Question

Given the following information, calculate the expected return and standard deviation for a portfolio that has 35 percent invested in Stock A, 45 percent in Stock B, and the balance in Stock C. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Returns State of Probability of Economy State of Economy Boom 0.40 Bust 0.60 Stock A 15% 10 Stock B 18% Stock C 20% -10 Expected return Standard deviation

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

State of Economy Boom Bust Probability 40.00% 60.00% Stock A 15.00% 10.00% 12.00% 2.45% Stock B 18.00% 0.00% 7.20% 8.82% Stock C 20.00% -10.00% 2.00% 14.70% Expected return Standard deviation Portfolio's Stock Stock A Stock B Stock C Weight 35% 45% 20% Covariance(A,B) Covariance (A,C) Covariance (B,C) 0.002160 0.003600 0.012960 Variance of Portfolio 0.00603 Expeted Return of Portfolio Standard deviation of Portfolio 7.84% 7.76%

Cell reference -

B State of Economy Probability Stock B 0.18 Boom Bust 0.4 0.6 Stock A 0.15 0.1 =SUMPRODUCT($C$3:$C$4,D3:04) =SQRT(SUMPRODUCT (D5-D3:04)^2, $C$3:$C$4)) Stock C 0.2 -0.1 =SUMPRODUCT($C$3:$C$4,F3:F4) =SQRT(SUMPRODUCT(F5-F3:F4)^2,$C$3:$C$4)) Expected return Standard deviation =SUMPRODUCT($C$3:$C$4,E3:14) =SQRT(SUMPRODUCT(E5-E3:E4)^2,$C$3:$C$4)) moram Weight Portfolio's Stock Stock A Stock B Stock C 0.35 0.45 =1-C9-C10 15 Covariance(A,B) Covariance (A,C) Covariance (B,C) =SUMPRODUCT((D5-D3:04),(E5-E3:E4),C3:04) SUMPRODUCT((D5-D3:04),(F5-F3:F4),C3:04) =SUMPRODUCT(E5-E3:E4),(F5-F3:F4),C3:04) Variance of Portfolio =(C9*D6)^2+(C10*E6)^2+(C11*F6)^2+2*09*c10*C14+2*C9*C11*c15+2*C10*c11*c16 Expeted Return of Portfolio =C9*D5+C10*E5+C11*F5 Standard deviation of Portfolio =SQRT(C18)

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.