Question

Given the following information about the returns of stocks A, B, and C, what is the expected return of a portfolio invested 30% in stock A, 40% in stock B, and 30% in stock C?

State of economy	Probability	Stock A	Stock B	Stock C
Boom	0.14	0.33	0.36	0.26
Good	0.29	0.29	0.15	0.27
Poor	0.21	0	0.01	0.02
Bust	--	-0.19	-0.21	-0.11

Enter answer in percents.

Answer 1

Expected return= Summation of (percentage invested in the stock)*(Stock return)
Given that, the percentage of investment in stock A=30%, stock B=40% and stock C=30%

In boom state of economy, the returns on stock A=.33, stock B=.36 and stock C=.26

Expected return (boom state)=30%*0.33+40%*0.36+30%*0.26
=0.099+0.144+0.078
=0.321
Similarly we can calculate the expected return in good, poor and bust states of economy.

Expected return (good state)=30%*0.29+40%*0.15+30%*0.27
=30%*0.29+40%*0.15+30%*0.27
=0.087+0.06+0.081
=0.228

Expected return (poor state)=30%*0+40%*0.01+30%*0.02
=0+0.004+0.006
=0.01

Expected return (bust state)=30%*(-0.19)+40%*(-0.21)+30%*(-0.11)
=-0.057-0.084-0.033
=-0.174

Now, we need to multiply the above returns with the probability of getting these returns in different states of economy.
Given that, the probability of boom state of economy is 0.14, good state is 0.29, poor state is 0.21.
Now, total probability should be equal to 1.
So, probability of bust economy=1-probability of other three states of economy=1-0.14-0.29-0.21=0.36

Expected return of the portfolio=0.14*0.321+0.29*0.228+0.21*0.01+0.36*(-0.174)
=0.04494+0.06612+0.0021-0.06264
=0.05052 or 5.05% (Rounded to two decimal places)