## Risk-Return Model

In finance, the Markowitz model of risk-return optimisation is a portfolio selection model that derives a set of weights for an investment portfolio that minimises the total variance of returns, subject to an initial capital constraint.

Dr Harry M. Markowitz was the first person who develop the first modern portfolio analysis model. Harry Markowitz developed it in the 1950s.

Markowitz started with the new idea of risk aversion of the average investor and their desire to maximise 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 in the efficient choice portfolio. An efficient portfolio is a combination of securities that provide the highest return for a given level of risk and the lowest risk for a given level of return.

Markowitz’s 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 optimisation is based on the following assumptions:-

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

Combining 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 in which the above objectives can be secured.

### Markowitz Diversification

Markowitz’s model suggests that risk can be reduced by the 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 its own guidelines for diversification on the basis of scientific research.

- The investment has different kinds of risk characteristics. Some are systematic or market-related risks, and others are unsystematic or company-related risks.
- 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 laid 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. As such, the investor should choose security.

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

## Summary

The Markowitz model is a model of risk-return optimisation that provides an efficient way to calculate the expected return and variance from investing in financial securities. In addition, the Markowitz model provides a formula for calculating the variance as a function of the expected return and volatility.

The model assumes that investors have the option to buy a collection of assets (stocks, bonds, cash, etc.) or a single asset in the form of equity (stock or bond). The assets are represented as vectors in the real n-dimensional space, where n is the number of assets.