Question

Consider the following information:

				Rate of Return If State Occurs
State of	Probability of
Economy	State of Economy			Stock A	Stock B	Stock C
Boom		0.16		0.363	0.463	0.343
Good		0.44		0.133	0.113	0.183
Poor		0.34		0.023	0.033	−0.075
Bust		0.06		−0.123	−0.263	−0.103

Requirement 1:

Your portfolio is invested 29 percent each in A and C and 42 percent in B. What is the expected return of the portfolio? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Expected return of the portfolio

%

Requirement 2:

(a)	What is the variance of this portfolio? (Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).)

Variance of the portfolio

(b)	What is the standard deviation of this portfolio? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Standard deviation

%

Answer 1

State of	Probability of
Economy	State of Economy		Stock A		Stock B			stock C
Boom		0.16		0.363		0.463		0.343
good		0.44		0.133		0.113		0.183
poor		0.34		0.023		0.033		-0.075
bust		0.06		-0.123		-0.263		-0.103
		weight		0.29		0.42		0.29
		return		0.11704		0.11924		0.10372
		weight * return		0.0339416		0.0500808		0.0300788
		E(X)	11.41%
		weight * return^2		0.003972524864		0.005971634592		0.003119773136
		E(X^2)	0.01306393259
		variance	0.00004
		standard deviation	0.67%

Hence

Expected return = 11.41%

variance = 0.00004

standard deviation = 0.67%