Question

6

. How much total capital would you allocate to a risk free rate of 4% if your risk aversion

coefficient is A=4 and you can also invest in any portfolio consisting of the two following

perfectly negatively correlated assets:

Asset A: expected return 1% Standard Deviation: 17%

Asset B: Expected 10% Standard deviation: 30%

Answer 1

First we will select portfolio out of A and B on the basis of Return to Risk ratio      
Return to Risk ratio =Expected Return/Standard deviation      
Asset A ratio = 1%/17%=   0.05882352941  
Asset B ratio = 10%/30%=   0.3333333333  
Return to Risk ratio of B is more. so Investment will be made in Asset B risky portfolio      

Asset B Expected Return = 10%

Standard deviation of B = 30%

Risk free rate = 4%

risk aversion coefficient =A = 4
      
Formula for investment in risky portfolio      
Weight of Risky portfolio = ( Expected return of Risky portfolio - Risk free rate)/(risk aversion coefficiennt * Std. dev. of Risky portfolio ^2)      
(Er (P) - Rf)/ (A*Sd^2)      
(10%-4%)/(4*(30%)^2)      
{0.1666666667      
Weight of Risky is 0.1667  
So weight of Risk free = 1-0.1667=   0.8333  

0.8333 of Total capital would be invested in risk fre Asset.