Question

State         Probability                 R_A                   R_M      

1                 10%                         16%                 10%

   2                 40%                         7%                   18%

   3                 40%                         12%                 -5%

   4                 10%                         -8%                 9%  

1. Calculate the expected returns on security A and the market.

2. Calculate the variances and the standard deviations of security A and the market.

3. Calculate the coefficient of variations (CV) for security A and the market. Does A initially seem to be more or less attractive than a market portfolio? Why? What other consideration might affect your answer and how?

Answer 1

Expected returns
A=10%*16%+40%*7%+40%*12%+10%*(-8%)=8.400%

M=10%*10%+40%*18%+40%*(-5%)+10%*9%=7.100%

Variance
A=(10%*(16%-8.400%)^2+40%*(7%-8.400%)^2+40%*(12%-8.400%)^2+10%*(-8%-8.400%)^2)=0.003864

M=(10%*(10%-7.100%)^2+40%*(18%-7.100%)^2+40%*(-5%-7.100%)^2+10%*(9%-7.100%)^2)=0.010729

Standard deviation

A=sqrt(0.003864)=6.216%

M=sqrt(0.010729)=10.358%

Coefficient of variation CV
A=6.216%/8.400%=0.74

M=10.358%/7.100%=1.458873239

A seems to be more attractive as it has lower CV

Other consideration will be the systematic risk of A and expected returns viz a viz required returns of A