## What is Mean-Variance Analysis?

Mean-Variance Analysis is a technique that investors use to make decisions about the financial instrument to invest in, based on the amount of risk that they can accommodate. Ideally, investors expect to earn higher returns when they invest in riskier assets. When measuring the level of risk, investors consider the variance (which is the volatility of returns produced by an asset) against the expected returns of that asset.

The mean-variance analysis is a component of the Modern Portfolio Theory (MPT). The theory is based on the assumption that investors make rational decisions when they possess sufficient information. One of the theory’s assumptions is that investors enter the market to maximize their returns while at the same time avoiding unnecessary risks.

When choosing a financial asset to invest in, investors consider the asset with low variance when given an opportunity to choose between two options with the same returns. An investor can achieve the right diversification by investing in securities with varied variances and expected returns, such that a loss by one stock is countered by a gain from another asset.

### Main Components of Mean-Variance Analysis

The mean-variance analysis is comprised of two main components, which include:

#### 1. Variance

Variance measures how distant or spread the numbers in a data set are from the mean. A large variance indicates that the numbers are spread out far apart from each other and the mean, while a small variance indicates that there is a low spread from the numbers and the mean.

The variance may also be zero, which shows that the numbers are identical to each other. When analyzing a portfolio of investments, the variance can be used to show how the returns of a security are spread out during a given period, whether daily or weekly.

#### 2. Expected return

The expected return is the estimated return that a security is expected to produce. Investors use the expected return to determine the loss or profit that they expect to earn from an asset with a known rate of return. Since it is based on historical data, the expected rate of return is not 100% guaranteed.

If two securities offer the same expected rate of return, but one of them comes with a lower variance, the investor should invest in the security with lower variance.

Similarly, if two securities show the same variance but one of the securities offers a higher expected return, the investor should go with the security with a higher return. When trading multiple securities, an investor can choose securities with different variances and expected returns.

### Example: Calculating Expected Return

Assume a portfolio comprising of the following two stocks:

Stock A: $200,000 with an expected return of 5%.

Stock B: $300,000 with an expected return of 7%.

The total value of the portfolio is $500,000, and the weight of each stock is as follows:

Stock A = $200,000 / $500,000

= 40%

Stock B = $300,000 / $500,000

= 60%

Therefore, the expected rate of return is obtained as follows:

= (40% x 5%) + (60% x 7%)

= 2% + 4.2%

= **6.2%**

### Investing Strategies

When drafting an investment strategy, the goal of every investor is to create a portfolio of stocks that offer the highest long-term returns without getting into high levels of risk. The Modern Portfolio Theory is based on the idea that investors are risk-averse and, therefore, focus on creating a portfolio that optimizes the expected return according to a specific level of risk. Investors understand that risk is an inherent part of high-return stocks, and the solution is to diversify the investment portfolio.

The portfolio can comprise stocks, bonds, mutual funds, etc. which when combined, come with varying levels of risk. If one security decreases in value, the loss is compensated by a gain in another security. If the investor owns only one asset, it means that if the security decreases in value, the investor will lose his entire investment.

A portfolio comprised of various types of security is considered a better diversification option compared to a portfolio comprised of the same type of security. A portfolio comprised of one type of security faces the risk of reacting negatively when subjected to a bad economic factor.

### Related Readings

CFI offers the Financial Modeling & Valuation Analyst (FMVA)™ certification program for those looking to take their careers to the next level. To keep learning and advancing your career, the following resources will be helpful: