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Portfolio Variance is a measure of the riskiness of a portfolio. It can be measured using returns-based analysis or holdings-based analysis. Portfolio Variance is not interpretable because it is in units of returns-squared. The more intrepetable portfolio standard deviation can be found simply by taking the square root of portfolio variance.
Synonym: portfolio variability
With returns-based analysis a variance of portfolio returns is calculated by summing the squares of the differences from the average return and dividing by the number of observations.
Portfolio Variance can also be measured using holdings-based
analysis by taking the sum of the weights squared times each cell of the
covariance matrix. Matrix multiplication operations in Excel using the
=MMULT() function offer a clever
way to calculate portfolio variance. A simple two-stock example of the
portfolio variance formula is provided below.
The ABC Weight^2 above means the portfolio weight to ABC is squared. Portfolio standard deviation is the square root of portfolio variance.
For context, while variance isn't as interpretable as the related standard deviation measure, it is the measure often included in portfolio risk calculations in textbooks. The term MVO, for Mean Variance Optimization, refers to the selection of a portfolio with the highest expected mean, or average, return while minimizing expected portfolio variance. It is a key component of Modern Portfolio Theory.
Eve: And finally, take the square-root of
Liz: Yes, and don't forget to do the same to units of returns-squared.
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True. The returns-based version is for measuring performance after the fact.
Still unclear on Portfolio Risk? Check out the Quant 101 Series where we provide a free data source and 27 videos to help you understand the nuances of stock and portfolio risk.
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