Question

Consider the following information: Rate of Return If State Occurs State of Probability of State of Economy Stock A Stock B Economy 15 Stock C Boom 39 49 29 Good .55 15 20 -09 .08 Poor Bust .25 .05 -01 -.07 20 -.24 -10 Your portfolio is invested 24 percent each in A and C, and 52 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b-1. What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.) b-2. What is the standard deviation? (Do not round intermediate calculations and enter а. your answer as a percent rounded to 2 decimal places, e.g., 32.16.) s Expected return а. % b-1. Variance b-2. Standard deviation %

Answer 1

State of	Probability of
Economy	State of Economy		Stock A		Stock B			stock C
Boom		0.15		0.39		0.49		0.29
good		0.55		0.15		0.2		0.08
poor		0.25		-0.01		-0.09		-0.07
bust		0.05		-0.2		-0.24		-0.1
		weight		0.24		0.52		0.24
		return		0.1285		0.149		0.065
		weight * return		0.03084		0.07748		0.0156
		Expected return of portfolio E(X)	12.39%
		weight * return^2		0.00396294		0.01154452		0.001014
		E(X^2)	0.01652146
		variance of portfolio	0.00117
		standard deviation of portfolio	3.41%

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)