# 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.