Question

Question 1. Portfolio Analysis (2 points) a) Assume the following about assets A and B: E[7]0.1, -0.09, E[TB] =0.08, o -0.04. Which one has lower absolute risk and which one has lower relative risk? (1): b) Find the mean return, E[r.), and variance, oz. of a portfolio consisting of 70% of your total wealth invested in asset A (w4=0.70), and 30% of your total wealth invested in asset B (Wg= 0.30). The correlation between assets A and B (P3) = 0.25 (1): (2): 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

a. The lower absolute risk is for asset B as it has lower variance

Relative risk = variance /return

for asset A = 0.09/0.1 = 0.9

for asset B = 0.04/0.08 = 0.5

Lower relative risk is for asset B

b.  

	Expected return	Investment Proportion	Standard Deviation	Correlation
A	0.10	70%	0.30
B	0.08	30%	0.20	0.25
Total		100%
Expected return of portfolio (Erp)	9.40%
Variance of portfolio (σp^2)	5.40%

1 Correlation Expected return 0.1 10.08 Investment Proportion 0.7 0.3 =SUM(C2:03) Standard Deviation =SQRT(9%) =SQRT(4%) 2 A 3 B 4 Total 5 Expected return of portfolio (Erp) 6 Variance of portfolio (op^2) 0.25 =B2*(C2/C4)+B3*(C3/04) =D2^2*(C2/C4)^2+D3^2*(C3/C4)^2+2*D2*(C2/C4)*D3*(03/04) *E3)

c.

	Expected return	Investment Proportion	Standard Deviation	Correlation
A	0.10	70%	0.30
B	0.08	30%	0.20	-0.50
Total		100%
Expected return of portfolio (Erp)	9.40%
Variance of portfolio (σp^2)	3.51%

E Expected return Investment Proportion Correlation 0.1 0.7 Standard Deviation =SQRT(9%) =SQRT(4%) 0.08 2 A з в 4 Total 5 Expected return of portfolio (Erp) 6 Variance of portfolio (op^2) 0.3 =SUM(C2:C3) =B2*(C2/C4)+B3*(C3/04) =(D2^2*(C2/C4)^2+D3^2*(C3/C4)^2+2*D2*(C2/C4) *D3*(C3/C4)*E3)

The riskiness of portfolio changes because of negative correlation. The riskiness is now reduced.