Markowitz Portfolio Theory Explained

Markowitz Model Assumptions

Harry Markowitz was the first to investigate financial markets in this way. He developed the theory of portfolio selection based on the best conditions for the placement of capital in a situation of uncertainty.

Investor Motivation & Portfolio Goals

Markowitz focuses his work on defining the factors that motivate the investor when investing. It is based on the utility function of the investor that depends on the profitability he wants to obtain and the risk he can assume. What it intends is to compose an optimal portfolio of securities for an investor, this being the best possible among all those that can be formed. It will be a search for a portfolio where performance is maximized for a given risk or vice versa. The investor has to opt for a certain profit-risk combination depending on whether he prefers to earn more and assume more risk or prefers to assume less risk and earn less.

Measuring Portfolio Risk and Return

Mathematical expectation is accepted as a measure of profitability of a security, and as a measure of the risk that a security carries, we will use the variance or standard deviation. The conduct of the investor will be to choose the portfolio that provides the highest return and the lowest risk. This is rational behavior.

Mathematical Optimal Portfolio Method

For the determination of the optimal portfolio in an analytical way, Markowitz establishes a problem of mathematical programming that must be solved. This can be of two types:

Primal and Dual Problem Types

• PRIMAL: In this program, the solution is the combination of securities that provides us with the highest profitability for a given risk.
• DUAL: The solution is the combination of securities that provides us with the minimum risk for a given level of profitability.

Graphical Optimal Portfolio Method

The determination of the optimal portfolio graphically is divided into the search for 3 stages:

Stages of Graphical Determination

1. Get the border of efficient portfolios.
2. The specification of the investor's attitude towards risk.
3. The optimal portfolio determination. This is the point at which the curve of efficient portfolios is tangent to an indifference curve.

Diversification and Risk Reduction

When the correlation is perfect and negative, diversification can completely eliminate portfolio risk.