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# Portfolio Variance Definition, Calculation and Quiz

While the original focus of Modern Portfolio Theory was on portfolio variance, the community of financial professionals prefers standard deviation.
1. Define - Define Portfolio Variance.
2. Context - use Portfolio Variance in a sentence.
3. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 18, 2021
The calculation of portfolio variance can be performed using holdings-based data or a series of portfolio returns over time. See when to use each one below.

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## Understanding the Importance of Portfolio Variance

Beginner

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.

• Portfolio Variance = ABC Weight^2 * ABC Variance + XYZ Weight^2 * XYZ Variance + 2 * (ABC Weight * XYZ Weight * Covariance of ABC and XYZ))

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.

### In a Sentence

Eve:  And finally, take the square-root of portfolio variance.
Liz:  Yes, and don't forget to do the same to units of returns-squared.

### Video

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### Video Script

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### Quiz

Portfolio Variance is easier to interpret than portfolio standard deviation because the units are measured in returns. | True or False?

False

Portfolio Variance calculated using holdings is more commonly used when forecasting portfolio risk, like in an optimization program. | True or False?

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.

### Related Terms

Our trained humans found other terms in the category portfolio risk you may find helpful.

## What's Next?

• For all Glossary terms, click Outline.
• To review Portfolio Specific Risk, hit Back.
• Which came first? Knowledge transfer or appreciation, click Tip.
• Next, for an introduction to Quantitative Analysis, click Next.

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