# Determinants of Stocks for Optimal Portfolio

## 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.