Question

Question 1. Portfolio Analysis (2 points) a) Assume the following about assets A and B: E[r]=0.1, o =0.09. E[ra] -0.08, o; -0.04. Which one has lower absolute risk and which one has lower relative risk? (1): (2) b) Find the mean return, E[r], and variance, o. of a portfolio consisting of 70% of your total wealth invested in asset A (Wx=0.70), and 30% of your total wealth invested in asset B (w3= 0.30). The correlation between assets A and B (P.) = 0.25 c) Now assume that the correlation is -0.5. Use the information above to calculate the variance of this new portfolio. Explain how the riskiness of the portfolio changes.

Answer 1

1.
Absolute risk is measured by variance. Lower variance means lower absolute risk. Asset B has lower absolute risk.

2.
Coefficient of Variation=sqrt(variance)/expected return
A=sqrt(0.09)/0.1=3
B=sqrt(0.04)/0.08=2.5
Relative risk is measured by coefficient of variation.
Asset B has lower relative risk

3.
Expected return=70%*10%+30%*8%=9.4000%
Variance=(70%)^2*0.09+(30%)^2*0.04+2*70%*sqrt(0.09)*30%*sqrt(0.04)*0.25=0.05400

4.
Variance=(70%)^2*0.09+(30%)^2*0.04+2*70%*sqrt(0.09)*30%*sqrt(0.04)*(-0.5)=0.03510

Riskiness of the portfolio is directly related with correlation. Hence, riskiness decreases.