# Portfolio Variance

## What is 'Portfolio Variance'

Portfolio variance is the measurement of how the actual returns of a group of securities making up a portfolio fluctuate. Portfolio variance looks at the standard deviation of each security in the portfolio as well as how those individual securities correlate with the others in the portfolio. In other words, portfolio variance looks at the covariance or correlation coefficient for the securities in the portfolio.

Next Up

## BREAKING DOWN 'Portfolio Variance'

Generally, the lower the correlation between securities in a portfolio, the lower the portfolio variance. Portfolio variance is calculated by multiplying the squared weight of each security by its corresponding variance and adding two times the weighted average weight multiplied by the covariance of all individual security pairs. Modern portfolio theory says that portfolio variance can be reduced by choosing asset classes with a low or negative correlation, such as stocks and bonds. This type of diversification is used to reduce overall risk.

## Portfolio Variance Example

The most important quality of portfolio variance is it is a combination of the individual variances of each of the assets and their co-variances. This means that the overall portfolio variance will be lower than simply a weighted average of the constituents individual variances.

The equation for the portfolio variance of a two-asset portfolio takes into account five variables. They are:

w(1) = the portfolio weight of the first asset

w(2) = the portfolio weight of the second asset

o(1) = the standard deviation of the first asset

o(2) = the standard deviation of the second asset

Cov(1,2) = the covariance of the two assets, which can be sampled to: q(1,2)o(1)o(2), where q(1,2) is the correlation between the two assets

The formula is:

Variance = (w(1)^2 x o(1)^2) + (w(2)^2 x o(2)^2) + (2 x (w(1)o(1)w(2)o(2)q(1,2))

For example, assume there is a portfolio that consists of two stocks. Stock A is worth \$30,000 and has a standard deviation of 25%. Stock B is worth \$70,000 and has a standard deviation of 15%. The correlation between the two stocks is 0.65. Given this, the portfolio weight of Stock A is 30% and 70% for Stock B. Plugging in this information into the formula, the variance is calculated to be:

Variance = (30%^2 x 25%^2) + (70%^2 x 15%^2) + (2 x 30% x 25% x 70% x 15% x 0.65) = 2.69%

Variance is not a particularly easy statistic to interpret on its own, so most analysts calculate the standard deviation, which is simply the square root of variance. In this example, the square root of 2.69% is 16.4%.

RELATED TERMS
1. ### Mean-Variance Analysis

The process of weighing risk against expected return. Mean variance ...
2. ### Variance

The spread between numbers in a data set, measuring Variance ...
3. ### Budget Variance

A periodic measure used by governments, corporations or individuals ...
4. ### Variance Swap

A type of volatility swap where the payout is linear to variance ...
5. ### Unfavorable Variance

An accounting term that describes instances where actual costs ...
6. ### Modern Portfolio Theory - MPT

A theory on how risk-averse investors can construct portfolios ...
Related Articles
1. Managing Wealth

### Calculating Portfolio Variance

Portfolio variance is a measure of a portfolioâ€™s volatility, and is a function of two variables.
2. Markets

### Explaining Variance

Variance is a measurement of the spread between numbers in a data set.
3. Investing

### Exploring The Exponentially Weighted Moving Average

Learn how to calculate a metric that improves on simple variance.
4. Managing Wealth

### The Workings Of Equity Portfolio Management

Achieve analytical efficiency by applying your evaluation to a key set of stocks.
5. Investing

### Find The Highest Returns With The Sharpe Ratio

Learn how to follow the efficient frontier to increase your chances of successful investing.
6. Investing

### Calculating Covariance For Stocks

Learn how to figure out how two stocks might move together in the future by calculating covariance.
7. Managing Wealth

### What Exactly Does A Portfolio Analyst Do?

Portfolio analysts have the exciting role of working between the investment team layers and they touch various aspects of an investment organization.

### How to Create a Risk Parity Portfolio

Learn about how risk parity uses leverage to create equal exposure to risk among different asset classes in portfolio construction.
9. Managing Wealth

### Using Normal Distribution Formula To Optimize Your Portfolio

Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.
10. Managing Wealth

### Manage Investments And Modern Portfolio Theory

Modern Portfolio Theory suggests a static allocation which could be detrimental in declining markets, making it necessary for continuous risk assessment. Downside risk protection may not be the ...
RELATED FAQS
1. ### How can I measure portfolio variance?

Find out more about portfolio variance, the formula to calculate portfolio variance and how to calculate the variance of ... Read Answer >>
2. ### What is the difference between expected return and variance?

Learn about expected return and variance, the difference between the two measures and how to calculate the expected return ... Read Answer >>
3. ### Is variance good or bad for stock investors?

Learn how high variance stocks are good for some investors and how diversified portfolios can reduce variance without compromising ... Read Answer >>
4. ### Can a mean variance analysis be done for any investment?

Learn how mean variance analysis is used in modern portfolio theory to create an optimal mix of assets to maximize return ... Read Answer >>
5. ### What is the difference between standard deviation and variance?

Understand the difference between standard deviation and variance; learn how each is calculated and how these concepts are ... Read Answer >>
6. ### What types of assets lower portfolio variance?

Learn what type of assets reduce portfolio variance and how modern portfolio theory uses correlation coefficients. Read Answer >>
Hot Definitions
1. ### Brazil, Russia, India And China - BRIC

An acronym for the economies of Brazil, Russia, India and China combined. It has been speculated that by 2050 these four ...
2. ### Brexit

The Brexit, an abbreviation of "British exit" that mirrors the term Grexit, refers to the possibility of Britain's withdrawal ...
3. ### Underweight

1. A situation where a portfolio does not hold a sufficient amount of a particular security when compared to the security's ...
4. ### Russell 3000 Index

A market capitalization weighted equity index maintained by the Russell Investment Group that seeks to be a benchmark of ...
5. ### Enterprise Value (EV)

A measure of a company's value, often used as an alternative to straightforward market capitalization. Enterprise value is ...
6. ### Security

A financial instrument that represents an ownership position in a publicly-traded corporation (stock), a creditor relationship ...