What is a 'Mean-Variance Analysis'

Mean-variance analysis is the process of weighing risk, expressed as variance, against expected return. Investors use mean-variance analysis to make decisions about which financial instruments to invest in, based on how much risk they are willing to take on in exchange for different levels of reward. Mean-variance analysis allows investors to find the biggest reward at a given level of risk or the least risk at a given level of return.

BREAKING DOWN 'Mean-Variance Analysis'

Mean-variance analysis is one part of modern portfolio theory, which assumes that investors will make rational decisions about investments if they have complete information. One assumption is that investors want low risk and high reward. There are two main parts of mean-variance analysis: variance and expected return. Variance is a number that represents how varied, or spread out, the numbers in a set are. For example, variance may tell how spread out the returns of a specific security are on a daily or weekly basis. The expected return is a probability expressing the estimated return of the investment in the security. If two different securities have the same expected return, but one has lower variance, the one with lower variance is the better pick. Similarly, if two different securities have approximately the same variance, the one with the higher return is the better pick.

In modern portfolio theory, an investor would choose different securities to invest in with different levels of variance and expected return.

Sample Mean-Variance Analysis

It is possible to calculate which investments have the greatest variance and expected return. Assume the following investments are in an investor's portfolio:

Investment A: Amount = $100,000 and expected return of 5%

Investment B: Amount = $300,000 and expected return of 10%

In a total portfolio value of $400,000, the weight of each asset is:

Investment A weight = $100,000 / $400,000 = 25%

Investment B weight = $300,000 / $400,000 = 75%

Therefore, the total expected return of the portfolio is the weight of the asset in the portfolio multiplied by the expected return:

Portfolio expected return = (25% x 5%) + (75% x 10%) = 8.75%Portfolio variance is more complicated to calculate, because it is not a simple weighted average of the investments' variances. The correlation between the two investments is 0.65. The standard deviation, or square root of variance, for Investment A is 7 percent, and the standard deviation for Investment B is 14 percent. 

In this example, the portfolio variance is:

Portfolio variance = (25% ^ 2 x 7% ^ 2) + (75% ^ 2 x 14% ^ 2) + (2 x 25% x 75% x 7% x 14% x 0.65) = 0.0137

The portfolio standard deviation is the square root of the answer: 11.71 percent.

  1. Portfolio Variance

    Portfolio variance is the measurement of how the actual returns ...
  2. Yield Variance

    Yield variance describes the difference between actual output ...
  3. Budget Variance

    A budget variance is a measure used to quantify the difference ...
  4. Efficiency Variance

    Efficiency variance is the difference between the theoretical ...
  5. Sales Mix Variance

    Sales mix variance compares the actual mix of sales with the ...
  6. Analysis Of Variance - ANOVA

    Analysis of variance (ANOVA) is a statistical analysis tool that ...
Related Articles
  1. Trading

    Exploring the Exponentially Weighted Moving Average

    Learn how to calculate a metric that improves on simple variance.
  2. Investing

    Using Historical Volatility To Gauge Future Risk

    Use these calculations to uncover the risk involved in your investments.
  3. Investing

    Understanding The Sharpe Ratio

    The Sharpe ratio describes how much excess return you are receiving for the extra volatility that you endure for holding a riskier asset.
  4. Financial Advisor

    Example of Applying Modern Portfolio Theory (MPS)

    See how an investor can maximize expected return for a given level of risk by altering the proportions of the assets held.
  5. Investing

    Optimize your portfolio using normal distribution

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

    Explaining Expected Return

    The expected return is a tool used to determine whether or not an investment has a positive or negative average net outcome.
  7. Investing

    Is Apple's Stock Over Valued Or Undervalued?

    Despite several drawbacks, the CAPM gives an overview of the level of return that investors should expect for bearing only systematic risk. Applying Apple, we get annual expected return of about ...
  8. Investing

    How to Create a Low-Risk, High-Return Portfolio

    Modern portfolio theory states diversification will create a lower-risk, higher-return portfolio.
  9. Investing

    How To Manage Portfolio Risk

    Follow these tips to successfully manage portfolio risk.
  10. Investing

    Understanding Quantitative Analysis Of Hedge Funds

    Learn how hedge fund performance quantitatively requires metrics such as absolute and relative returns, risk measurement, and benchmark performance ratios.
  1. 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 >>
  2. How do you calculate variance in Excel?

    To calculate statistical variance in Microsoft Excel, use the built-in Excel function VAR. Read Answer >>
  3. What is the difference between the expected return and the standard deviation of ...

    Learn about the expected return and standard deviation and the difference between the expected return and standard deviation ... Read Answer >>
  4. How do I know when to "rebalance" my investments?

    In order to have a disciplined approach using "rebalancing style" investing, you must first setup a defined model that specifies ... Read Answer >>
  5. How is standard deviation used to determine risk?

    Understand the basics of calculation and interpretation of standard deviation, and how it is used to measure and determine ... Read Answer >>
  6. What is the difference between variance and covariance?

    Learn about the differences between covariance and variance, and how to use them to minimize your stock portfolio's risk ... Read Answer >>
Trading Center