# Markowitz Model of Risk-Return Optimization | Assumptions

Markowitz model is an optimal financial investment strategy to maximize the expected return for an investor while maintaining a desired level of risk.

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. He 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’s Risk and Return Theory

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

**Investors are rational and risk-averse**: The theory assumes that investors are rational and seek to maximize their returns while minimizing their risks. Investors will always prefer a portfolio with higher expected returns and lower risk.

**Asset returns are normally distributed**: Markowitz’s theory assumes that asset returns follow a normal distribution. This means that the returns are symmetrically distributed around the mean, and the majority of returns fall within a certain range.

**Correlation between assets is known**: The theory assumes that the correlation between assets can be accurately measured. This allows investors to construct portfolios that are well-diversified and minimize risk.

**No transaction costs**: Markowitz’s theory assumes no transaction costs are associated with buying and selling assets. This allows investors to freely move in and out of different assets without incurring any additional costs.

**Investment horizon is long-term**: The theory assumes that investors have a long-term investment horizon and are willing to hold their portfolios for an extended period of time. This allows investors to benefit from the long-term growth potential of their investments.

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 to secure the above objectives.

## Markowitz Diversification

Markowitz diversification, also known as portfolio diversification, is a strategy used in investment management to reduce risk by investing in various assets that are not perfectly correlated.

Markowitz diversification is based on the idea that if you invest in things that aren’t perfectly linked, you can lower the risk of your portfolio without lowering your expected returns. This is because the performance of different assets tends to vary depending on how the market is doing. By having a diversified portfolio, an investor can lessen the effect of bad performance by any asset, which can help the portfolio’s overall performance to be more stable over time.

Markowitz’s diversification means looking at how the different assets in a portfolio are related to each other and choosing assets that are not related to each other well. Most of the time, statistical tools like correlation coefficients, covariance matrices, and optimization algorithms help with this process.

But it’s important to remember that diversifying a portfolio can’t eliminate all risk. There is always the chance that something unexpected, like a global economic crisis, could hurt the performance of all the assets in a portfolio at the same time. Also, if you have too many assets, your chances of making big gains are spread out over a lot of them. This can lower your expected returns.

## Parameters of Markowitz Diversification

Markowitz’s model has set down its own guidelines for diversification based on 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 risks 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.

The higher the expected return, the lower the standard deviation or variance and the lower 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 can 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.