Question

The expected returns for Stocks A, B, C, D, and E are 7%, 10%, 12%, 25%, and 18% respectively. The corresponding standard deviations for these stocks are 12%, 18%, 15%, 23%, and 15% respectively. Based on their coefficients of variation, which of the securities is least risky for an investor? Assume all investors are risk-averse and the investments will be held in isolation.

a. ​E

b. ​B

c. ​D

d. ​C

e. ​A

Answer 1

Expected return of stock A = RA = 7%, Standard deviation of stock A = σA = 12%

Expected return of stock B = RB = 10%, Standard deviation of stock B = σB = 18%

Expected return of stock C = RC = 12%, Standard deviation of stock C = σC = 15%

Expected return of stock D = RD = 25%, Standard deviation of stock D = σD​​​​​​​ = 23%

Expected return of stock E = RE = 18%, Standard deviation of stock E = σE​​​​​​​ = 15%

Coefficient of Variation = CV = Standard deviation/Expected return

Coefficient of Variation of A = CVA​​​​​​​ = σA/RA = 12%/7% = 1.71428571428571

Coefficient of Variation of B = CVB​​​​​​​ = σB/RB = 18%/10% = 1.8

Coefficient of Variation of C = CVC​​​​​​​ = σC/RC = 15%/12% = 1.25

Coefficient of Variation of D = CVD​​​​​​​ = σD/RD = 23%/25% = 0.92

Coefficient of Variation of E = CVE​​​​​​​ = σE/RE = 15%/18% = 0.833333333333333

Based on the coefficient of variation, a risk-averse investor would prefer best risk-reward ratio i.e., stock with lowest CV

Based on the coefficient of Variation, stock E is least risky

Answer -> E (Option a)