Consider the following information: Rate of Return if State O State of Economy R

Question

Consider the following information: Rate of Return if State O State of Economy Recession Normal Boom Probability of State of Economy 0.10 0.60 0.30 Stock A 0.05 0.07 0.12 Stock B -0.21 0.12 0.33 Required: (a) Calculate the expected return for Stock A. (Do not round your intermediate calculations.) [Click to select) (b) Calculate the expected return for Stock B. (Do not round your intermediate calculations.) Click to select) (Click to select) [(Click-oselect) ] (c) Calculate the standard deviation for Stock A. (Do not round your intermediate calculations.) (d) Calculate the standard deviation for Stock B (Do not round your intermediate calculations.)

Explanation / Answer

a.

Expected return = 0.10 * 0.05 + 0.60 * 0.07 + 0.30 * 0.12

= 0.005 + 0.042 + 0.036

= 0.083 or 8.3%.

b.

Expected return = 0.10 * -0.21 + 0.60 * 0.12 + 0.30 * 0.33

= - 0.021 + 0.072 + 0.099

= 0.15 or 15%.

c. Variance = 0.10 (0.05 - 0.083)2 + 0.60 (0.07 - 0.083)2 + 0.30 (0.12 - 0.083)2

= 0.0001089 + 0.0001014 + 0.0004107

= 0.000621

Standard deviation = square root of 0.000621

= 0.0249 or 2.49%.

d.

Variance = 0.10 ( - 0.21 - 0.15)2 + 0.60 (0.12 - 0.15)2 + 0.30 (0.33 - 0.15)2

= 0.01296 + 0.00054 + 0.00972

= 0.02322

Standard deviation = 0.1524 or 15.24%.

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