Markowitz portfolio theory, also known as Modern Portfolio Theory (MPT), is a framework developed by economist Harry Markowitz in the 1950s that helps investors understand the trade-off between risk and return when constructing a portfolio. The main idea behind MPT is that investors should not just focus on the expected return of individual assets, but rather on the overall risk and return of the portfolio as a whole.

According to MPT, the most important factor in determining the risk and return of a portfolio is its diversification. Diversification refers to the practice of including a variety of assets in a portfolio in order to spread out the risk. By holding a diverse range of assets, an investor can potentially reduce the impact of any one asset's performance on the overall portfolio. This is because different assets tend to have different levels of risk and return, and they may not all be affected by the same market conditions.

To understand the importance of diversification, it is helpful to consider the concept of portfolio variance. Portfolio variance is a measure of the dispersion of returns around the expected return of a portfolio. A portfolio with a high variance will have a wider range of possible returns, which means it is more risky. On the other hand, a portfolio with a low variance will have a narrow range of possible returns, which means it is less risky. By diversifying a portfolio, an investor can potentially reduce the variance and therefore the risk of the portfolio.

One way that MPT helps investors construct a diversified portfolio is through the use of the efficient frontier. The efficient frontier is a graph that plots the expected return of a portfolio against its variance. It shows the various combinations of risk and return that are possible for a given set of assets. The efficient frontier curve represents the set of portfolios that offer the highest expected return for a given level of risk. By constructing a portfolio that falls on the efficient frontier, an investor can potentially maximize the expected return for a given level of risk.

Another important concept in MPT is the use of expected return and standard deviation as measures of risk and return. Expected return is the average return that an investor can expect to receive from an asset over a given time period. Standard deviation is a measure of the dispersion of returns around the expected return. A high standard deviation indicates a high level of risk, while a low standard deviation indicates a low level of risk.

In conclusion, Markowitz portfolio theory is a useful framework for understanding the trade-off between risk and return when constructing a portfolio. It helps investors understand the importance of diversification and the role of expected return and standard deviation in measuring risk and return. By following the principles of MPT, investors can potentially construct portfolios that offer a high expected return for a given level of risk.