What Is a Mean-Variance Analysis?
Mean-variance analysis compares variance-expressed risk to the expected return. Investors choose investments using mean-variance analysis. Investors choose risk based on reward. Investors can find the highest reward or lowest risk with mean-variance analysis.
Knowing MVA
Modern portfolio theory uses mean-variance analysis to assume investors will make rational investment decisions with complete information. One assumption is that investors want low risk and high reward. Mean-variance analysis involves variance and expected return. Variance measures how diverse a set’s numbers are. Variance can show how spread out a security’s daily or weekly returns are—a probability expressing the expected return of a security investment. When two securities have the same expected return, the one with a lower variance is better. If two securities have similar variance, the higher return is better.
Modern portfolio theory suggests investing in securities with different variances and expected returns. This strategy differentiates investments to reduce the risk of catastrophic losses in rapidly changing market conditions.
Mean-Variance Analysis Example
Calculate which investments have the highest variance and expected return. Suppose an investor owns these investments:
Investment A: $100,000, 5% return.
Investment B: $300,000, 10% return.
The weight of each asset in a $400,000 portfolio is calculated as follows: Investment A weight = $100,000 / $400,000 = 25%.
Investment B weight = $300,000/$400,000 = 75%
Therefore, the portfolio’s total expected return is the asset weight times the expected return.
Portfolio expected return = 8.75% (25% x 5% + 75% x 10%). Portfolio variance is not a weighted average of investment variances, making it harder to calculate. Both investments are 0.65 correlated. Investment A has a 7% standard deviation, and Investment B has 14%.
Portfolio variance in this example:
Portfolio variance = 0.0137 (25% x 75% x 7% x 14% x 0.65)
The portfolio standard deviation is the square root of the answer: 11.71%.
Conclusion
- Investors use mean-variance analysis to help them decide what investments to make.
- The study helps determine which investments have the best chance of giving them the most money with the same level of risk.
- The range shows how spread out a specific asset’s daily or weekly returns are.
- The expected return is a chance that shows how much money you think you will make from investing in the security.
- If two assets have the same predicted return, but one has less risk, buying the one with less risk is better.
- It is also better to buy the security with the more significant return if the range of the two securities is about the same.
