Efficient Portfolio Construction

A REPORT ON PORTFOLIO CONSTRUCTION & PERFORMANCE EVALUATION

Department of Finance University of Dhaka

Efficient Portfolio Construction & Performance Evaluation

Prepared for Prepared By

Date of Submission: 9th February 2014

Table of Contents Executive Summary------------------------------------------ 4 Introduction----------------------------------------------------5-6 Background Theory--------------------------------------------7-8 Portfolio Construction Steps--------------------------------9-22 Performance Evaluation-------------------------------------23-26 Conclusion-------------------------------------------------------27

Executive SummaryKnowledge of constructing an efficient portfolio is very important to learn as a student of finance. Efficient portfolio construction is not only needed by a manager who works in a brokerage firm or investment institution but also any individual investor who actively trades in the financial market. While there are many techniques to go for an efficient set, I think the excel solution is quite easy to understand. The data used for analysis collected from Dhaka stock exchange. The original trade data is then summarized to know about the risk and return pattern to construct a portfolio consisting 10 assets.First of all the theory behind the construction is described and then I showed the step by step process of choosing assets in six different scenarios: maximizing excess return per unit of risk when short sell is not allowed, minimizing risk when short sale not allowed, maximizing excess return per unit of risk when short sale is allowed, minimizing risk when short sale is allowed, minimizing risk when short sale is not allowed, minimizing risk for a given return when short sale is allowed.

I have chosen different asset classes so that the unsystematic risk can be diversified away. My report consists of 10 assets from 5 different asset classes. The entire report is a fundamental analysis of asset valuation. This analysis uses very simple solver solution so that its not free from flaws, but by completing this report I have got a good idea about the overall concept of selecting risky assets in a portfolio.

INTRODUCTION

Origin of the reportThis report was assigned to me by our honorable Portfolio managements course teachers Mrs. Pallabi Siddiqua and Mr. Sajib Hossain as a key tool of completing my courses overall agenda.Objective of the ReportThe following objectives are fulfilled while making this report:Familiarity with the stock marketOverlooking the price changes, volume information and overall trading situation of DSEKnowing and understanding the systems and major concerns while selecting a bunch of asset classes and including them to the portfolioLooking at the overall industry conditions and observing some selecting companies which will be a pathway for future analysis. Determining efficient portfolio under different situations.MethodologyThe study mainly focuses on Efficient Portfolio construction. This study is mainly based on primary data collected from the DSE as well as secondary data collected from different published articles, books, websites and journals. The basic method that is used to analyze the data is use of solver function for maximizing theta and minimizing risk. Limitations Constructing efficient portfolio is not an easy task to conduct. Several software exists to accurately estimate the risk and return pattern of a portfolio. While doing my simple analysis I used Microsoft Excel and its solver function to make my estimation which is subject to several limitations. I hope this initial knowledge will help me to do better in the future.

Background Theory

There are several ways of doing technical analysis. This report uses the simple technique of doing such analysis using Microsoft Excel spreadsheet software. I have collected trading data from Dhaka Stock Exchange of ten assets from 5 different asset classes. I showed portfolio construction in six different scenarios. My analysis is a simple suggestion for asset selection with within the selected asset portfolio.

Efficient Portfolio is a portfolio offering 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. 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.

Efficient Portfolio

Our main objective in this report is to find the efficient portfolio with a portfolio of 10 securities which are of A category listed in DSE before 2008. We are working on Monthly data. The CML equation can be written as maximizing the objective function: Subject to:( Wt) =1 when short sell is allowed. An additional constraint wi 0 when short sell is not allowed.

Construction Steps of an Efficient Portfolio

Steps followed in determining efficient portfolio:I have followed the following steps for constructing efficient portfolio- Step-1: Selection of Listed companies:There are numerous number of companies listed in DSE and CSE. I have selected 10 listed companies of DSE. As I am using data of five years I have selected companies which are listed before 2008. My selected companies are Asset ClassCompanyCategory

Pharmaceuticals IndustrySquire PharmaA

Beximco pharmaA

ACI LTDA

Cement IndustryHeidelberg cementA

Meghna cementA

Banking SectorDhaka BankA

Dutch Bangla BankA

Food& beverages industryBangasA

Fu wangA

Insurance SectorMeghna life insuranceA

Step-2: Collecting Price related Data:I used monthly closing price of each companies from January2008 to December 2012. Some companies have split their share recently. I multiplied the price with split ratio and assumed the situation to be pre split situation. All the companies have paid dividend throughout the year. I 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 I 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.

Price Data are categorized in excel sheet like this:

Then I placed the Cash dividend related data in the excel sheet. Not every company declares dividend in every month. I have collected dividend related information from DSE and place the dividend per share in a separate sheet:

Next I placed stock dividend related data in a separate excel sheet. Like cash dividend stock dividends data are collected from DSE and placed to the companies according to their declaration month.

I placed right issuance related numerical information next. Only Fu wang issued 100% right share in 2010 at 10 taka offer price which is shown in the very two next excel sheets.

Some stock gets spilled during 2010 and 2011. For calculating return this information is mandatory.

Step-3: Determination of return:In the next step I calculated return for each month. Thus I got 59 returns for each company. We know return R = [Price of T1*(1+stock dividend)*(1+right issue)*stock splits+ cash dividend price of T-1-Right offer Price]/price of T-1Or the return can be calculated as Cash dividend+ Capital Gain First I calculated Dividend yield which is Dividend per share /price per share

Next I calculated the capital gain of each companys stock:

Total return is calculated by adding both dividend yield and Capital gain:

Step-4 Calculating Mean return: To calculate mean return first I transposed the return series by copying the whole series and pasting it special n transposed format, and I have got all rows became columns and columns get to rows like this :

Mean return is calculated from transposed data:

Step-5 Calculating Risk Free ReturnThen I calculated Risk free rate for the 5 year period. I calculated that by multiplying every years Bangladesh Bank T-bill Rate by 12 and dividing by 12. After that adding the rates and dividing by 59. I multiplied the rate of 2008 with 11 because as we started from 2008 we cant get the return for January.

Step-6 Calculating Excess Return:Then I calculated Excess return by subtracting risk free return from Mean return. The equation is-Excess Return = Rm-Rf

Step-7 Calculating Variance & Covariance matrix Then I calculated Variance and covariance of each company using VAR and COVAR functions:

Step-8 Calculating Excess portfolio return Then I Calculated Excess portfolio returns by multiplying each excess return with respective weight and adding all:

Step-8 Calculating portfolio Variance & Standard Deviation:

W1W2W3W4W5W6W7W8W9W101,12,13,,110 12,2, 23,,210 13, 23, 3,,310. .. .. .. . . .. . 110, 210 310,.., 10Then I calculated the portfolio variance p using the theory of matrix .We know in variance we need to multiply individual variance covariance with weight square. So, my multiplication was like following-

p =[W1,W2,W3,W4,..,W10]

Portfolio Standard Deviation:We know portfolio standard deviation p is the square root of standard deviation. Thats why we calculated the square root of the portfolio standard deviation.

Step-8 Calculating Theta Next I calculated the theta. We know- = (Rm Rf)/ pExcess Return = Rm RfSo, = Excess Return / p

Step-10 Calculating Portfolio ReturnThen I calculated portfolio return. It is the sum of weighted average of mean return of each company.

Step-10 Using Solver ad-ins:Finally I used the solver function to find the optimum weight for following six situations. The situations are-1. Maximizing Theta allowing short sell2. Maximizing Theta by not allowing short sell3. Minimizing Risk (Standard Deviation) by allowing short sell4. Minimizing Risk (Standard Deviation) by not allowing short sell5. Minimizing Risk (Standard Deviation) by allowing short sell for a given return6. Minimizing Risk (Standard Deviation) by not allowing short sell for a given returnThese situations are described below-

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 was-1.Wi = 1

My findings are I have to short sell excluding only squire pharma and Meghna lifes stock to maximize my Theta Maximizing Theta by not allowing short sell:In this situation I maximized theta by not allowing short sell. In this situations the constrains are-1. Wi = 12. Wi >= 0

My findings are I dont have to invest in Beximco Pharma Meghna Cement ACI pharma Heidelbarg Cement Dhaka Bank Dutch Bangla Bank Bangas Fuwang

Minimizing Risk (Standard Deviation) by not allowing short sell:Then I tried to find the weights in which risk will be minimal. I have not allowed short sell. Constraints are-1. Wi = 12. Wi >= 0My findings are I got minimum standard deviation if I invest in only Square Pharma Bangas Dhaka Bank Minimizing Risk (Standard Deviation) by allowing short sell:Then I allowed short sell to get the weight at minimum risk. The only constraint is1. Wi = 1Then I have to short sell the stocks of Squire Pharma. Minimizing Risk (Standard Deviation) by not allowing short sell for a given return:Then I considered a situation in which I can earn a monthly return of 3.5% and my risk will be minimal. I have also not allowed short sell. My constraints are-1. Wi = 12. Wi >= 0My finding is I should invest in below portion to minimize my Standard DeviationSquarepharmaBeximco pharmaACI LTDheidelbarg cementMeghna cementDhaka BankDutch Bangla BankBangasFu wangMeghna life insurance

0.0885783960.0239216040.11250.11250.11250.11250.11250.11250.11250.1

Minimizing Risk (Standard Deviation) by allowing short sell for a given return:Then I considered a situation in which I can earn a monthly return of 3.5% and my risk will be minimal.. I have also allowed short sell. My only constraint is-1. Wi = 1My finding is I should short sell Square pharmaceuticals stock to earn a monthly return of at least 3.5.

Portfolio Performance Evaluation

Measuring of portfolio performance has become an essential topic in the financial markets for the portfolio managers, investors and almost all that have something to do in the field of finance and it plays a very important role in the financial market almost all around the world. Earlier then 1950, portfolio managers and investors measured the portfolio performance almost on the rate of return basis. During that time, they knew that risk was a very important variable in determining investment success but they had no simple or clear way of measure it. In 1952 Markowitz created the idea of Modern Portfolio Theory and proposed that investors expected to be compensated for additional risk and provided a framework for measuring risk. In early 1960, after the development of portfolio theory and capital asset pricing model in subsequence years, risk was included in the evaluation process. The capital asset pricing model of William Sharpe and John Litner marks the birth of asset pricing theory. The attraction of capital asset pricing model was that it offered power predictions about how to measure risk and the relation between expected return and risk. Treynor (1965) was the first researcher developing a composite measure of portfolio performance. He measured portfolio risk with beta and calculated portfolio market risk premium and later on in 1966 Sharpe developed a composite index which is similar to the Treynor measure, the only difference being the use of standard deviation instead of beta. In 1967 Sharpe index evaluated funds performance based on both rate of return and diversification but for a completely diversified portfolio Treynor and Sharpe indices would give identical ranking. Jensen in 1968, on the other hand, attempted to construct a measure based on the security market line and he showed the difference between the expected rate of return of the portfolio and expected return of a benchmark portfolio that would be positioned on the security market line.According to Prof. K. Spremann, Portfolio measurement has not only the goal to inform about the quality of a portfolio performance but and thats even more important to decompose and analyze the success factors of a portfolio.

Systems of EvaluationDifferent composite measures of portfolio performance evaluation are used in real world. Some are given below along with the analysis of performance of portfolio comprising:Squire Pharma

Beximco pharma

ACI LTD

Heidelberg cement

Meghna cement

Dhaka Bank

Dutch Bangla Bank

Bangas

Fu wang

Meghna life insurance

Sharpe ratio:The Sharpe ratio (also known as the Sharpe index, the Sharpe measure) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk (and is a deviation risk measure), named after William Forsyth Sharpe.The Sharpe ratio has as its principal advantage that it is directly computable from any observed series of returns without need for additional information surrounding the source of profitability. Ratio: (Rp-Rf)/pMy portfolio Sharpe ratio is -5.43329068 whereas market Sharpe ratio is -0.475197674meaning that market ratio is in bad situation than my portfolio performance excess return over risk free rate for per unit of risk. Though is it hard to identify whether portfolio performance outperforms with individual Sharpe ratio.

Treynor ratio:Treynor ratio (Treynor measure), named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk (e.g., Treasury Bills or a completely diversified portfolio), per each unit of market risk assumed.The Treynor ratio relates excess return over the risk-free rate to the additional risk taken; however, systematic risk is used instead of total risk.The higher the Treynor ratio, the better the performance of the portfolio under analysis. Ratio: (Rp-Rf)/ LimitationsLike the Sharpe ratio, the Treynor ratio (T) does not quantify the value added, if any, of active portfolio management. It is a ranking criterion only. The portfolio with a higher total risk is less diversified and therefore has a higher unsystematic risk which is not priced in the market.

My portfolio Treynor ratio is 0.491708805whereas market treynor ratio is 0.133170985,Which lower than the portfolio Traynor ratio. From this perspective portfolio performance is better than market index return. More over treynor ratio only dealt with the systematic risk rather than total risk because unsystematic risk is minimized by adding securities in the portfolio. Jensens Alpha:A risk-adjusted performance measure that represents the average return on a portfolio over and above that predicted by the capital asset pricing model (CAPM), given the portfolio's beta and the average market return. This is the portfolio's alpha. In fact, the concept is sometimes referred to as "Jensen's alpha..

The basic idea is that to analyze the performance of an investment manager you must look not only at the overall return of a portfolio, but also at the risk of that portfolio.

Here alpha value for this portfolio is. -0.106155707.

M-squared:M squared is an extension of sharpe ratio in that it is also based in total risk. The idea behind M squared is to create a mimicking portfolio by combining a risky portfolio (Pr) and risk free asset so that risk of the mimicking portfolio becomes equal to the risk of the market portfolio. Because risk of the mimicking portfolio is equal to the risk of the market , so difference between return of mimicking portfolio and market portfolio should be equal . If return difference is positive, then mimicking portfolio outperforms the market portfolio and vice versa. M squared: (Rp-Rf)*(/ ) - (Rm-Rf)Like Sharpe ratio , M squared gives similar ranking , If M squared is zero, then portfolio performances similar to market and it M squared is positive that portfolio outperforms the market. Information ratio: The Information ratio is a measure of the risk-adjusted return of a financial security (or asset or portfolio). It is also known as Appraisal ratio and is defined as expected active return divided by tracking error, where active return is the difference between the return of the security and the return of a selected benchmark index, and tracking error is the standard deviation of the active return.The information ratio is often used to gauge the skill of managers of mutual funds, hedge funds, etc. In this case, it measures the active return of the manager's portfolio divided by the amount of risk that the manager takes relative to the benchmark.The higher the information ratio, the higher the active return of the portfolio, given the amount of risk taken, and the better the manager. Top-quartile investment managers typically achieve annualized information ratios of about one-half.Generally, the information ratio compares the returns of the manager's portfolio with those of a benchmark such as the yield on three-month Treasury bills or an equity index such as the S&P 500.My information Ratio is calculated as -12.3341.

Conclusion:Construction of an efficient portfolio by considering various scenarios can be done with many sophisticated techniques. But for a new learner it is quite a well approach to start with an Excel Solver function. Ten companies that I have chosen have different risk and return pattern. I have chosen those companies to diversify away its systematic risk. Different industries have different risk which is seen when I did all these analysis. It is very possible to be not properly correct in estimation as I am an initial learner of that topic, so I hope my flaws will be taken lightly and informative suggestions will be given to improve my future analytical skills

2 | Page