Construction of an Optimal Stock

8/6/2019 Construction of an Optimal Stock

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resented BYASHER WILSON

-LOUIS ASOMAH OKYERE.CHRISTIAN N DARKOERIC MEVEMEO

supervisorvincent kofi dedu

ONSTRUCTION OF AN OPTIMAL STOCKORTFOLIO USING MARKOWITZ EFFICIENTFRONTIER


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outline

1.Introduction

2.Problem Statement

3.Objectives

4.Methodology

5.Data Analysis

6.Conclusion7.Recommendation


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introduction

-The GSE All Share Index recorded a% ,decrease of 48 at the end of 2009

. %this is a sharp contrast to the 55 77gain recorded during the same period in

.2008 These figures reveal the high volatility

of the GSE and the deepening globalrecession coupled with Ghana s slowing

( . %)GDP rate 4 7 is an indication ofeven greater perilous times ahead for.stock investments


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PROBLEM STATEMENT

Given the current gloomy investmentclimate evidenced by the sharp decline of

- ;the GSE All Share Index stock

What is the most appropriate investmentstrategy? How do investors with huge stock

investments manage risks without

compromising on returns?


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Objectives

We seek to provide potential stock investors with modernstrategies for selecting an optimal stock portfolio on.the Ghana Stock Exchange

,To achieve our general objective our study seeks toachieve the following

Derive an optimal portfolio of selected stocks on the.GSE utilising the Efficient Frontier

Recommend optimal portfolio selection approaches for.investors with different risk preference levels

-Formulate a model suitable for the selection of any n.asset portfolio using MATLAB


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Modern portfolio theory

( )Modern portfolio theory MPT is an investmenttheory which tries to maximize return and

minimize risk by carefully choosing.different assets

Asset returns are normally distributed random.variables

MPT models a portfolio as a weightedcombination of assets so that the return of

a portfolio is the weighted combination of.the assets' returns By combining different assets whose returns

,are not correlated MPT seeks to reduce the.total variance of the portfolio


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Markowitz Efficient frontier

fficient frontier

C eturn A B

risk - ,For a given portfolio of n assets everypossible asset combination can be plotted- .in risk return space

The line along the upper edge of thisregion is known as the efficient frontier. Combinations along this line represent

portfolios for which there is the lowest.risk for a given level of return


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Types of investors

Investors are typically classified bytheir risk preference levels, in generalthere are three types:

.a :Risk Neutral Such a person is onlyinterested in expected returns and is.indifferent to risk

.b :Risk Lover The utility of an investments

expected value is less than the expected.values of its utility.c :Risk Averse An investor who prefers a

certain outcome to an uncertain one with

.the same expected value


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Expected returns of listed gse stocks


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Standard deviations of listed gse stocks


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five Selected stocks

.1

Benso Oil Palm Plantation BOPP

:Industry Agriculture: . : . %Risk 0 036 Return 3 20

.2 Cal Bank limited CAL :Industry Banking

: . : . %and Finance Risk 0 036 Return 3 11.3 Fan Milk Limited FML

:Industry Food and: . : . %Beverage Risk 0 064 Return 6 44

.4 Camelot Ghana Limited CMLT :Industry Manufacturing

: . : . %Risk 0 029 Return 4 54

.5 -Accra Brewery Company Limited ABL

:Industry Food and Beverage: . : . %Risk 0 043 Return 2 53


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Monthly returns vs time


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Matlab Code>> returns = [3.1981 3.1094 6.4366 4.5435 2.5257];

>> STDs = [0.0356 0.0363 0.6439 0.0289 0.0430];

>> correlations = [1 -0.1428 0.2886 -0.0731 0.1817;

-0.1428 1 0.0716 -0.7623 -0.2112;

0.2886 0.0716 1 0.4529 0.9484;

-0.0731 -0.7623 0.4529 1 0.6993;

0.1817 -0.2112 0.9484 0.6993 1];

>> covariances = corr2cov(STDs , correlations);>> portopt (returns , covariances , 10)

>> weights = exprnd (1,1000,5);

>> total = sum (weights , 2);

>> total = total (:,ones (5,1));

>> weights = weights./total;

>> [portRisk , portReturn] = portstats (returns , covariances , weights);

>> hold on

>> plot(portRisk , portReturn , '.r')

>> title('Mean Variance Efficient Frontier and Random Portfolios')

>> [PortRisk, PortReturn, PortWts] = frontcon(returns, covariances, 10)

>> hold off


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Efficient frontier graphs


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Returns, weights and risksortfolio Weights

PTIMALPORTFOLIO RISK RETURN BOPP CAL FML CMLT ABLORTFOLIO 1 .0 0093 .3 8039 %15 %37 %0 %48 %0ORTFOLIO 2 .0 0134 .4 0964 %0 %31 %0 %69 %0ORTFOLIO 3 .0 0229 .4 389 %0 %11 %0 %89 %0ORTFOLIO 4 .0 0637 .4 6815 %0 %0 %7 %93 %0ORTFOLIO 5 .0 1578 .4 974 %0 %0 %23 %77 %0ORTFOLIO 6 .0 2545 .5 2665 %0 %0 %38 %62 %0ORTFOLIO 7 .0 3517 .5 559 %0 %0 %54 %46 %0ORTFOLIO 8 .0 449 .5 8516 %0 %0 %69 %31 %0ORTFOLIO 9 .0 5464 .6 1441 %0 %0 %85 %15 %0ORTFOLIO 10 .0 6439 .6 4366 %0 %0 %100 %0 %0


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Portfolio 1 weight


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Conclusion

A risk loving investor should invest all his capital into

Portfolio 10 which consists of only FML stocks since it( . %).yields the greatest expectation of return 6 44

The risk neutral investor is free to invest in any of theportfolio weights available depending on his risk

.preference at the time of selection

A risk averse investor should invest in Portfolio 1 and: %should allocate his portfolio weight as follows 15 into

, . % . %BOPP stocks 37 5 into CAL and finally 47 5 into CMLT.stocks This portfolio will attain the lowest possible

. .portfolio risk of 0 0093


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Recommendation

Since our optimal portfolio model can be-used for n assets we recommend that

prudent investors develop portfolios

with a larger number of stocks to

.capitalize on diversification


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THANK YOU FOR YOUR TIME

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Construction of an Optimal Stock