Question

The following table provides stock return distributions in the coming year for three companies, A, B, and C.

State of Economy	Probability of State of Economy	Stock A Rate of Return	Stock B Rate of Return	Stock C Rate of Return
Normal	0.65	14.3%	16.7%	18.2%
Recession	0.35	-9.8%	5.4%	-26.9%

(a) Consider a portfolio that is invested 40% in Stock A, 30% in Stock B, and the remainder in Stock C. What is the expected return on the portfolio?

(b) What is the standard deviation on the portfolio returns above?

please show your workings.

Answer 1

Answer

(a)

Expected Return = SUM (Return x Probability)

Return stock A =(0.65*0.143)+(0.35* - 0.098)

=0.058

=5.8%

Return stock B= (0.65*0.167)+(0.35*0.054)

=0.127

=12.7%

Return stock C= (0.65*0.182)+(0.35*0.269)

=0.212

=21.2%

(b) standard deviation   

√ probability *(Return - Expected return) ^2

standard deviation of stock A = √ 0.65(0.143-0.058)^2+0.35(0.098-0.058)^2

=0.069

=6.9%

Standard deviation of stock B=  √0.65(0.167-0.127)^2+0.35(0.054-0.127)^2

=0.053

=5.3%

Standard deviation of stock c=√0.65(0.182-0.122)^2+0.35(0.269-0.212)^2

=0.041

4.1%