According to the attached info
According to the attached information, based on total risk andreturn, which of the investments should a risk-averse investorprefer? 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 alltoo risky.
- B. The investments are equally desirable because they have thesame risk/return relationship.
- C. Investment B
- D. Investment C
- E. Investment A
Answer:
Ans:- In this question, we will find the coefficient ofvariation (CV) of each security and will choose the one which hasthe lowest CV.
Note:- Coefficient of variation (CV) measures the risk per unitof return, Low value in the coefficient of variation means thesecurity is less risky and vice-versa, or in other words, it tellsthe 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 Respectiveweights * Respective return.
Wa*Ra+Wb*Rb……………Wn*Rn, where W is the weights from ato 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 hasthe lowest risk per unit of return, Therefore as a risk-averseinvestor I would invest in C. option D is the rightanswer.
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