Question

Consider the following information:

		Rate of Return If State Occurs
State of	Probability of
Economy	State of Economy	Stock A	Stock B
Recession	.25	.04	–.17
Normal	.30	.10	.17
Boom	.45	.15	.37

a.	Calculate the expected return for the two stocks. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Expected return for A	%
Expected return for B	%

b.	Calculate the standard deviation for the two stocks. (Do not round your intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Standard deviation for A	%
Standard deviation for B	%

Answer 1

(A) EXPECTED RETURN

Expected Returns - Stock A

= [0.04 x 0.25] + [0.10 x 0.30] + [0.15 x 0.45]

= 0.01 + 0.03 + 0.0675

= 0.1075

= 10.75%

Expected Returns - Stock B

= [-0.17 x 0.25] + [0.17 x 0.30] + [0.37 x 0.45]

= -0.0425 + 0.051 + 0.1665

= 0.175

= 17.50%

(B) STANDARD DEVIATION

Stock A

Variance

= [(4 – 10.75)² x 0.25] + [(10 – 10.75)² x 0.30] + [(15 – 10.75)² x 0.45]

= 11.3906 + 0.1688 + 8.1281

= 19.6875

Therefore, Standard Deviation = Square Root of (19.6875) = 4.44%

Stock B

Variance

= [(-17 – 17.50)² x 0.25] + [(17 – 17.50)² x 0.30] + [(37 – 17.50)² x 0.45]

= 297.56 + 0.08 + 171.11

= 468.75

Therefore, Standard Deviation = Square Root of (468.75) = 21.65%