Question

According to the attached information, based on total risk and return, which of the investments should a risk-averse investor prefer? Assume that only one investment can be purchased.

Return on Investment:

Economic Condition Probability A B C

Boon 0.5 25.0% 40.0% 5.0%

Normal 0.4 15.0 20.0 10.0

Recession 0.1 -5.0 -40.0 15.0

Expected Return 18.0% 24.0% ?

Standard Deviation 9.0% 23.3% 3.3%

• A. The investments should all be rejected because they are all too risky.
• B. The investments are equally desirable because they have the same risk/return relationship.
• C. Investment B
• D. Investment C
• E. Investment A

Answer 1

Ans:- In this question, we will find the coefficient of variation (CV) of each security and will choose the one which has the lowest CV.

Note:- Coefficient of variation (CV) measures the risk per unit of return, Low value in the coefficient of variation means the security is less risky and vice-versa, or in other words, it tells the riskiness of the asset as compared to its return.

It is calculated by CV= Standard deviation / Mean.

The expected return of C will be calculated by Respective weights * Respective return.

Wa*Ra+Wb*Rb...............Wn*Rn, where W is the weights from a to n and Rn is the return from a to n.

= 0.5*5%+0.4*10%+0.1*15% = 8%

Now, CV of A = 9%/18% = 0.5

CV of B = 23.3% / 24% = 0.97.

CV of C = 3.3% / 8% = 0.41.

From the above analysis, it is clear that security C has the lowest risk per unit of return, Therefore as a risk-averse investor I would invest in C. option D is the right answer.