Question

Consider the following information:

  

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B
Recession	.10	.03	–.20
Normal	.70	.08	.14
Boom	.20	.13	.32

Calculate the standard deviation for stock a and b.

Answer 1

			Stock A	Stock B
Standard deviation			2.69%	13.43%
Working:
# 1	Calculation of expected return of both stock:
			Stock A			Stock B
	State of Economy	Probability of State of Economy	Rate of return			Rate of return
		a	b	c=a*b		d	e=a*d
	Recession	0.10	0.03	0.0030		-0.2	-0.0200
	Normal	0.70	0.08	0.0560		0.14	0.0980
	Boom	0.20	0.13	0.0260		0.32	0.0640
	Expected return			0.0850			0.1420
# 2	Calculation of variance of both stock:
			Stock A			Stock B
	State of Economy	Probability of State of Economy	Rate of return	Expected return		Rate of return	Expected return
		a	b	c	d=((b-c)^2)*a	e	f	g=((e-f)^2)*a
	Recession	0.10	0.03	0.0850	0.000303	-0.2	0.1420	0.011696
	Normal	0.70	0.08	0.0850	0.000017	0.14	0.1420	0.000003
	Boom	0.20	0.13	0.0850	0.000405	0.32	0.1420	0.006337
	Variance				0.000725			0.018036
# 3	Calculation of stnadard deviation :
	Standard deviation		=	Variance ^ (1/2)
	So, Standard deviation of:
	Stock A		=	0.000725	^ (1/2)	=	0.026926
	Stock B		=	0.018036	^ (1/2)	=	0.134298