Question

Given the following information, please estimate the expected return and risk for the portfolio

Security	Security 1	Security 2	Security 3
E(R)	0.015	0.02	0.05
Weight	33%	33%	34%
	Security 1	Security 2	Security 3
Security 1	Var=0.05	Corr=0.5	Corr=0.3
Security 2		Var=0.06	Corr=0.6
Security 3			Var=0.07

Answer 1

Weight of security 1 = W(1) = 33%, Weight of security 2 = W(2) = 33% and Weight of security 3 = W(3) = 34%

Expected Return Security 1 =E(1) =0.015, Expected Return Security 2 =E(2) =0.02, Expected Return Security 3 =E(3) =0.05

Expected return on Portfolio = W(1) x E(1) + W(2) x E(2) + W(3) x E(3)

= 33% x 0.015 + 33% x 0.02 + 34% x 0.05 = 0.00495 + 0.00660 + 0.017000 = 0.0285500 = 2.855%

Variance of security 1 = V(1) = 0.05

S(1) = 0.223606

Variance of security 2 = V(2) = 0.06

S(2) = 0.244948

Variance of security 3 = V(3) = 0.07

S(3) = 0.264575

Correlation between security 1 and security 2 = Corr(1,2) = 0.5

Correlation between security 2 and security 3 = Corr(2,3) = 0.6

Correlation between security 1 and security 3 = Corr(1,3) = 0.3

Variance of Portfolio = V(P) = W(1)² x V(1) + W(2)² x V(2) + W(3)² x V(3) + 2 x W(1) x W(2) x S(1) x S(2) x Corr(1,2) + 2 x W(2) x W(3) x S(2) x S(3) x Corr(2,3) + 2 x W(1) x W(3) x S(1) x S(3) x Corr(1,3)

= (33%)² x 0.05 + (33%)² x 0.06 + (34%)² x 0.07 + 2 x 33% x 33% x 0.223606 x 0.244948 x 0.5 + 2 x 33% x 34% x 0.244948 x 0.264575 x 0.6 + 2 x 33% x 34% x 0.223606 x 0.264575 x 0.3

= 0.0054450 + 0.0065340 + 0.0080920 + 0.0059646 + 0.0087256 + 0.0039826 = 0.0387438

Risk of Portfolio = Standard deviation of portfolio = S(P)

S(P) = 0.1968344 = 19.68344% = 19.68%