Question

P13-7 Calculating Returns and Standard Deviations [LO1]

Consider the following information

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B
Recession	0.20	0.04	-0.19
Normal	0.70	0.08	0.14
Boom	0.10	0.13	0.33

  

Required:

(a)	Calculate the expected return for Stock A. (Do not round your intermediate calculations.)
	(Click to select)7.70% 7.85% 9.34% 10.03% 6.76%

  

(b)	Calculate the expected return for Stock B. (Do not round your intermediate calculations.)
	(Click to select)9.30% 9.33%1 0.77% 8.84% 9.67%

  

(c)	Calculate the standard deviation for Stock A. (Do not round your intermediate calculations.)
	(Click to select)2.37% 1.67% 2.49% 2.25% 2.46%

  

(d)	Calculate the standard deviation for Stock B. (Do not round your intermediate calculations.)
	(Click to select)15.23% 10.77% 16.99% 14.46% 15.83%

Answer 1

a) Expected return of Stock A is 7.7%

Probability	Stock A	Expected return
0.2	0.04	0.008
0.7	0.08	0.056
0.1	0.13	0.013
	Expected return	7.70%

b) Expected return of stock B is 9.30%

Probability	Stock B	Expected return
0.2	-0.19	-0.038
0.7	0.14	0.098
0.1	0.33	0.033
	Expected return	9.30%

c) Standard deviation of stock A is 2.37%

Probability	Stock A	Expected return	Deviation from mean	Squared	Squared * probability
0.2	0.04	0.008	-0.037	0.001369	0.000274
0.7	0.08	0.056	0.003	0.000009	0.000006
0.1	0.13	0.013	0.053	0.002809	0.000281
	Expected return	0.077		Variance	0.000561

Standard deviation = square root of variance

= 2.37%

d) The standard deviation of stock B is 15.23%

Probability	Stock B	Expected return	Deviation from mean	Squared	Squared * probability
0.2	-0.19	-0.038	-0.28	0.080089	0.0160178
0.7	0.14	0.098	0.05	0.002209	0.0015463
0.1	0.33	0.033	0.24	0.056169	0.0056169
	Expected return	0.09		Variance	0.023181

Standard deviation = 15.23%