Question

Expected Returns: Discrete Distribution

The market and Stock J have the following probability distributions:

Probability	rM	rJ
0.3	12%	21%
0.4	10	4
0.3	17	12

a.Calculate the expected rate of return for the market. Round your answer to two decimal places.
%

b. Calculate the expected rate of return for Stock J. Round your answer to two decimal places.
%

c. Calculate the standard deviation for the market. Round your answer to two decimal places.
%

d. Calculate the standard deviation for Stock J. Round your answer to two decimal places.
%

Answer 1

a. The correct answer is 12.70%

Note :

	Probability	Rm	Expected Return ( Probability * Expected Return)
Recession	0.30	0.12	0.03600
Normal	0.40	0.10	0.04
Boom	0.30	0.17	0.05
	Expected Return		0.127000
	Expected Return   %		12.70

b. The correct answer is 11.50%

Note:

	Probability	Rj	Expected Return   ( Probability * Expected Return
Recession	0.30	0.21	0.0630
Normal	0.40	0.04	0.0160
Boom	0.30	0.12	0.0360
		Expected Return	0.1150
		Expected Return  %	11.50

c. The correct answer is 2.93%

Note:

Stock	Probability	Probable Return Rm	Deviation ( Probable Return- Expected Return)	Deviation Squared	Product ( Deviation Squared* Probability)
Recession	0.30	12	-0.7	0.49	0.147
Normal	0.40	10	-2.7	7.29	2.916
Boom	0.30	17	4.3	18.49	5.547
			Variance		8.61
			Standard Deviation (Square root of Variance)		2.93

d. The correct answer is 7.05%

Note :

Stock B	Probability	Probable Return	Deviation ( Probable Return- Expected Return)	Deviation Squared	Product ( Deviation Squared* Probability)
Recession	0.30	21.00	9.5	90.25	27.075
Normal	0.40	4.00	-7.5	56.25	22.5
Boom	0.30	12.00	0.5	0.25	0.075
			Variance		49.65
			Standard Deviation		7.05