Question

Consider the following information: Probability of Rate of Return if State Occurs State of Economy Economy Recession Stock A Stock B -35 25 20 010 Normal 55 090 Boom 25 240 48 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.)

Answer 1

1. Computation of expected return of the two stocks

Stock A: 11.15%

Stock B: 18.75%

Expected return of stock (X̅) = Probability * return

Expected return of stock A = 11.15%

Economy	Probability of state of economy (P)	Rate of return	Expected Return (X)
(I)	(II)	(III)	IV = (II *III)
Recession	.20	.010	.002
Normal	.55	.090	.0495
Boom	.25	.240	.06
Expected return of stock (X̅)			.1115 (11.15%)

Expected return of stock B = 18.75%

Economy	Probability of state of economy (P)	Rate of return	Expected Return (X)
(I)	(II)	(III)	IV = (II *III)
Recession	.20	-.35	-.070
Normal	.55	.25	.1375
Boom	.25	.48	.120
Expected return of stock (X̅)			.1875 (18.75%)

2. Computation of standard deviation for two stocks

Stock A: 8.03%

Stock B: 28.52%

Standard Deviation (SD) =   √(∑ P (X - x̅)²)

P = Probability

X = Return of the stock

x̅ = Expected return of the stock

Standard Deviation (SD) of stock A

Economy	Probability of state of economy (P)	Rate of return	(X - X̅ )	P(X - X̅)2
(I)	(II)	(III)	(IV)	(V) = (II) * (IV)2
Recession	.20	.010	.010 - .1115 = -.1015	.20 * (-.1015)2 =.002060
Normal	.55	.090	.090 - .1115 = -.0215	.55 * (-.0215)2 =.000254
Boom	.25	.240	.240 - .1115 = .1285	.25 * (.1285)2 = .004128
Total ( ∑P(X - X̅)2)				.006442

x̅ = Expected return of the stock = .1115 (see the above working)

Standard Deviation (SD) = √(∑ P (X - x̅)²)

                              =

V.006442

                                                =.08026

                                                =8.03%

Standard Deviation (SD) of stock B

Economy	Probability of state of economy (P)	Rate of return	(X - X̅ )	P(X - X̅)2
(I)	(II)	(III)	(IV)	(V) = (II) * (IV)2
Recession	.20	-.35	.-35 -.1875 = -.5375	.20 * (-.5375)2 = .057781
Normal	.55	.25	.25 - .1875 = .0625	.55 * (.0625)2 = .002148
Boom	.25	.48	.48 - .1875 = .2925	.25 * (.2925)2 = .021389
Total ( ∑P(X - X̅)2)				.081318

x̅ = Expected return of the stock = .1875 (see the above working)

Standard Deviation (SD) = √(∑ P (X - x̅)²)

=

V.081318

                                                =.28516

                                                =28.52%