Mean-Variance Analysis

What Is a Mean-Variance Analysis?

Mean-variance analysis is the most common way of weighing risk, communicated as variance, against expected return. Investors utilize mean-variance analysis to go with investment choices. Investors weigh how much risk they will take on in exchange for various levels of reward. Mean-variance analysis allows investors to track down the greatest reward at a given level of risk or the least risk at a given level of return.

Grasping Mean-Variance Analysis

Mean-variance analysis is one piece of modern portfolio theory, which accepts that investors will arrive at rational conclusions about investments assuming they have complete data. One assumption is that investors look for low risk and high reward. There are two fundamental parts tof mean-variance analysis: variance and expected return. Variance is a number that addresses how changed or spread out the numbers are in a set. For instance, variance might tell how spread out the returns of a specific security are on a daily or week by week basis. The expected return is a likelihood communicating the estimated return of the investment in the security. Assuming two unique securities have a similar expected return, yet one has lower variance, the one with lower variance is the better pick. Likewise, in the event that two unique securities have around a similar variance, the one with the higher return is the better pick.

In modern portfolio theory, an investor would pick various securities to invest in with various levels of variance and expected return. The goal of this strategy is to separate investments, which diminishes the risk of catastrophic loss in the event of quickly changing market conditions.

Illustration of Mean-Variance Analysis

It is feasible to work out which investments have the best variance and expected return. Expect 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 every asset is:

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

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

Accordingly, the total expected return of the portfolio is the weight of the asset in the portfolio duplicated by the expected return:

Portfolio expected return = (25% x 5%) + (75% x 10%) = 8.75%. Portfolio variance is more muddled to work out in light of the fact that it's anything but 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 An is 7%, and the standard deviation for Investment B is 14%.

In this model, 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 response: 11.71%.

Highlights

On the off chance that two distinct securities have a similar expected return, however one has lower variance, the one with lower variance is preferred.
The expected return is a likelihood communicating the estimated return of the investment in the security.
Mean-variance analysis is an instrument utilized by investors to weigh investment choices.
The variance shows how spread out the returns of a specific security are on a daily or week after week basis.
The analysis assists investors with deciding the greatest reward at a given level of risk or the least risk at a given level of return.
Also, in the event that two unique securities have around a similar variance, the one with the higher return is preferred.