Question

Consider the following information on returns and probabilities:

Invest 1/2 of your money in Asset A and 1/2 in Asset B.

State      Probability           A             B                           

Boom         .25                   12%       4%         

Bust            .75                   6%         18%      

what is the standard deviation of the return on the portfolio?

		a. 1.7
		b. 2.9
		c. 3.9
		d. 4.6
		e. 5.5
		f. 6.9
		g. 7.5
		h. 9.0
		i. 8.2
		j. 11

Answer 1

E(B)Boom = Wp x E(P1) + Wq E(Q1)

                    =(0.50 x 0.12) + (0.50 x 0.04)

                   =0.06 +0.02= 0.0800

E(b)bust = Wp x E(P2) + Wq E(Q2)

                 =(0.50 x 0.06) + (0.50 x 0.18)

                 =0.03+0.09

                = 0.1200

E(r)Portfolio = p1 x E (B) + p2 x E (b)

                        =(0.25 x 0.0800) + (0.75 x 0.1200)

                       = 0.0200+0.0900

                       =0.1100

VarPortfolio = p1 [(E(B) -E(r))2]+ p2 [(E(b) -E(r))2]

                        =[0.25 (0.0800 - 0.1100)2] + [0.75 (0.1200 - 0.1100)2]

                       =[0.25 (-0.0300)2] + [0.75 (0.0100 )2]

                        =[0.25 x 0.000900 + [0.75 x 0.000100

                     = 0.000225 + 0.000075

                      = 0.000300

Std dev =√ variance =√ 0.000300= 1.7 percent

Hence Option “a” i.e 1.7 correct