searching new addition to the portfolio
management and minimizes time, cost and overcome understanding barrier and biases.
Though risk return is expected to be basic principle.
References
Ashraf, M. A., and Noor, M. S. I. (2010) Impact of Capitalization, on asset Price Bubble in Dhaka
Stock Exchange. Journal of Economic Cooperation and Development, 31(4), pp. 127-152.
Bondt, De W. (2002) Bubble psychology. In W. Hunter and G. Kaufman (eds.), Asset
Price Bubbles: Implications for Monetary, Regulatory, and International Policies.
Financial Assets and Investing
38
Chitnis, A. (2010) Performance Evaluation of Two Optimal Portfolios by Sharpe’s Ratio. Global
Journal of Finance and Management, ISSN 0975-6477, Vol. 2, No. 1, pp. 35-46.
Dutt, D. (November, 1998) Valuation of common stock – an overview. The Management
Accountant.
Elton, E. J., and Gruber, M. J. (2003) Modern Portfolio Theory and Investment Analysis. 6th
ed.,
John Wiley and Sons Inc.
Elton, E. J., Gruber, M. J., and Padberg, M. W. (1976) Simple Criteria for Optimal Portfolio
Selection. The Journal of Finance, Vol. 31, Issue 5, pp. 1341-1357.
Fama E. F., and French K. R. (1992) The cross Section of Expected Stock Returns. The Journal of
Finance, Vol. xlvii, No. 2, pp. 427-465.
Fama E. F., and French K.R. (2004) The capital asset pricing model: Theory and evidence. The
Journal of Economic Perspectives, Vol. 18, No. 3, pp. 25-46.
Kahneman, D., and Tversky, A. (March, 1979) Prospect Theory: An Analysis of Decision under
Risk. Econometrica, 47(2), pp. 263-291.
Levy, H., De Giorgi, E. G., and Hens, T. (2011) Two Paradigms and Nobel Prizes in Economics:
A Contradiction or Coexistence? Journal of Financial Economics, 99, pp 204-215.
Lintner. J. (February, 1965) The Valuation of Risk Assets and the Selection of Risky Investments
in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, Vol. 47, No. 1,
pp. 13-37 .This article can be retrieved from http://www.jstor.org/stable/1924119.
Markowitz, H. (Mar., 1952) Portfolio Selection. The Journal of Finance, Vol. 7, No. 1, pp. 77-91.
Mossin J. (Oct., 1966) Equilibrium in a Capital Asset Market. Econometrica, Vol. 34, No., pp. 768-
783 The Econometric Society. The URL for the article is http://www.jstor.org/stable/1910098.
Perold, A. F. (2004) The Capital Asset Pricing Model. Journal of Economic Perspectives, Vol. 18,
No. , pp. 3–24.
Rahman, J. (2010) Bubble in DSE,World Press, Dhaka.
Rosser, J. B. (2000) From Catastrophe to Chaos: a General Theory of Economic Discontinuities.
Kluwer Academic, 2nd
ed.
Savabi, F., Shahrestani, H., and Bidabad, B. (May, 2012) Generalization and combination of
Markowitz – Sharpe’s theories and new efficient frontier algorithm. African Journal of Business
Management, Vol. 6 (18), pp. 5844-5851, Available online at http://www.academic
journals.org/AJBM.
Sharpe, W. F. (Sep., 1964) Capital Asset Prices: A Theory of Market Equilibrium under Conditions
of Risk. The Journal of Finance, Vol. 19, No. 3 pp. 425-442.
Siegel, J. J. (2003) What is an asset price bubble; an operational definition. European financial
management, Vol. 9, No. 1, pp. 11-24.
Tua, J, and Zhou, G. (2011) Markowitz meets Talmud: A combination of sophisticated and naive
diversification strategies. Journal of Financial Economics, 99, pp. 204-215. This journal can be
retrieved from http:// www.elsevier.com/locate/jfec .
The data of market index (DSI all-share Price Index) have been retrieved from
http://www.dsebd.org.
DOI: 10.5817/FAI2012-3-3
No. 3/2012
39
Appendices
Appendix 1 Ranking of stocks based on excess return to beta (Ri – Rf)/ββββ
Stock
name
Mean
return
(Ri)
Excess
return
(Ri-Rf)
ß
Unsystematic
risk
Excess return
to beta
(Ri – Rf)/β
1 Prime bank 22.68 14.18 1.19 0.013002995 11.86
2 City bank 22.42 13.92 1.18 0.013350371 11.78
3 South East bank 20.89 12.39 1.10 0.00905719 11.25
4 Heidelberg cement 20.01 11.51 1.05 0.008846751 10.93
5 National bank 19.17 10.67 1.00 0.019022971 10.57
6 National life 18.23 9.73 0.95 0.016065578 10.14
7 IDLC 17.53 9.033 0.92 0.012170718 9.79
8 Summit power 17.45 8.95 0.91 0.023953808 9.74
9 Green Delta 16.82 8.32 0.88 0.020022446 9.39
10 Bex pharma 16.66 8.16 0.87 0.014456726 9.30
11 Jamuna oil 15.16 6.66 0.79 0.021457785 8.34
12 Square pharma 14.53 6.03 0.76 0.016859043 7.87
13 Lafarge surma 12.29 3.79 0.64 0.006325083 5.86
14 Titas gas 10.53 2.03 0.55 0.012807507 3.68
Risk free return Rf is 8.5 %.
Souce: Author`s calculation
Appendix 2 Case of no short sales
Stock
name
Ri-Rf β бei2 [(Ri-Rf)
*β]/бei2
β2
/бei2
∑(Ri-Rf)
*β/бei2
∑β2
/бei2 c
1
Prime
Bank
14.18 1.19 0.013003 1304.074 109.87 1304.07 109.87 4.61
2
City
Bank
13.92 1.18 0.01335 1232.427 104.55 2536.50 214.42 6.55
3
South East
Bank
12.39 1.10 0.009057 1507.954 133.99 4044.45 348.41 7.76
4
Heidelberg
Cement
11.51 1.05 0.008847 1372.228 125.53 5416.68 473.95 8.38
5
National
Bank
10.67 1.00 0.019023 566.461 53.59 5983.14 527.54 8.54
Financial Assets and Investing
40
6
National
life Insur.
9.73 0.95 0.016066 581.662 57.36 6564.80 584.90 8.66
7 IDLC 9.03 0.92 0.012171 684.783 69.93 7249.59 654.84 8.76
8
Summit
Power
8.95 0.91 0.023954 343.347 35.22 7592.93 690.07 8.80
9
Green
Delta
8.32 0.88 0.020022 368.611 39.22 7961.55 729.29 8.82
10
Bex
pharma
8.16 0.87 0.014457 495.351 53.23 8456.90 782.52 8.85
11 Jamuna oil 6.66 0.79 0.021458 247.911 29.69 8704.81 812.21 8.84
12
Square
pharma
6.03 0.76 0.016859 274.132 34.78 8978.94 847.00 8.80
13
Lafarge
surma
3.79 0.64 0.006325 388.645 66.29 9367.59 913.30 8.62
14 Titas gas 2.03 0.55 0.012808 88.0483 23.87 9455.64 937.17 8.52
Variance of market = 0.0058
Souce: Author`s calculation
Appendix 3 Optimum portfolio – no short sales and short sales allowed
No short sales Short sales allowed
Stock
name
β/бei2 (Ri-Rf)
/β
C Z
%
invested
C Z
%
invested
1
Prime
bank
91.92 11.86 8.62 298.68 0.19 8.52 307.86 0.27
2 City bank 88.49 11.78 8.62 280.27 0.18 8.52 289.12 0.25
3
South east
bank
121.62 11.25 8.62 320.39 0.20 8.52 332.56 0.29
4
Heidelberg
cement
119.12 10.93 8.62 275.26 0.17 8.52 287.17 0.25
5
National
bank Ltd.
53.07 10.57 8.62 103.50 0.07 8.52 108.81 0.10
6
National
life
59.75 10.14 8.62 90.84 0.06 8.52 96.81 0.09
7 IDLC 75.80 9.79 8.62 88.83 0.06 8.52 96.41 0.08
No. 3/2012
41
8
Summit
power
38.34 9.74 8.62 43.19 0.03 8.52 47.03 0.04
9
Green
Delta
44.25 9.39 8.62 34.45 0.02 8.52 38.87 0.03
10
Bex
pharma
60.68 9.30 8.62 41.61 0.03 8.52 47.67 0.04
11 Jamuna oil 37.20 8.34 8.62 0.00 8.52 -6.37 -0.01
12
Square
pharma
45.42 7.87 8.62 0.00 8.52 -29.08 -0.03
13
Lafrage
surma
102.37 5.86 8.62 0.00 8.52 -272.10 -0.24
14 Titas gas 43.17 3.68 8.62 0.00 8.52 -208.59 -0.18
Total 1577.06 1.0 Total 1136.19 1.0
Note: PLFSL and PGCB excluded due to negative beta.
Souce: Author`s calculation
Appendix 4 Criteria: Excess return over beta > risk free rate (on data from January
2010 to June 2012)
Stock Name Criteria: Excess return over beta > risk free rate
1 Beximco Pharma
a = - 0.20
b = 0.81
2 Square Pharma
a = - 0.22
b = 0.55
3 PGCB
a = - 0.15
b = 0.94
4 Jamuna Oil
a = - 0.14
b = 1.07
5 Prime Bank
a = - 0.1632
b = 0.92
6 Summit Power
a = - 0.1646
b = 0.96
7 National Bank(NBL)
a = - 0.1665
b = 0.80
8 Heidelberg Cement
a = - 0.24
b = 0.52
Financial Assets and Investing
42
9 Lafarge Surma
a = - 0.25
b = 0.48
10 Titas Gas
a = - 0.1464
b = 0.95
11 City Bank
a = - 0.18
b = 0.90
Note: Criteria – Excess Return over beta > risk free rate; β >0.
Risk free rate for the period from January 2010 to June 2012 is considered 11.5% (treasury bill
rate). Criteria is not met, because excess return over beta is less than risk free rate.
Souce: Author`s calculation