Question

Asset A has an expected return of 15% and Asset B has an expected return of 12%. Based on a probability distribution, the standard deviation for Asset A is 10% and the standard deviation for Asset B is 5%.

a.) Based only on the standard deviation, which investment is less risky? Discuss your reasons for your selection including why you feel that asset is less risky.

b.) Calculate the coefficient of variation for each asset and post your answers. Based on the coefficient of variation, which asset is the best asset to invest in? Verify your selection by including a discussion of risk and return for the asset you selected.

Answer 1

Asset	Expected Return	Standard Deviation
A	15%	10%
B	12%	5%

Solution a) Standard deviation is a measure of how each possible outcome deviates from expected value. This deviation is nothing but the risk an investor would have to bear.
Hence, based only on standard deviation, Investment B is less risky as its standard deviation is only 5% as compared to 10% for Investment A.

Solution b) The standard deviation provides useful measure of dispersion. However, we cannot compare standard deviations of different projects having different expected values. This is possible with coefficient of variation, which translates the standard deviation of different probability distributions, so that they can be compared. The coefficient of variation for a probability distribution is the ratio of its standard deviation to its expected value.

Coefficient of variation = Standard Deviation / Expected Return

For Investment A = 10% / 15% = 0.6667

For Investment B = 5% / 12% = 0.4167

Hence, considering coefficient of variation of both the investments, Investment B is to be preferred as it has a lower coefficient of variation as compared to Investment A.