# Markowitz Model of Risk-Return Optimization

Harry M. Markowitz introduced a new concept of risk measurement and their application to the selection of portfolios. Dr. Harry M. Markowitz was the first person who developed the first modern portfolio analysis model.

Markowitz started with the new idea of risk aversion of the average investor and their desire to maximize the expected return with the least risk. He provided a theoretical framework to analyse the risk and returns and their inter-relationship. His framework helps to the choice efficient portfolio and an efficient portfolio is that combination of securities which provide the highest return for a given level of risk and lowest risk for a given level of return.

Markowitz model is called the “Full covariance model” because with the help of this model the investor can find out the efficient set of the portfolio by finding out the trade-off between risk and return, between the limit of zero and infinity.

**Assumptions of Markowitz Theory**

The Markowitz model theory of risk and return optimization based on the following assumptions:-

- Under this theory, we assume that investors are rational and they behave in such a way to maximize their satisfaction with a given level of income and money.
- Investors have a right to get fair and correct information on the returns and risk.
- The market is very efficient and the information absorbed quickly in the market.
- Investors are risk-averse and they try to minimize the risk and maximize the return on the securities.
- The decisions of the investors are bases on excepted returns and variance or standard deviation of these returns from the mean.
- The investor prefers to higher returns to lower returns on the combination of securities at a given level of risk.

The combination of various assets offers a higher expected return with the same or lower risk with the same or higher expected return. Diversification of securities is the best way to which the above objectives can be secured.

**Markowitz Diversification **

Markowitz model suggests that risk can be reduced by diversification of securities into a number of scrips. Example:- Two scrips A and B, With B considerably less risky than A, a portfolio composed of some of the A and some of the B may be less risky than a portfolio composed of only less risky B.

AB

Expected return 40% 30%

Risk of security 15% 10%

The coefficient of correlation, between A and B can have any of the three possibilities i.e. -1, 0.5 or +1.

Let us assume investment in A is 60% and in b 40%.

Return on portfolio = (40*0.6) + (30*0.4)
= 36% Risk on portfolio = (15*0.6) + (10*04) = 13%, which is the normal risk |

**Parameters of Markowitz Diversification**

Markowitz model has set down own guidelines for the diversification on the basis of scientific research.

- The investment has a different kind of risk characteristics. Some are the systematic or market-related risk and the other is the unsystematic risk or company-related risk.
- Diversification of securities involves a proper number of securities in a portfolio. There should be no less or more than securities in a single portfolio.
- The securities have no correlation or negative correlation.
- The proper choices of the companies and securities or assets whose returns are not correlated as well as whose risk are mutually offsetting to reduce the overall risk.

**There are three parameters for building up the efficient set of a portfolio** **as lays down by Markowitz:-**

- Expected return
- Standard deviation from mean to measure the variability of returns.
- Covariance and variance of one asset return to other assets returns.

When higher the expected return lower will be the standard deviation or variance and lower is the correlation. In such, it is better for the investor to choose security.

On another hand, if the covariance of security’ return is negative then the total risk of the securities may be lowered as compared to the risk of individual security isolation.