Question

6.There are two assets in one portfolio, X and Y. The weight for Asset X is 48%.

Asset X has a 50-50 chance of earning a return of 10% or 20%.

Asset Y's expected return is 23% and the standard deviation is 33%.

Assume the correlation coefficient between X and Y is 0.53.

Calcualte the expected return of the portfolio.

Calculate the standard deviation of the portfolio return.

Answer 1

Expected return of Asset X (R1):

Expected return = 0.5*10%+0.5*20%

= 15%

Expected return of asset Y(R2) = 23%

Weight of asset X (W1)=48%

Weight of asset Y(W2) = 100%-48% = 52%

Expected return of portfolio = W1*R1+W2*R2

=0.48*15%+0.52*23%

= 19.16%

Calculation of standard deviation of Asset X:

Probability (1)	Return (2)	Return-Expected return (3)	Square of Return-Expected return (4)	Variance (5) (1*4)
0.5	10%	0.1-0.15=-0.05	(-0.05)^2=0.0025	0.00125
0.5	20%	0.20-0.15=0.05	(0.05)^2=0.0025	0.00125
			Variance	0.0025

Standard deviation = Square root of Variance

= Square root of 0.0025

= 0.05 or 5%

Standard deviation of X (Std1) = 5%

Standard deviation of Y (Std2) = 33%

Correlation coefficient (corr12) = 0.53

Variance of portfolio = (W1)^2*(Std1)^2+(W2)^2*(Std2)^2+2*W1*W2*Std1*Std2*Corr12

= (0.48)^2*(0.05)^2+(0.52)^2*(0.33)^2+2*0.48*0.52*0.05*0.33*0.53

= 0.000576+0.029446+0.0043655

= 0.0343875

Standard deviation of portfolio = Square root of Variance of portfolio

= Square root of 0.0343875

= 0.1854 or 18.54%