Question

Consider the following information: Rate of Return if State Occurs Probability of State of Economy Stock A Stock B State of Economy Recession Normal Boom .02 .15 .50 -30 .18 .35 .10 .15 .31 a. Calculate the expected return for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. Calculate the standard deviation for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Stock A expected return Stock B expected return Stock A standard deviation Stock B standard deviation b.

Answer 1

a.	Stock A expected return			10.55%
	Stock B expected return			15.35%
Working:
	Stock A:					Stock B:
	State of economy	Probability	Rate of return			State of economy	Probability	Rate of return
		a	b	c=a*b			a	b	c=a*b
	Recession	0.15	0.02	0.30%		Recession	0.15	-0.30	-4.50%
	Normal	0.50	0.10	5.00%		Normal	0.50	0.18	9.00%
	Boom	0.35	0.15	5.25%		Boom	0.35	0.31	10.85%
	Total			10.55%		Total			15.35%
b.	Stock A standard deviation			4.25%
	Stock B standard deviation			19.94%
Working:
	Calculation of Variance:
	Stock A:					Stock B:
	State of economy	Probability	Rate of return	Expected return		State of economy	Probability	Rate of return	Expected return
		a	b	c	d=((b-c)^2)*a		a	b	c	d=((b-c)^2)*a
	Recession	0.15	0.02	10.55%	0.001097	Recession	0.15	-0.30	15.35%	0.030849
	Normal	0.50	0.10	10.55%	0.000015	Normal	0.50	0.18	15.35%	0.000351
	Boom	0.35	0.15	10.55%	0.000693	Boom	0.35	0.31	15.35%	0.008572
	Variance				0.001805	Variance				0.039773
	Calculation of standard deviation:
	Stock A:					Stock B:
	Standard deviation	=	Variance ^ (1/2)			Standard deviation	=	Variance ^ (1/2)
		=	0.001805	^(1/2)			=	0.039773	^ (1/2)
		=	4.25%				=	19.94%