Minimum variance portfolio formula matrix

In the following figure, we highlight the min variance portfolio using the red dot.

How is variance used in constructing a portfolio?

The minimum variance portfolio or minimum risk portfolio is a so-called risk-based approach to portfolio construction. Global minimum variance portfolio The min variance portfolio is related to modern portfolio theory and the efficient frontier. In the Excel file below, we apply this approach to come up with a minimum variance portfolio calculator. It is clear from the figure that the portfolio with the lowest standard deviation that can be constructed from the set of securities that the investor can invest in.

The expected returns of the portfolio can be calculated as where is the vector of expected returns. Minimum variance portfolio calculator The above formulas provide a closed-form solution to calculate the global minimum variance portfolio.

Minimum Variance Portfolio - Breaking Down Finance

The weights of the min variance portfolio are given as where is a column vector of ones. On this page, we explain the relationship between the minimum variance portfolio and the efficient frontier, provide formulas to determine the minimum variance portfolio weights, and provide and Excel sheet that implements the approach.

It is important to note that we do not need the expected returns to determine the weights. The expected returns of the portfolio can be calculated as. Download the Excel file: Minimum Variance Portfolio. Risk, however, is easier to estimate. To do this, all we need is the covariance matrix.

Portfolio Variance: Definition, Formula, Calculation, and Example

This means that, instead of using both risk and return information as in the Markowitz portfolio selection , the portfolio is constructed using only measures of risk. One reason why investors might want to opt for a risk-based approach, is the fact that expected or future returns are very hard to estimate. It can easily be calculated using software that allows for matrix algebra.

This leads to a more robust portfolio that is less subject to estimation risk.

Minimum variance portfolio The minimum variance portfolio or minimum risk portfolio is a so-called risk-based approach to portfolio construction. In particular, it is a unique portfolio that is on the efficient frontier. The weights of the min variance portfolio are given as. Minimum variance portfolio formula To calculate the minimum variance portfolio weights, we can make use of the following minimum variance portfolio formula.

The portfolio minimum variance equals.