## Determinants of Stocks for Optimal Portfolio

The primary goal of this

research is to empirically test the Markowitz Modern Portfolio Theory (MPT) or

mean-variance analysis. To that end, all elements of MPT were computed using

live data from companies listed on the Karachi Stock Exchange. Diversification

can reduce non-systematic risk because portfolio return is a weighted average

return; thus, consensus on diversification’s risk-reduction capabilities is

unanimous. However, there is no agreement on the number of stocks or assets

that must be included in a portfolio; this varies from market to market and

from period to period, even within the same market. Decisions in the

theoretical framework of economics are based on rational choice while keeping

scarcity of resources and preference in mind. Markowitz identified a trade-off

between risk and return or how to maximize utility within the constraints of

available resources [(Kaplan 1998)]. The Markowitz model assumes that investors

want to maximize their return at a given level of risk or minimize risk in order

to achieve the required return. This is why the Markowitz model is also known

as the mean-variance theory [Fama and French (2004)]. The computation of

weights is important in portfolio management theory. When we say a portfolio is

well-diversified, it means that wealth has been distributed among different

assets in an appropriate proportion (weights), whereas when we say a portfolio

is poorly diversified, it means that assets are not properly weighted. As a

result, any change in the weight, variance, and covariance of individual stocks

will alter the risk level [Statman (1987)]. Mathematically, it is possible to

demonstrate that a minimum portfolio with equal weights occurs when securities

have equal variance. Weights can be computed to achieve the lowest possible

variance and can be derived to produce zero variance when the correlation

coefficient is -1.0 [Reilly and Brown (1999)]. Investing in the stock market is

a risky decision because actual returns differ significantly (deviate) from

expected returns. Markowitz (1952) was the first to recognize how an investor

could reduce the standard deviation or risk specific to a specific stock (i.e.,

non-systematic) by selecting stocks with appropriate weights [Brealey et al.

(2011)].

The expected return, mean-variance, standard deviation, and covariance, or coefficients of correlation,

are key parameters in the Markowitz model that can be estimated using

historical data. The goal is to use the mean-variance model to determine the

optimal portfolio [Kisaka et al., (2015)]. Weights of individual stocks that

are dependent on covariance can be computed with greater precision in the

global minimum variance portfolio (GMVP); in fact, weights are dependent on

covariance rather than mean [[Kan and Zhou (2007)]. An efficient portfolio

frontier can be developed from GMVP Markowitz for investors who want to

optimize their investment portfolio (1952). In their discussion of Modern

Portfolio Theory (MPT), Bailey and Prado (2013) define the efficient frontier

as an average excess return (over and above the risk-free rate) for any given

risk level. According to Alexander and Christoph (2005), the concept of the

efficient frontier has become an integral part of modern investment theory. In

this paper, the researcher applied Harry Markowitz’s modern portfolio theory to

build a portfolio with the highest possible return against a variety of risk

levels on the Karachi Stock Exchange (KSE-100) Zivot (2013) also supports Harry

Markowitz’s modern theory of portfolio and claims that by focusing on the

efficient portfolio, the risk-return problem can be simplified. He created the

model in R software for this purpose. His codes were used in this study to

evaluate the optimal tangency portfolio based on historical data from

thirty-one Pakistani companies’ stocks. Section II follows the introduction

(Section I). It contains a review of the literature. The data (Section III) is

divided into data selection methodology, descriptive statistics enumeration,

determining the criteria to determine the global minimum portfolio, determining

the efficient frontier portfolio, and developing a tangency portfolio to

determine the minimum risk locus. Finally, in Section IV, the data analysis is

followed by the conclusion.