Abstract
In the face of investment risk, investors generally diversify and form an investment portfolio consisting of several assets. The problem is the fiery proportion of funds that must be allocated to each asset in the formation of investment portfolios. This paper aims to study the optimization of the Markowitz investment portfolio. In this study, the Markowitz model discussed is that which considers risk tolerance. Optimization is done by using the Lagrangean Multiplier method. From the study, an equation is obtained to determine the proportion (weight) of fund allocation for each asset in the formation of investment portfolios. So by using these equations, the determination of investment portfolio weights can be determined by capital.
Highlights
Investment Portfolio is a group of investments owned by an institution or individual
Materials and Methods The material used in this study is Markowitz's investment portfolio model, which considers investor risk tolerance
The study methods used include the formation of mean vectors, the formation of covariance matrices, formation of average equations and variance of portfolios, the formation of investment portfolio models in the form of Markowitz mean variants, where the optimization process used is Lagrangean multiplier, and Kuhn-Tucker's theorem
Summary
Investment Portfolio is a group of investments owned by an institution or individual. The form can vary, such as bonds, mutual funds, property, stocks, and other investment instruments. For people who invest in shares, there is the term Stock Portfolio, which is a collection of investment assets in the form of shares. An investor can diversify into various investment products to produce optimal returns & minimize risk (Ardia and Boudt, 2013). This is by the advice to not put all eggs in one basket so that all eggs do not break if the basket falls. The risk borne in an investment can be reduced because all money is not put into one investment instrument. The more assets (basket), the lower the risk (Bjork et al, 2011)
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