Question

Answer the following question based on the information below:

State of Economy	Probability	Stock A’s return	Stock B’s return
Boom	.4	15%	- 30%
Recession	.6	5%	40%

If you invest $50,000 in each of stocks A and B, what is the expected return for your portfolio?

Group of answer choices

16.0%

15.0%

15.5%

17.5%

16.5%

Answer 1

Given,

Probability of boom (P_b) = 0.4

Probability of recession (P_r) = 0.6

Investment in each stock = $50000

Solution :-

Stock A's expected return = (15%) x (P_b) + (5%) x (P_r)

= (15%) x (0.4) + (5%) x (0.6)

= 6% + 3% = 9%

Stock B's expected return = (-30%) x (P_b) + (40%) x (P_r)

= (-30%) x (0.4) + (40%) x (0.6)

= -12% + 24% = 12%

Since investment in each stock is same, weight of each stock would be 0.5

Expected return of portfolio = (Stock A's expected return) x (0.5) + (Stock B's expected return) x (0.5)

= (9%) x (0.5) + (12%) x (0.5)

= 4.5% + 6% = 10.5%

Thus, expected return of your portfolio is 10.5%