## Mean Variance Analysis

## Why is mean-variance analysis important?

Mean-variance analysis is crucial because it enables investors to assess the risk of an asset. MPT assumes that when given all the information about an investment, investors will make logical decisions. To lessen the risk of loss in the event of subpar investments or a decline in the profitability of the market, an investor includes investments with a variety of variances and expected returns. To assess an investment’s risk and whether it will help them create a solid portfolio with a variety of variance to reduce risk, experts use mean-variance analysis. Investors also call this portfolio optimization.

An essential component of Modern Portfolio Theory is mean-variance analysis. Instead of focusing on an investment’s merits alone, this theory takes the investor’s entire portfolio into account. It employs a method created to assist investors in maximizing their returns based on minimal market risk. Market risk is the possibility that an investment won’t make a profit or cost the investor money. Using MPT, investors can build diversified portfolios that offer a stable rate of return at a low level of risk.

## What is mean-variance analysis?

Modern Portfolio Theory (MPT) uses mean-variance analysis to balance an investment’s risk and potential return. Investors use this analysis to evaluate their investment choices by comparing the amount of risk they are willing to assume with the potential return on their investment. The ideal ratio is either high reward for low risk, or low reward for high risk.

The investment with the lowest risk, or the potential to lose money, is the better investment, for instance, if two different investments have the same potential for return in terms of profit. By taking the variances between each value in a data set and the mean, and then squareing the variances to make them positive, you can determine the variance mean. The data set in this instance would be a history of profit returns from a single investment. the values in the data set by the sum of the squares. Here is the formula:

Number of data points (differences between each data point in the data set – the mean)2 / (number of data points in the set) is the formula for variance.

## What are the main components of mean-variance analysis?

The main components of mean-variance analysis are:

**Variance**

Variance is the difference between two numbers in a set. If a variance is greater, it indicates that the difference between the two numbers in the set is large; if a variance is smaller, it indicates that the difference is small. For instance, the set [2,4] has a lower variance than [2,7] between two sets.

The variance is significant because investments generate a profit, and this profit can fluctuate. In contrast to another investment that has a higher variant and can provide a higher return on investment, a good investment will have a low variance, which means the profit is more reliable. The variance describes the volatility of the investment. Investors typically assess the variance of an investment over a year.

**Expected return**

The expected return on an investment is the amount of money you anticipate making from it. On the basis of previous returns and the investments’ historical volatility, you can determine the expected return. When you determine the expected return, you can predict how much profit an asset will probably bring in.

Using the CAPM, or capital asset pricing model, you can determine the expected return. The CAPM calculates the expected return as:

Risk-free rate + (beta x market risk premium)

Here are some definitions of these terms to help further clarify this formula:

**Optimization**

Once you have determined the variance and the anticipated return, you can make a calculated risk-based investment decision. The analysis can reveal which investment has lower risk and might be a better investment when two investments have the same expected return. To ensure you are earning the most money for the same amount of risk, choose the investment with the highest return if you have two investments with the same amount of variance.

## An example of mean-variance analysis

Here is an example of a portfolio:

Investment A: $100,000 with an expected return of 10%

Investment B: $200,000 with an expected return of 5%

Investment C: $200,000 with an expected return of 15%

The total value of the entire portfolio is $500,000. Investment A accounts for 20% of the portfolio’s weight, while Investments B and C each make up 40%. The weight of each investment can then be multiplied by its expected return.

Investment A: (10% x 20%) = 2%

Investment B: (5% x 40%) = 2%

Investment C: (15% x 40%) = 6%

Total value of expected return = 10%

You can use a data set that includes the returns from prior years to calculate the variance:

Investment A

The average for these returns is 7.5%

Investment B

The average for these returns is 2.5%

Investment C

The average for these returns is 2.5%

The deviation can then be calculated by finding the difference between each return and the average:

Investment A: 2.5% for both data points

Investment B: 7.5% for both data points

Investment C: 12.5% for both data points

The deviation is then squared, divided by the data set’s numbers, and its square root is taken to yield the standard deviation for each investment’s returns.

Investment A: 2.5%² ÷ 2 = √3% = 2%

Investment B: 7.5%² ÷ 2 = √28% = 5%

Investment C: 12.5%² ÷ 2 = √78% = 9%

You can evaluate the strength of your portfolio now that you have determined the risk of variance and the reward of returns. This portfolio, according to the MPT, has both high variance and high risk as well as low variance and low risk. If you needed to choose between Investment B and Investment A to diversify your portfolio, you could trade Investment B for an investment that has higher returns or lower risk because Investment A has lower risk than Investment B. This would give you an optimized portfolio.

## FAQ

**What is meant by mean-variance analysis?**

The process of weighing risk, expressed as variance, against anticipated return is called mean-variance analysis. Investors use mean-variance analysis to make investment decisions. Investors assess their willingness to accept a certain level of risk in exchange for a given level of reward.

**What is mean-variance Optimisation?**

Based on the level of risk they are willing to accept (risk tolerance), investors can choose which financial instruments to invest in using the mean-variance analysis method. In theory, when investors invest in riskier assets, they should expect to see higher returns.

**What is the mean-variance criterion?**

Mean-variance optimization is a key element of data-based investing. It involves comparing an asset’s risk to its likely return and basing investment decisions on that risk/return ratio.