Term paper

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PRESENTED BYSAIED MAHMUD ZUBAYERPGDCM, 1ST BATCHID-2015-01-06

“Efficient portfolio construction”

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EXECUTIVE SUMMARY

Most investment portfolios are designed to meet a specific future financial need—either a single goal or a multifaceted set of objectives. To best meet that need, the investor must establish a disciplined method of portfolio construction that balances the potential risks and returns of various types of investments.

This paper reviews my analysis into the investment decisions involved in constructing a diversified portfolio. The term “Construction of efficient portfolio” in common practice refers to selection of securities and their continuous shifting in a way that the holder gets maximum returns at the minimum possible risk. A portfolio manager by the virtue of his knowledge, background and experience helps his clients to make investment in profitable avenues.

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EXECUTIVE SUMMARY

This paper discusses how to create a diversified portfolio by focusing on eight major steps:

Calculating Portfolio Weight by Maximizing Theta without allowing short

sell Calculating Portfolio Weight by Maximizing Theta with allowing short sell Calculating Portfolio Weight by Minimizing Risk without allowing short

sell Calculating Portfolio Weight by Minimizing Risk with allowing short sell Calculating Portfolio Weight by Maximizing Portfolio Return for a given

Risk without allowing short sell Calculating Portfolio Weight by Maximizing Portfolio Return for a given

Risk with allowing short sell Calculating Portfolio Weight by Minimizing Risk for a given return

without allowing short sell Calculating Portfolio Weight by Minimizing Risk for a given return

without allowing short sell

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INTRODUCTION:

Security analyzing and selection of portfolios and managing them in the right manner helps in improving the investor’s awareness about the trends and changes that exist in the market and helps the investors as a very attractive avenue for investment. In these investments, generally both rationale and emotional responses are involved. So, investing in financial securities is considered to be one of the attractive areas for investing and saving while it is also acknowledged to be one of the most risky areas for investment. Creation of an optimum portfolio helps to reduce risk, without sacrificing returns. Portfolio management deals with the analysis of individual securities as well as with the theory and practice of optimally combining securities into good portfolios. An investor who understands the fundamental principles and analytical aspects of portfolio management has a better chance of earning higher returns.

It is widely accepted that investors should aim to maximize the level of return for a given level of risk. Alternatively they aim at minimizing the risk for a given level of return. This is done by constructing a portfolio of assets which as a whole is subject to the investor’s risk appetite.

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INTRODUCTION:

In this paper, 10 stocks from different sectors are taken for study. The risk and return of all the stocks are studied individually. Based on the study top five stocks are selected for forming optimum portfolio. The final step in the process is to determine the number of shares of each stock to be purchased. This method helps us to carefully select the stocks and also the proportion of investment to be made in each stock, thereby yielding higher returns.

The study will start by providing an overview of efficient portfolio construction to apply excel solver and its most important elements, namely risk, return and diversification. Secondly, the study will identify and discuss various alternative investments in securities that are believed to hold the potential for better diversification and move investors closer to attaining a true market portfolio. Lastly, the study will attempt to prove the hypothesis that these investments do hold the potential of improving the diversification of existing portfolios.

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OBJECTIVES OF THE STUDY:

The main objective of this project is to find the optimum portfolio from the selected companies in different sectors. At the end of the analysis a portfolio of 10 stocks with maximum return for a given risk is constructed which shows how much proportion of money is to be invested in each security wholly taken from different sectors.

These sectors are generally consistently performing as these kinds of sectors are depended by the public in a large extent. Main objective is to maximize the value of theta which is the portfolio excess return for each unit of portfolio risk.

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Main objective is to maximize the value of theta which is the portfolio excess return for each unit of portfolio risk.

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Objective of the study are as under:

Maximize Theta: When short sale is allowed When short sale is not allowed Minimize Risk:- When short sale is allowed When short sale is not allowed Maximize portfolio return for a given risk: When short sale is allowed When short sale is not allowed Minimize risk for a given return: When short sale is allowed When short sale is not allowed

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BACKGROUND OF THE STUDY

This report entitled “Construction of Efficient Portfolio” is prepared for the fulfillment of the course title Financial Modeling, Course No. 304. Everybody earns and spends money. But to optimize this earning & spending and to accommodate the future uncertainties, inflation etc., there needs to be proper planning & management of wealth. Investment decision is one of major part of this management of wealth. Because, sometimes may have enough money in hand and sometimes not. If excess money is invested in a proper manner, then it can encounter the problem during deficit. Portfolio management is an important management process of wealth, which maximizes the return for desirable risk level. In portfolio management, emphasis is given on the investment in the capital market. For this reason, study on security market is so essential. Evaluating efficient portfolio that maximize the return & minimize the risk compare to other portfolio is very much important.

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SCOPE OF THE STUDY:

I have prepared the assignment as a part of the Course Study of Financial Modeling, Course Code-D304. To achieve the objective it is needed to collect the price of the different companies. For achieving the objectives, the study will be focused on different steps for maximizing return on portfolio based on the shares listed in Dhaka Stock Exchange Limited considering the price, volume, P/E, EPS, Price to book value ratio and other criteria of different companies.

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METHODOLOGY:

To attain the objective, I have collected the required data & information for preparing the report. Those data & information were collected from various sources & then analyzed. The following are the sources of data and information:

Collection of data & information: Secondary data & information: Observation & collection of data from DSE Conversation with the executives & officers of Dhaka stock

exchange Ltd. Collection of Annual Report of Listed companies from DSE library Monthly review of Dhaka Stock Exchange Ltd Several kind of academic Test-Book. Different publications regarding stock exchange function Price index Dividend information Right Information

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LIMITATION OF THE STUDY

Some limitations that I have faced want to mention from report preparation point of view.

Shortcoming of practical experience to comprehend the conceptual framework of this type of report.

My sample for analysis includes only four year's data i.e. from July 2011 to June 2015, so, it may affect the result of the analysis.

This study was limited only to the 10 companies. As a result it has a narrow outlook of overall industry.

The study is based on the secondary data collected from the published annual report of the companies and website of DSE like www.dsebd.org. So limitation of the secondary data will remain with the study.

Every person has its own thinking and believes so in this research work may include personal bias during the research work.

Analytical tools, which are used in the study, may have their own limitations, which may apply to this study too.

It was very difficult to incorporate all the data in the report due to the limitation from the organization and thus certain information is not incorporated.

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CONSTRUCTION OF THE EFFICIENT PORTFOLIO:

Efficient portfolios may contain any number of asset combinations. We examine efficient asset allocation by using excel solver.

The make-up of any portfolio is subject to decisions being made on one of three levels namely:

The capital allocation decision – which refers to the choice

investors need to make between investing in a risk-free asset and a risky asset portfolio.

The asset allocation decision – which describes the distribution of risky investments across different asset classes. (Construction of the optimal risky asset portfolio).

Security selection decision – which describes the choice of particular securities held within each asset class

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SECTOR SELECTION:

All data are collected from the based on trading of Dhaka Stock Exchange Limited. There are 22 sectors in Dhaka Stock Exchange Limited. Here, I selected the following Sectors based on the previous positive performance in DSE:Fuel and Power

Pharmaceuticals and ChemicalsBankEngineeringFood and Allied

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SELECTION CRITERIA:

Here sector and shares are selected based on the following issues:Price Earning Ratio for the last Five yearsPrice to Book value ratio for the last five yearsMarket CapitalizationListed before January 01, 2011Listed in Dhaka Stock Exchange LimitedRelative higher lower P/E ratio of the companies with comparing market average.

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ASSET SELECTION:

Asset Selection:

Fuel and Power DESCO TITASGAS

Pharmaceuticals and ChemicalsThe Ibn SinaSquare PharmaBeximco Pharma

BankThe City BankEastern Bank

EngineeringBSRM SteelSinger BD

Food and AlliedOlympic BD

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THE CALCULATION PROCESS:

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ACCUMULATING PRICE FROM JULY 01, 2015 TO JUNE 30, 2015 Price of July, 2011

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DIVIDEND ADJUSTMENT AND RETURN SERIES:

Formula of Return Series

Return of November,2011

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ARRANGING MEAN RETURN:

Mean return for DESCO

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CALCULATING CORRELATION MATRIX

The correlation coefficient is a simple statistic that describes the variability of asset returns relative to other assets for the purpose of asset allocation. Determining how the asset classes correlate is an important step in the process of optimizing the allocation of assets. Without this normalized form of the covariance, it would be very difficult to evaluate the relative variability of asset returns.

Asset allocation accounts for over 90% of success as an investor. Assessing how assets complement one another is a crucial step in the process of asset allocation.

Correlation describes on a scale of -1 to +1 the relative movement of two securities' prices or one security relative to an index, with +1 being perfectly positively correlated, -1 being perfectly negatively correlated and 0 indicating no correlation. The correlation coefficient, R, which is the normalized form of the covariance, is a measure of relative variation.

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Perfect positive correlation is like moving in lock step. Perfectly positively correlated securities do not complement each other and therefore provide no diversification.

Perfectly negatively correlated securities' prices move in the opposite direction from each other by the exact same amount. For example, if stock A and stock B are perfectly negatively correlated, stock B will decline by 10% when stock A rises 10% and stock A will decline by 15% when stock B rises 15%. Perfectly negatively correlated investments would provide 100% diversification, as they would form a portfolio with zero variance, which translates to zero risk. Unfortunately, in the real world such investments don't exist, but there are a few assets that tend to be negatively correlated to most other asset classes. These assets provide excellent diversification.

CALCULATING CORRELATION MATRIX

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CALCULATING CORRELATION MATRIX:

Correlation of DESCO with itself

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CALCULATING CORRELATION MATRIX:

Correlation of DESCO with itself

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CALCULATING AVERAGE MEAN RETURN:

Average Mean return of DESCO

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CALCULATING RISK FREE RETURN

Calculating risk free return over the last 5 years

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TRANSPOSE THE AVERAGE MEAN RETURN TO THE COVARIANCE MATRIX

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CALCULATION OF INDIVIDUAL SECURITIES EXCESS RETURN:

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CALCULATING WEIGHT FACTOR IN COVARIANCE MATRIX

Preparing the weight Vector

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CALCULATION OF PORTFOLIO EXCESS RETURN:

Formula for portfolio Excess return

Portfolio Excess Return

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PREPARING THE COVARIANCE MATRIX:

Covariance of DESCO with itself

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PREPARING THE COVARIANCE MATRIX:

Covariance of DESCO with TITASGAS

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CALCULATING PORTFOLIO VARIANCE

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CALCULATING PORTFOLIO VARIANCE:

Portfolio Variance

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CALCULATING PORTFOLIO STANDARD DEVIATION

Portfolio Standard Deviation

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CALCULATING THETA

Calculating Theta

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CALCULATING TOTAL WEIGHT

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CALCULATING MATRIX PORTFOLIO RETURN

Portfolio Return

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PORTFOLIO CONSTRUCTION:

Objectives: Maximize the Theta Ө= Rp-Rf/σp

Here,Ө=Theta, Rp= Portfolio Return, Rf= Risk free return,σp = Standard Deviation of Portfolio return The Main objective in a portfolio construction is to

maximize the value of Theta (Ө) which is the portfolio excess return for each unit of portfolio risk.

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CONSTRUCTION THE FUNCTION

When short sell is allowed: Various constraints may preclude a particular investor from choosing portfolios on the efficient frontier, however. Short sale restrictions are only one possible constraint. Short sale is a usual regulated type of market transaction. It involves selling assets that are borrowed in expectation of a fall in the assets’ price. When and if the price declines, the investor buys an equivalent number of assets at the new lower price and returns to the lender the assets that were borrowed.

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When short sell is allowed:Return: the general formula of expected return for n assets is:

where: n= the number of securities;Wi = the proportion of the funds invested in security i;rirp= the return on ith security and portfolio p; andE()=the expectation of the variable in the parentheses.

The return computation is nothing more than finding the weightedaverage return of the securities included in the portfolio.

1

( )n

P i ii

E r w E r

1

n

ii

w = 1.0;

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n= the number of securities; wi=the proportion of the funds invested

in security i; rirp= the return on ith security and

portfolio p; and E()=The expectation of the variable in

the parentheses.

1

( )n

P i ii

E r w E r

wi >= 0

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The variance of a single security is the expected value of the sum of the squared deviations from the mean, and the standard deviation is the square root of the variance. The variance of a portfolio combination of securities is equal to the weighted average covariance of the returns on its individual securities:

2

1 1

Var Cov ,n n

p p i j i ji j

r w w r r

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0

Z’

Z

A

P

V

Expected Return

Standard Deviation

B

without short sales

with short sales

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The assumption of no short selling, investors could sell the lowest-return asset B (here, we assume that ). If the number of short sales is unrestricted, then by a continuous short selling of B and reinvesting in A the investor could generate an infinite expected return. The efficient frontier of unconstraint portfolio is shown in above Figure. The upper bound of the highest-return portfolio would no longer be A but infinity (shown by the arrow on the top of the efficient frontier). Likewise the investor could short sell the highest-return security A and reinvest the proceeds into the lowest-yield security, thereby generating a return less than the return on the lowest-return assets. Given no restriction on the amount of short selling, an infinitely negative return can be achieved, thereby removing the lower bound of B on the efficient frontier. Hence, short selling generally will increase the range of alternative investments from the minimum-variance portfolio to plus or minus infinity.

Relaxing the assumption of no short selling in this development of the efficient frontier involves a modification of the analysis of the efficient frontier of constraint (not allowed short sales). Next section, we introduce the mathematical analysis of the efficient frontier with/without short selling constraints by excel solver.

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CONSTRUCTION OF PORTFOLIO RETURN:

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EFFICIENT PORTFOLIOS IN EXCEL USING THE SOLVER

The solver is an Excel Add‐In created by Frontline Systems (www.solver.com) that can be used to solve general optimization problems that may be subject to certain kinds of constraints. In this note we show how it can be used to find portfolios that minimize risk subject to certain constraints.

The solver add‐in must be activated before it can be used within Excel. In Excel 2007, you activate addins by clicking on the office button and then clicking on the Excel Options box at the bottom of the menu.

This opens the Excel options dialogue box. Click Add‐Ins, which displays the available Add‐Ins for Excel. Make sure the Solver Add‐In is an Active Application Add‐In.

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EFFICIENT PORTFOLIOS IN EXCEL USING THE SOLVER

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CALCULATING PORTFOLIO WEIGHT BY MAXIMIZING THETA WITHOUT ALLOWING SHORT SELL BY EXCEL SOLVER:

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CALCULATING PORTFOLIO WEIGHT BY MAXIMIZING THETA WITH ALLOWING SHORT SELL BY EXCEL SOLVER:

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CALCULATING PORTFOLIO WEIGHT BY MINIMIZING RISK WITHOUT ALLOWING SHORT SELL BY EXCEL SOLVER

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CALCULATING PORTFOLIO WEIGHT BY MINIMIZING RISK WITH ALLOWING SHORT SELL BY EXCEL SOLVER

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CALCULATING PORTFOLIO WEIGHT BY MAXIMIZING PORTFOLIO RETURN FOR A GIVEN RISK WITHOUT ALLOWING SHORT SELLHERE, WE ASSUME THAT THE RISK RATE IS 8%

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CALCULATING PORTFOLIO WEIGHT BY MAXIMIZING PORTFOLIO RETURN FOR A GIVEN RISK WITH ALLOWING SHORT SELL

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CALCULATING PORTFOLIO WEIGHT BY MINIMIZING RISK FOR A GIVEN RETURN WITHOUT ALLOWING SHORT SELL

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CALCULATING PORTFOLIO WEIGHT BY MINIMIZING RISK FOR A GIVEN RETURN WITHOUT ALLOWING SHORT SELL

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CONCLUSION

The objective of portfolio management is to create and maintain efficient portfolios. Efficient portfolios are portfolios which yield the greatest return for any given level of risk. Portfolio is collection of different securities and assets by which we can satisfy the basic objective “Maximize yield minimize risk”. Further we have to remember some important investing rules which are related to the trading and set by the concerned regulator.Asset allocation accounts for over 90% of success as an investor, which is why to need a means to allocate capital efficiently across a specific set of assets. The Capital Allocation Line explains the basic procedure for the allocation of capital and modern portfolio theory explains how to identify the optimal allocation using mean-variance criteria to identify what's known as the Efficient Frontier, a concept that was first described by Harry Markowitz in 1952.Portfolio diversification is the means by which investors minimize or eliminate their exposure to company-specific risk, minimize or reduce systematic risk and moderate the short-term effects of individual asset class performance on portfolio value. In a well-conceived portfolio, this can be accomplished at a minimal cost in terms of expected return. Such a portfolio would be considered to be a well-diversified.

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REFERENCES

Efficient Portfolio Construction by Mahmood Osman Imam, Professor of Finance, DU

Website of the different listed Companies

www.dsebd.org Annual Report of different listed

Companies Research and Information Department

of DSE Corporate Finance by Stephen A. Ross

http://www.goldensonbd.com/

http://www.dsebd.org/

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