Question

Consider the following information:

  

				Rate of Return If State Occurs
State of	Probability of
Economy	State of Economy			Stock A			Stock B
Recession		.17			.05		−	.21
Normal		.62			.09			.08
Boom		.21			.16			.25

  

Calculate the expected return for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	Expected return
Stock A	%
Stock B	%

  

Calculate the standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	Standard deviation
Stock A	%
Stock B	%

Answer 1

Expected Return = (Prob(R) * Return in R) + (Prob(N) * Return in N) + (Prob(B) * Return in B)

Where prob = probability

R = Recession

N = Normal

B = Boom

Now, Return of A = (0.17 * .05) + (.62 * 0.09) + (0.21 * 0.16)

= 0.0979 OR 9.79%

Now, Return of B = (0.17 * .21) + (.62 * 0.08) + (0.21 * 0.25)

= 0.1378 OR 13.78%

Answer Part B

Standard Deviation of A

State of Economy	Given Return (X)	Expected Return (X1)	(X-X1)2	Probability	(X-X1)*Probability
Recession	5%	9.79%	22.94	.17	3.90
Normal	9%	9.79%	0.6241	.62	0.39
Boom	16%	9.79%	38.56	.21	8.10
				TOTAL	12.39

Standard Deviation = { ∑((X-X1)*Probability)^1/2  }

= (12.39)^1/2

= 3.52

Standard Deviation of B

State of Economy	Given Return (X)	Expected Return (X1)	(X-X1)2	Probability	(X-X1)*Probability
Recession	21%	13.78%	52.13	.17	8.86
Normal	8%	13.78%	33.41	.62	20.71
Boom	25%	13.78%	125.89	.21	26.44
				TOTAL	56.01

Standard Deviation ={ ∑((X-X1)*Probability)^1/2  }

= (56.01)^1/2

= 7.48

Standard Deviation of A = 3.52

Standard Deviation of B = 7.48

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