Question

State         Probability                 r_A                    r_M       

   1                 20%                         15%                 12%

   2                 30%                         8%                   6%

   3                 30%                         4%                   1%

   4                 20%                         -6%                 -2%  

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 variation (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=20%*15%+30%*8%+30%*4%+20%*(-6%)=5.400%

M=20%*12%+30%*6%+30%*1%+20%*(-2%)=4.100%

Variance
A=(20%*(15%-5.400%)^2+30%*(8%-5.400%)^2+30%*(4%-5.400%)^2+20%*(-6%-5.400%)^2)=0.004704

M=(20%*(12%-4.100%)^2+30%*(6%-4.100%)^2+30%*(1%-4.100%)^2+20%*(-2%-4.100%)^2)=0.002389

Standard deviation

A=sqrt(0.004704)=6.859%

M=sqrt(0.002389)=4.888%

Coefficient of variation CV
A=6.859%/5.400%=1.2702
M=4.888%/4.100%=1.1922

A seems to be less attractive as it has higher CV

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