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\title{Diversification and Portfolio Performance of the Pharmaceutical Sector of Bangladesh}
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             \author[1]{Fairuz  Chowdhury}

             \author[2]{Fairuz  Chowdhury}

             \affil[1]{  BRAC University, 66 Mohakhali , Dhaka-1212}

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\date{\small \em Received: 13 February 2015 Accepted: 3 March 2015 Published: 15 March 2015}

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\begin{abstract}
        


The pharmaceutical industry is one of the thrust sectors of the economy of Bangladesh. Here, in this report I evaluate how individual players or the companies under review for this report namely Beximco Pharmaceuticals, Ambee Pharmaceuticals, Square Pharmaceuticals and Renata Pharmaceuticals are performing individually and the impact on their portfolio performance when they combine to form a portfolio. While doing this I also evaluate whether the effects of diversification hold for this sector. To evaluate portfolio performance, I used common measures such as Sharpe ratio and M-Squared. To perform all these, I had to calculate the standard deviation and returns of the individual assets over a four year period, along with calculating the covariances between their returns. Based on these calculations, I estimated the standard deviation and returns of the portfolio constructed. To check the effects of diversification and to calculate the ratios these data were used.

\end{abstract}


\keywords{diversification, m-squared, portfolio performance, sharpe ratio.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
harmaceutical sector is one of the success stories for the economy of Bangladesh. This is one of the thust sectors of the economy with it being a billion taka industry. But that does necessarily mean that all the companies present would do well, in terms of the value they provide to their shareholders, at the same time. The value to the shareholders is through capital appreciation and dividend gain. It is highly unlikely that all companies will show the same growth in earnings at the same time. The change in earnings impacts the value of firm; which in turn impacts the wealth of the shareholder.\par
A look at the earnings growth of the different companies in this sector specifies the claim above. While this year, ACI showed a growth in earnings of 34\%, Beacon Pharma showed a decline in growth by 20\%  {\ref (EBL Securities, 2015)}. So, while in investing in a certain company can be beneficial; at the same time it can be sacrificial.\par
Diversification looks to nullify the firm-specific or unsystematic risk associated with a certain risk class. For a reasonably well-diversified portfolio, only market risk matters \hyperref[b4]{(Brealey, Myers, \& Marcus, 2001)}. Thus, in a well diversified portfolio, one gets compensated for the market risk, not the unsystematic risk. As one adds new securities to the portfolio, he/she is coming up with the new portfolios. At the same time, one needs to look at the performance of the new portfolios. The performance evaluation of the portfolios can be based on Capital Asset Pricing Model (CAPM) or other multi factor models. Some of the common performance evaluation ratios based on CAPM are Sharp ratio, Treynor ratio, M-Squared (M 2 ) and Jensen's Alpha.\par
The main objective of this study is to check while adding new securities to the portfolio does the effects of diversification take place for the Pharmaceutical sector, and to check the performance of the new portfolios created along the way using Sharp ratio and Modigliani risk-adjusted performance (M 2 ). 
\section[{II.}]{II.}\par
Literature Review P a) Pharmaceutical Sector of Bangladesh So, comes one of the basic concepts of finance: diversification. Diversification is a procedure of minimizing risk by investing in different stocks, preferably without sacrificing return. The aim of this is to lower the risk of the portfolio held by an investor.\par
The pharmaceutical industry is one of the most technologically advanced sectors currently in existence.........local companies fulfilling 98\% of the drug requirements , a picture contrary to that of 20 years ago, when 75\% of the drugs were imported  {\ref (EBL, 2015)}.\par
The top three companies in this sector are Square Pharmaceutical, Incepta Pharmaceutical and Beximco Pharmaceutical with companies combined holding around 40 percent of the market share. The domination of the local companies has ensured that none of multinationals is in the top 10 list when it comes to market share (Bangladesh's Corporate World, 2013). 
\section[{b) Portfolio Return and Risk i. Portfolio Return}]{b) Portfolio Return and Risk i. Portfolio Return}\par
The return on a portfolio is simply a weighted average of the returns on the individual securities. We can find the return of portfolio consisting of n securities by this:???? = ??1??1 + ??2??2 + ? ? ? + ???????? Where: ???? = return on portfolio ??1 = weight of security 1 ??1 = return on secutiy 1\par
In a large portfolio, the number of terms involving covariance between two securities is much greater than the number of terms involving variance of a single security \hyperref[b8]{(Ross et al. , 2003)}. Thus, variance plays the key role in determining the portfolio variance. To get the standard deviation of the portfolio, we have to square root the portfolio variance. The total risk of a portfolio diminishes as we keep adding securities. The portfolio's variance can never drop to zero as only the unsystematic risk is falling, the systematic risk cannot be diversified away. If we plot a portfolio risk versus number of securities graph, as plotted below, we can see that the unsystematic risk decreases as we increase the number of securities in a portfolio. For a reasonably welldiversified portfolio, only market risk matters \hyperref[b4]{(Brealey et al., 2001)} . Investors holding diversified portfolios are mostly concerned with macroeconomic risks, not about microeconomic risks peculiar to a particular company or investment project as micro risks are washed out in diversified portfolios \hyperref[b4]{(Brealey et al., 2001)}.\par
i 
\section[{. Capital Asset Pricing Model (CAPM)}]{. Capital Asset Pricing Model (CAPM)}\par
As we have already explained that only market or systematic risk exists in a well diversified portfolio so investors won't be compensated for the diversifiable risk in an efficient market. Therefore, investors would be compensated for the market risk involved with investing ??2 = weight of security 2 ??2 = return on secutiy 2 ???? = weight of security n ???? = return on secutiy n\par
The weight, W here means the percentage of investment in a certain security and return, R means the return on that security.\par
ii. Types of Risk Investment risk depends on the dispersion or spread of possible outcomes and the standard measures are variance and standard deviation \hyperref[b4]{(Brealey, Myers, \& Marcus, 2001)}. In finance, we divide total risk into two components: a systematic portion, called systematic risk, and the remainder, related to the firm or industry is called firm-specific or unsystematic risk. The distinction is expressed as: systematic risk, any risk that affects a large number of assets, each to a greater or lesser degree while unsystematic risk, risk that specifically affects a single asset or certain class of securities. While systematic risk is risk that is inherent in the overall market and affects the market as a whole; unsystematic risk is risk that is local or limited to a particular asset or industry and does not impact assets outside that asset class (CFA Institute, 2013). Example of systematic risk is change in interest rates; and example of unsystematic risk is failure of drug trial of a pharmaceutical company.\par
Total Risk = Systematic Risk + Unsystematic Risk Standard deviation of an individual stock is the measure of total risk which comprises of both the systematic and unsystematic risk. In short, while unique or unsystematic risk arises because many of the perils that surround an individual company are peculiar to that company and perhaps its direct competitors: market risk or systematic risk stems from economy wide perils that threaten all businesses \hyperref[b4]{(Brealey et al., 2001)}.\par
iii. Portfolio Risk The variance of the portfolio is dependent on standard deviation of individual stocks and covariance or correlation between stocks present in the portfolio.\par
While the variances of individual securities measure the variability of individual security's return. C\par
in a portfolio of securities. The systematic risk of an asset/portfolio is measured by beta. Beta measures the responsiveness of a security/ portfolio to movements in the market portfolio \hyperref[b8]{(Ross et al. , 2003)}. Investors are compensated for the risk they are taking by this beta measurement.\par
The Capital Asset Pricing Model (CAPM) is an economic model for valuing stocks, securities and assets by relating risk and expected return. The CAPM is based on the idea that the investors demand additional required return called risk premium for taking additional risk (Sharpe, F.W., 2014). This can be said to be the simplest form of return generating model.???? = ???? + ??(???? ? ????)\par
Where, Re =expected return of a security/portfolio Rf =risk free rate ? =beta of the security/portfolio Rm-Rf = Difference between expected return on market and risk-free rate This formula above, called the capital-assetpricing model implies that the expected return on a security/portfolio is linearly related to its beta. \hyperref[b2]{Blume (1993)} stated that the CAPM provides a model, not only explains the equilibrium risk/return relationship, but the linear relationship between the systematic risk and the expected returns. 
\section[{d) Performance of Portfolio}]{d) Performance of Portfolio}\par
Investors need to know whether it is worth investing in a certain sector or institutional stocks. This can be based on CAPM or multi factor models. Two of the commonly used ratios for portfolio performance evaluation are Sharpe ratio and M-Squared (M 2 ).\par
i 
\section[{. Sharpe Ratio}]{. Sharpe Ratio}\par
The Sharpe ratio is a measure that helps investors figure out how much return they're getting in exchange for the level of risk they're taking on \hyperref[b7]{(Marte, 2012)}. This ratio measures the return on investment for each unit of risk taken i.e. for each unit of total risk taken. Sharpe ratio is defined as risk premium of a portfolio divided by its standard deviation. It is also known as the reward to variability ratio and assumes that the investor does not own any other assets other than that in his portfolio. The portfolio with the highest Sharpe ratio has the worst performance while that with the highest Sharpe ratio has the best performance (CFAInstitute, 2013).\par
Sharpe ratios work best when figured over a period of at least three years and through looking at the fund's risk-adjusted performance over several years offers insight on how the fund weathered different market environments \hyperref[b7]{(Marte, 2012)}. It has two limitations: one being the use of total risk as the measure, and second: It can be difficult to interpret and use for comparisons in periods when some funds' returns are below the Treasury-bill return but can be telling when comparing two funds that compete in the same category \hyperref[b7]{(Marte, 2012)}.\par
ii. Modigliani-Modigliani Measure (M-Squared) Adjusting returns for risk is essential and the methodology employed should be universally representative, M-Squared is an attempt to provide a risk-adjusted measure of performance \hyperref[b0]{(Baigent, 2015)}. It is derived from the widely used and is an extension of the Sharpe ratio in that it is based on total risk, not beta risk (CFAInstitute, 2013). The equation is:?? 2 = (???? ? ????) ???? ???? ? (???? ? ????)\par
Where: gives rankings which is similar to that of Sharpe ratio, but in percentage terms. A portfolio that has a positive M 2 value shows the portfolio is performing better than the market while a M 2 value of zero refers to the point that the portfolio matches the performance of the market.???? = 
\section[{III.}]{III.} 
\section[{Research Methodology}]{Research Methodology}\par
For this report, we collected our all information from secondary sources. For the analysis purpose, we collected data from DHAKA STOCK EXCHANGE. To conduct the research, we take the closing share price of the last date of every month from 2010-2013 of the four company from the trade information of DSE.\par
For the research purposes, we analyzed four pharmaceutical companies, namely, Square Pharmaceuticals, Ambee Pharmaceuticals, Renata Pharmaceuticals and Beximco Pharmaceuticals. Using the closing prices of a company's stocks over two months we calculate the monthly return.\par
The monthly return is calculated using: Return = (closing price of this month -closing price of the previous month) /closing price of the previous month.\par
Once we calculated the monthly returns over the four year period we estimated the average return 
\section[{Year ( )}]{Year ( )}\par
C during this period using h the AVERAGE function of Excel. At the same time using the STANDARD DEVIATION function we found out the standard deviation of the return for every company.\par
Using the same return computations we calculate the co-variances between returns of any two companies. Once we get the standard deviation and covariances we calculate the portfolio variance. Once we have the portfolio variance we can estimate the portfolio standard deviation for the different combinations of portfolios. Using these data, we check for the effects of diversification and performance of the portfolios. 
\section[{a) Standard Deviation}]{a) Standard Deviation}\par
Standard deviation is applied to the annual rate of return of an investment to measure the investment's volatility. Volatility is a measure of risk to determine the risk of a specific security. We use Excel Function to find out the SD.\par
Excel Function=STDEVP (Return of the four years) 
\section[{b) Covariances}]{b) Covariances}\par
Covariance measures how two variables move together. It measures whether the two move in the same.... it measures between two company's variable. We have got 8 covariances of these four pharmaceuticals. 
\section[{c) Portfolio Variances}]{c) Portfolio Variances}\par
The variance of a portfolio's return, ? P 2 is a function of the variance of the component assets as well as the covariance between individual securities. It is worthwhile to bear in mind that the variance of the portfolio with an increasing number of securities is more dependent on the covariances between individual securities.\par
For the computation purposes, we assume that equal investments happening in the different stocks of a portfolio. Therefore when we are taking a case of two stock portfolio, we assume the weight,w assigned to be .5 each. In case of a three stock portfolio, we assume the weight assigned to each individual security to be .33 each.\par
The formula for calculating the portfolio variance:\par
For two stock portfolio: From these variances we calculate the standard deviation of the portfolio (? P ) by using excel function SQRT.? P 2 = w A 2 *? 2 (R A ) + w 2 B *? 2 (R B ) + 2*(w A )*(w B )*Cov(R A , R B ) \{3.1\} For three stock portfolio ? P 2 = w 2 A *? 2 (R A ) + w 2 B *? 2 (R B ) + w 2 C *? 2 (R C ) +2*(w A )*(w B )*Cov(R A , R B )+ 2*(w A )*(w C )*Cov(R A , R C )+ 2*(w B )*(w C )*Cov(R B , R C ) \{3.2\} For four stock portfolio ? P 2 = w 2 A *? 2 (R A ) + w 2 B *? 2 (R B ) + w 2 C *? 2 (R C )+ w 2 D *? 2 (R D ) +2*(w A )*(w B )*Cov(R A , 
\section[{d) Portfolio Return}]{d) Portfolio Return}\par
Portfolio return is the actual return in monetary terms that the holder of the portfolio would make based on his/her proportional investment on the individual stocks on the portfolio. In actual terms, both dividends and capital appreciation are components of returns but here we use the capital appreciation/ depreciation to be the actual return. The weights assigned while calculating standard deviation of the portfolio is used here too i.e. the amount invested in each stock would be the same. For a two stock portfolio: Average return (AVG Return) comes from the company's return computation i.e. by summing the return over the period in computation divided by the number of observations and weight, w calculation is the same thing that we did for the portfolio variances. 
\section[{Return on portfolio for A\& B: w A (AVG Return}]{Return on portfolio for A\& B: w A (AVG Return} 
\section[{e) Effects of Diversification}]{e) Effects of Diversification}\par
We want to look into whether the effects of diversification i.e. reduction of risk with investing in increasing number of different stocks in a portfolio. We look into the fact that when we invest in different stocks whether the unsystematic risk decreases. We plot a graph with total risk in the y-axis and investment in different stocks in the x-axis. 
\section[{f) Portfolio Performance}]{f) Portfolio Performance}\par
For the analysis purpose, we take two commonly performance evaluation ratios: Sharpe ratio and M-Squared (M 2 ). In both these measures, we take into consideration the total risk; not systematic risk. These measures can be extended to multi-factor models but we are using these simple ratios based on only CAPM in this report.\par
i. Sharpe Ratio Sharp ratio is explained by portfolio's risk premium divided by portfolio risk. Here, we assume that the investor has invested only in the portfolio in question we take that the investor has the investor has invested in and in nothing else.\par
To calculate the Sharpe ratio, we need to estimate the monthly risk-free rate. This is calculated by taking the annual return from 10 year Treasury bond and converting to monthly return. This is done using the formula:?????????????? = (1 + ??????????????) 12 ? 1\par
Where, ?????????????? = Annual return of 10 year Treasury bond ?????????????? = monthly risk ? free rate\par
Once we get the risk-free rate from this equation we can calculate the Sharpe ratio for each portfolio.\par
The formula for calculating the Sharpe ratio is presented below: Sharpe ratio = (portfolio return ? Risk-free rate)/Standard deviation of portfolio 
\section[{ii. Modigliani-Modigliani measure}]{ii. Modigliani-Modigliani measure}\par
Modigliani-Modigliani measure, commonly known as M 2 measures the risk adjusted returns of the portfolio. For calculating this we need to calculate the return and risk profile of the market index. We took the market index and calculated the return the same way we did for individual stocks. For calculating the risk profile of the market we followed the same procedure we did for calculating the standard deviation of individual stock. The formula used:M 2 = (R p -R f )* ? M/ ? P -( R m-R f)\par
The portfolio return and portfolio standard deviation of individual portfolio calculated above are used here to estimate the M 2 . invested in portfolio consisting of Square Pharmaceuticals, Ambee Pharmaceuticals, Renata Pharmaceuticals and Beximco Pharmaceuticals shares; it means these are the only stocks in which the investor has invested in and in nothing else.\par
IV. 
\section[{Findings and Analysis}]{Findings and Analysis}\par
Four pharmaceutical companies are the targeted companies. These companies are: Square Pharmaceuticals, Beximco Pharmaceuticals, Renata Pharmaceuticals and Ambee Pharmaceuticals. The collected DSE indexes are used for the purpose of calculating the standard deviation, covariance and portfolio variance. 
\section[{a) Standard Deviation}]{a) Standard Deviation}\par
The standard deviation is the measure of total risk. Thus, the standard deviation is estimated to understand the riskiness of the companies. From our analysis the standard deviation for the four companies are calculated to be:  
\section[{b) Covariance}]{b) Covariance}\par
As we know, covariance is a measure of the relation between the movements of the stocks' returns. Portfolio variance is more dependent on the stock covariance than on standard deviation of individual stocks. The covariances calculated are as follows:  
\section[{d) Diversification}]{d) Diversification}\par
Diversification is a risk management skill which involves investing in different types of stocks. This is done to reduce the risk profile of the portfolio. This will mean that the negative performance of some stocks will be negated by the positive performance of other stocks. Thus, this in turn will lead to reduction of unsystematic risk.\par
Here, we can see that investment in portfolio of only square stocks is riskier than that of Square Pharmaceutical and Ambee Pharmaceutical. This holds true, in spite of the fact that total risk of Ambee Pharmaceutical stocks is greater. The diversification effects due to the covariance between the two sets of stocks. Here, we see that as investment in increasing number of firms take place, the total risks involved decreases. This in turn means we are diversifying away the firm specific or unsystematic risks. Thus, the effects of diversification hold for the pharmaceutical sector.  
\section[{e) Performance of Portfolio}]{e) Performance of Portfolio}\par
To estimate the performance of portfolio we need the risk and return profile of the individual stocks as well as that of the market. Thus, we need to find the return as well as the standard deviation of the market. Using all these information, we calculate the Sharp Ratio and M Squared of the portfolios.\par
Below, the risk-return profiles are presented. All the stocks, with the exception of Ambee Pharmaceutical performed poorly with respect to the market. All the stocks show high volatility when compared to the volatility of the market.\par
To make matter complex, it is observed that the monthly return of a 10 year Treasury bond is greater than that of market. Using the same assumption that we invest equally in all the different stocks in the portfolio we calculate the riskreturn profile of the portfolios. We took the portfolios in accordance to that investment profile used to calculate risk profile for diversification. The return-risk profiles of the portfolios are presented below: Table  {\ref 6} : Portfolio Return and Risk Sharpe Ratio\par
As we know investors are by nature risk averse, they require higher compensation for higher risk in the form of higher return.\par
A common measure of performance is the Sharpe Ratio, also known as the reward-to-variability ratio. The portfolio with the greatest Sharpe ratio has the best performance while the lower the Sharpe ratio, the worse the performance of the portfolio. M 2 gives rankings similar to that of Sharpe ratio. But these rankings are easier to interpret as these are expressed in percentage performance. Negative values here mean that the portfolios constructed based on stocks of this sector are performing poorer to the market. From the ranking perspective, portfolio consisting of Square Pharmaceutical and Ambee Pharmaceutical stocks is best while portfolio consisting of the four different stocks is performing the poorest. But these values also indicate that these portfolios perform poorer to the market on a risk-adjusted basis.  
\section[{Recommendation}]{Recommendation}\par
From the above findings, we can interpret that diversification works for this sector but the performance of the portfolios are poorer than the market. Thus, this analysis creates room for skepticism. Although diversification leads to reduction of risk but it takes a hit in the return analysis. From the investors' perspective, they should invest in stocks outside this sector. On top of all these, the return on 10 year Treasury bonds is greater that than of the market it can be suggested that a risk-averse investor should rather invest in the bonds. From the various companies' perspective, they should look at the business structure, operational mechanism and capital structure of Ambee Pharmaceutical as it is the only stock that is outperforming the market. 
\section[{VI.}]{VI.} 
\section[{Conclusion}]{Conclusion}\par
We can see that for this pharmaceutical sector, the effects of diversification hold. As the number of securities of different companies is introduced the total risk is reduced as the unsystematic risk minimizes. But, we see that the performance evaluated by the Sharpe ratio and M-Squared does not provide any positive reading. The period analyzed was just after the Global Recession so this can be one reason why the return on the market as a whole was poorer than that of 10 year Treasury bond. There is scope for further studies to check if investors diversified in different sectors, rather than one, could they avail better returns along with the effects of diversification. \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 1 :}\end{figure}
       \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.22464285714285714\textwidth}P{0.20035714285714284\textwidth}P{0.19428571428571428\textwidth}P{0.23071428571428568\textwidth}}
Number of\tabcellsep Total\tabcellsep Number of\tabcellsep Number of\\
Stocks in\tabcellsep Number of\tabcellsep Variance\tabcellsep Covariance\\
Portfolio\tabcellsep Terms\tabcellsep Terms\tabcellsep Terms\\
1\tabcellsep 1\tabcellsep 1\tabcellsep 0\\
2\tabcellsep 4\tabcellsep 2\tabcellsep 2\\
3\tabcellsep 9\tabcellsep 3\tabcellsep 6\\
10\tabcellsep 100\tabcellsep 10\tabcellsep 90\\
100\tabcellsep 10,000\tabcellsep 100\tabcellsep 9900\\
-\tabcellsep -\tabcellsep -\tabcellsep -\\
N\tabcellsep N\tabcellsep N\tabcellsep N -N\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.7083333333333334\textwidth}P{0.14166666666666666\textwidth}}
Standard Deviation (Square Pharma.)\tabcellsep 16.00\%\\
Standard Deviation (Beximco Pharma.)\tabcellsep 13.24\%\\
Standard Deviation (Renata Pharma.)\tabcellsep 16.03\%\\
Standard Deviation (Ambee Pharma.)\tabcellsep 23.77\%\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.7207770270270271\textwidth}P{0.12922297297297297\textwidth}}
Covariance (Square \&Beximco)\tabcellsep 0.004555\\
Covariance (Square \&Renata)\tabcellsep 0.018337\\
Covariance (Square \&Ambee)\tabcellsep 0.004407\\
Covariance (Beximco \& Square)\tabcellsep 0.004555\\
Covariance (Beximco \&Renata)\tabcellsep 0.008734\\
Covariance (Beximco \& Ambee )\tabcellsep 0.010446\\
Covariance (Renata \& Square)\tabcellsep 0.01834\\
Covariance (Renata \& Beximco)\tabcellsep 0.00873\\
Covariance (Renata \& Ambee)\tabcellsep 0.00459\\
Covariance (Ambee \& Square)\tabcellsep 0.00441\\
Covariance (A mbee\& Beximco)\tabcellsep 0.01045\\
Covariance (Ambee \& Renata)\tabcellsep 0.00459\\
c) Portfolio Standard Deviation\tabcellsep \\
\multicolumn{2}{l}{We know that portfolio standard deviation}\\
\multicolumn{2}{l}{is..............Finally, we assumed equal investment to take}\\
place in all four stocks.\tabcellsep \end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.2883928571428572\textwidth}P{0.19732142857142856\textwidth}P{0.36428571428571427\textwidth}}
\tabcellsep \tabcellsep Standard\\
\tabcellsep Variance\tabcellsep Deviation\\
Portfolio of Square\tabcellsep 0.026\tabcellsep 16.00\%\end{longtable} \par
 
\caption{\label{tab_3}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.24285714285714283\textwidth}P{0.33260869565217394\textwidth}P{0.2745341614906832\textwidth}}
\tabcellsep \multicolumn{2}{l}{Individual Stock}\\
\tabcellsep Monthly Return\tabcellsep Standard Deviation\\
Square\tabcellsep -2.71\%\tabcellsep 16.00\%\\
Ambee\tabcellsep 2\%\tabcellsep 23.77\%\\
Renata\tabcellsep -3\%\tabcellsep 16.05\%\\
Beximco\tabcellsep -1.87\%\tabcellsep 13.24\%\\
Market\tabcellsep 0.56\%\tabcellsep 9.64\%\\
Risk free Rate\tabcellsep \tabcellsep \\
\tabcellsep 0.78\%\tabcellsep \\
i.\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{P{0.5639423076923077\textwidth}P{0.28605769230769235\textwidth}}
Square \& Ambee\tabcellsep -0.06982688\\
Square, Ambee \& Renata\tabcellsep -0.136894851\\
Square, Beximco, Renata \&Ambee\tabcellsep -0.171278425\end{longtable} \par
 
\caption{\label{tab_5}Table 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_6}Table 8 :}\end{figure}
 			\footnote{© 2015 Global Journals Inc. (US)} 			\footnote{© 2015 Global Journals Inc. (US) 1} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Harrington et al.]{b3}\label{b3} 	 		\textit{},  		 			D R Harrington 		,  		 			R A Korajczyk 		,  		 			Amir 		.  		New York. p. .  	 
\bibitem[Brealey and Marcus ()]{b4}\label{b4} 	 		\textit{Fundamentals of Corporate Finance},  		 			Myers Brealey 		,  		 			Marcus 		.  		2001. United States of America: McGraw-Hill Primis Custom Publishing.  	 
\bibitem[Growth of the Pharmaceutical Sector of Bangladesh Bangladesh's Corporate World (2013)]{b1}\label{b1} 	 		‘Growth of the Pharmaceutical Sector of Bangladesh’.  		 \url{http://bangladesh-corporate-world.blogspot.com/2013/11/growth-of-pharmaceutical-sector-of.html}  	 	 		\textit{Bangladesh's Corporate World}  		2013. November 7.  	 
\bibitem[Baigent ()]{b0}\label{b0} 	 		‘M-Squared and ranking issues for risky assets’.  		 			G G Baigent 		.  	 	 		\textit{Applied Economics Letters}  		2015. 22  (4)  p. .  	 
\bibitem[Sharpe ()]{b9}\label{b9} 	 		\textit{net/methods\textunderscore capm.html Policy and strategy implications for investment management},  		 			F W Sharpe 		.  		 \url{http://www.valuebasedmanagement.}  		2014.  	 	 (Summary of Capital Asset Pricing Model. ICFA Continuing Education) 
\bibitem[Pharmaceutical Sector Overview ()]{b6}\label{b6} 	 		\textit{Pharmaceutical Sector Overview},  		2015. Dhaka.  		 			EBL Securites Limited (EBL 		 	 
\bibitem[Pricing of risk and Computation of Return. Corporate Finance and Portfolio Management ()]{b5}\label{b5} 	 		\textit{Pricing of risk and Computation of Return. Corporate Finance and Portfolio Management},  		2013. Wiley. p. 358.  		 			CFA Institute 		 	 
\bibitem[Ross et al. ()]{b8}\label{b8} 	 		\textit{Return and Risk-The Capital Asset Pricing Model. Corporate Finance},  		 			A W Ross 		,  		 			R W Wester Field 		,  		 			W Jaffe 		.  		2003. New York: McGraw-Hill/Irwin.  	 
\bibitem[Blume ()]{b2}\label{b2} 	 		‘The Capital Asset Pricing Model and the CAPM literature’.  		 			M E Blume 		.  	 	 		\textit{The CAPM controversy},  				1993.  	 
\bibitem[Marte (2012)]{b7}\label{b7} 	 		\textit{The Wall Street Journal},  		 			J Marte 		.  		 \url{http://www.-wsj.com/articles/SB10001424052702304692804577283773166995992}  		2012. April. September 2015.  	 
\end{bibitemlist}
 			 		 	 
\end{document}
