Modern portfolio theory (MPT) or mean-variance model was developed by Harry Markowitz and published in 1952 by the Journal of Finance. It is an investing model that enables risk-averse investors to maximize returns for a given amount of risk or minimize the risk for a given amount of returns. For developing the MPT he was later awarded a Nobel prize.

The risk of every investing portfolio returns has two components: systematic risk and unsystematic risk. The first is the market risks that cannot be diversified away. The second the specific risk of a stock and can be diversified away by increasing the number of stocks in the portfolio. By using mean-variance model every investor can reduce or eliminate the specific risk.

**The assumptions
of modern portfolio theory**

There are various assumptions made by Markowitz while developing the mean-variance model. Let’s see now the assumptions of modern portfolio theory:

- An investor either maximizes their portfolio return for a given level of risk or maximizes their return for the minimum risk.
- The investor’s utility function is concave and increasing, due to their risk aversion and consumption preference.
- Risk of a portfolio is based on the variability of returns from the said portfolio.
- Analysis is based on single period model of investment.
- An investor prefers to increase consumption.
- An investor is rational in nature.
- An investor is risk averse.

**How to
find the optimal investing portfolio for everyone**

Markowitz model or mean-variance model is a portfolio optimization model used to find the most efficient portfolio by analyzing various possible portfolios of the given securities. So, the first step is to create the efficient frontier, which is the set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. The second step is to select the optimal portfolio for yourself.

The efficient frontier is found by minimizing the risk of the portfolio, which is found by the following expression:

The expected return of the portfolio in the mean-variance model is found by the following expression:

*The sum of portfolio weights in the mean-variance model is always 1.*

The chart below shows a hyperbola showing all the outcomes for various portfolio combinations of risky assets. Portfolio along the lower part of the hyperbole will have lower return and eventually higher risk. The CLA represents a portfolio of all risky assets and the risk-free asset, which is usually a triple-A rated government bond and is calculated using CAPM model. The tangency portfolio is the point where the portfolio of only risky assets meets the combination of risky and risk-free assets.

There are many software that can be used to create the efficient frontier and for many of them it is necessary to pay a lot of money. The efficient frontier can also be created using Excel but it is not simple to do.

**Criticisms
about modern portfolio theory**

There are many critics for MPT, because its model of financial markets does not match the real world in many ways. The risk, return, and correlation measures used by mean-variance model are based on expected values, which means that they are statistical statements about the future. Such measures often cannot capture the true statistical features of the risk and return which often follow highly skewed distributions and can give rise to, besides reduced volatility, also inflated growth of return. In practice, investors must substitute predictions based on historical measurements of asset return and volatility for these values in the equations.