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how to calculate standard deviation and coefficient of variance of the expected return of one asset?...

how to calculate standard deviation and coefficient of variance of the expected return of one asset? Of a portfolio?

give examples

Expert Solution

Standard Deviation

The Standard Deviation of a portfolio conveys the volatility of the portfolio. Its computation is based on three imperative factors i.e., the standard deviation of each of the assets which is the part of a Portfolio, the corresponding weight of that individual asset in total portfolio and the correlation between each pair of an assets of the concerned portfolio.

The higher standard deviation signifies that the risk of portfolio is high and the return of the portfolio is more volatile and unpredictable. On the other hand, the lower standard deviation signifies less volatility and consequently the stable generation of returns of the portfolio.

The formula for calculating the Standard deviation of a portfolio is

Example:

Mr. A, an investor is willing to invest certain amount in any of the below mentioned portfolios

	The Rate of Return in preceding 3 years	Standard Deviation
Portfolio M	15%	11
Portfolio N	15%	5

Now, in case of Portfolio M, the standard deviation of 11 signifies that the returns of the portfolio can vary between 4% to 26 % i.e., (lowest = 15%-11 = 4%) & (Highest = 15% + 11 = 26%)

Whereas, in case of Portfolio N the standard deviation of 5 signifies that the returns of the portfolio can vary between 10% to 20% i.e., (lowest = 15%-5 = 10%) & (Highest = 15% + 5= 20%)

Therefore, Mr. A can choose any of the portfolio depending upon the risk he is willing to take. i.e., if he is willing to take more risk then he may opt for Portfolio M & if he is risk averse then he can opt for Portfolio N.

Coefficient of Variance

Coefficient of variation or CoV assists in measuring the volatility, or risk, which is assumed in comparison to the amount of return expected from investments. It is calculated by dividing the standard deviation of a portfolio by its expected rate of return.

Coefficient of Variance is calculated by using below mentioned formula

CoV= μ / σ

where:

σ =standard deviation of portfolio

μ= expected return of the portfolio

Example-

Mr. B, an investor is willing to invest in the following portfolio :

	Expected Return	Standard Deviation
Portfolio 1	10%	5
Portfolio 2	15%	7

Thus, the CoV of the portolio will be

Portfolio 1 = 0.50

Portfolio 2 = 0.46

It can be stated that the higher Coefficient of Variation offers higher risk per unit of return. Whereas, the lower coefficient of variation, it offers less risk per unit of return.

Thus, Mr. B can opt for Portfolio B if he is not willing to take more risk on his investment.

jeff jeffy answered 1 year ago

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