Consider the following information: Your portfolio is invested 32 percent each i

Question

Consider the following information:   

Your portfolio is invested 32 percent each in A and C, and 36 percent in B. What is the expected return of the portfolio? (Round your answer to 2 decimal places. (e.g., 32.16))

What is the standard deviation? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Rate of Return if State Occurs   State of Probability of   Economy State of Economy Stock A Stock B Stock C   Boom 0.10 0.30 0.40 0.20   Good
0.50

0.15

0.11

0.09
  Poor
0.35
%u2212 0.02
%u2212 0.05
%u2212 0.03
  Bust
0.05
%u2212 0.10
%u2212 0.15
%u2212 0.07

Explanation / Answer

a.)E(RA)=(0.1*0.3) + (0.5*0.15)+(0.35*(-0.02))+(0.05*(-0.1))=0.093

E(RB)=(0.1*0.4)+(0.5*0.11)+(0.35*(-0.05))+(0.05*(-0.15))=0.07

E(RC)=(0.1*0.2)+(0.5*0.09)+(0.35*(-0.03))+(0.05*(-0.07))=0.051

So E(R)=0.32*E(RA) + 0.36*E(RB) + 0.32*E(RC)=0.07128

So Expected return=0.07(2 decimals)

b.)P(Boom)=0.32*0.3 + 0.36*0.4 +0.32*0.2=0.304

P(Good)=0.32*0.15 + 0.36*0.11 + 0.32*0.09=0.1164

P(Poor)=0.32*-0.02 + 0.36*-0.05 +0.32*-0.03= - 0.034

P(Bust)=0.32*-0.1 + 0.36*-0.15 +0.32*-0.07= - 0.1084

Var=0.1*(0.304 - 0.07128)^2 + 0.5*(0.1164 -0.07128)^2 +0.35*(-0.034-0.07128)^2 +0.05*(-0.1084-0.07128)^2

=0.011927(rounded to 5 decimals)

c.)sd=sqrt(Var)=0.1092=0.11(2 decimals)

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