Standard Deviation problem of Stock portfolio, please help me with answer?

Question

You are given the following information about two risky assets.

Economic State/ Probability Stock A Stock B

Recession/ 0.28 8.0% 24.0%

Average/ 0.38 14.0% 16.0%

Boom/ 0.34 12.0% 4.0%

(a) Calculate the expected return and the standard deviation of Stock A and B.

(b) You composed a portfolio with 63% in Stock A and the remaining in Stock B. Calculate the portfolio expected return and the standard deviation.

Answer 1

(a).

Expected return of stock A

=uA

= ∑ rA*p(rA)

= 0.28*8.0%+ 0.38*14%+0.34*12%

= 0.28*0.08+0.38*0.14+0.34*0.12

= 0.1164 or = (0.1164*100%)=1.64%

Standard deviation of stock A

= sA

= ∑ [(rA-uA)^2]*p(rA)

= √{[(0.08-0.1164)^2]*0.28

+[(0.14-0.1164)^2]*0.38

+[(0.12-0.1164)^2]*0.34}

= 0.0242

Similarily, for stock B,

Expected return of stock B

= uB

= ∑ rB*p(rB)

= 0.28*24.0%+ 0.38*16%+0.34*4%

= 0.28*0.24+0.38*0.16+0.34*0.04

= 0.1416 or =(0.1416*100%) = 14.16%

Standard deviation of stock B

= sB

= ∑ [(rB-uB)^2]*p(rB)

= √{[(0.24-0.1416)^2]*0.28

+[(0.16-0.1416)^2]*0.38

+[(0.04-0.1416)^2]*0.34}

= 0.07968

(b). The remaining proportion of a portfolio in stock B

= (1-proportion of a portfolio in stock A)

= 1 - 63%

= 1- (63/100)

= 1- 0.63

= 0.37

Portfolio expected return

= uAB

= ∑ uA*p(uA) + uB *p(uB)

= 0.63*0.1164 + 0.37*0.1416

= 0.125724 = (0.125724*100%) = 12.5724

Portfolio standard deviation

= sAB

= ∑ sA*p(sA) + sB*p(sB)

= √{[(0.1164-0.125724)^2]*0.63

+[(0.1416-0.125724)^2]*0.37}

= 0.01216