Question

Consider the following information: Rate of Return if State Occurs State of Probability of State of Economy Stock A Stock B Stock C Economy Воom 0.10 0.18 0.48 0.33 0.15 Good 0.30 0.11 0.18 0.40 Роor 0.05 -0.09 -0.05 -0.32 0.20 -0.03 -0.09 Bust a. Your portfolio is invested 25 percent each in A and C and 50 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Answer is complete but not entirely correct. Expected return 9.96 % b-1. What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places.) Answer is complete but not entirely correct Variance 0.02366 b-2. What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Answer is complete but not entirely correct. Standard 15.38 % deviation

Answer 1

State of	Probability of
Economy	State of Economy		Stock A		Stock B			stock C
Boom		0.1		0.18		0.48		0.33
good		0.3		0.11		0.18		0.15
poor		0.4		0.05		-0.09		-0.05
bust		0.2		-0.03		-0.32		-0.09
		weight		0.25		0.5		0.25
		return		0.065		0.002		0.04
		weight * return		0.01625		0.001		0.01
		Expected return of portfolio E(X)	2.73%
		weight * return^2		0.00105625		0.000002		0.0004
		E(X^2)	0.00145825
		variance of portfolio	0.00072
		standard deviation of portfolio	2.68%

Expected return = sum of (probability of state * return of state)

E(X^2) =  sum of (probability of state * return of state^2)

variance = E(X^2) - (E(X))^2

Standard deviation = sqrt(variance)