Question

Given the following information for a portfoilio of 60 % in stock and 40% in bonds calculate:

1) The expected return of the portfolio

2) The risk of the portfolio Scenario

Scenario	Prob.	Stock Fund ROR	Bond Fund ROR
Severe Recession	0.10	-25	-10
Mild Recession	0.20	-8	1
Normal Growth	0.45	17	5
Boom	0.25	34	8

Answer 1

1). Expected Return = [Probability(i) * Return(i)]

=1

Stock's Expected Return = [0.10 * -25%] + [0.20 * -8%] + [0.45 * 17%] + [0.25 * 34%]

= -2.50% - 1.60% + 7.65% + 8.50% = 12.05%

Bond's Expected Return = [0.10 * -10%] + [0.20 * 1%] + [0.45 * 5%] + [0.25 * 8%]

= -1.00% + 0.20% + 2.25% + 2.00% = 3.45%

Portfolio's Expected Return = [0.60 * 12.05%] + [0.40 * 3.45%] = 7.23% + 1.38% = 8.61%

2). Portfolio's Standard Deviation = [{Probability(i) * (Expected Return - Return(i))}²]^1/2

=1

= [{0.6 * (8.61% - 12.05%)}² + {0.4 * (8.61% - 3.45%)}²]^1/2

= [7.1002%² + 10.6502%²]^1/2 = [17.7504%²]^1/2 = 4.21%