Question

Expected Return, Variance, Std. Deviation and Cofficient of Variation:
Magee Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns?

Round your answer to two decimal places. For example, if your answer is $345.6671 round as 345.67 and if your answer is .05718 or 5.7182% round as 5.72.

State of the Economy	Probability of State Occurring	Stock's Expected Return
Boom	30%	26.10%
Normal	50%	16.05%
Recession	20%	–14.10%
Available answers:

a.

15.67%

b.

14.25%

c.

12.11%

d.

9.97%

e.

14.96%

Answer 1

Expected return

Expected return = sum of (Probabilities_State x Return_State)

or, Expected return = (0.30 x 26.10%) + (0.50 x 16.05%) + (0.20 x -14.10%) = 13.035%

Variance

Variance = sum of [ (Return_State - Expected Return)² x Probability ]

or, Variance = [ (26.10% - 13.035%)² x 0.30 ] + [ (16.05% - 13.035%)² x 0.50 ] + [ (-14.10% - 13.035%)² x 0.20 ]

or, Variance = 203.015025%² or 203.02%² or 0.020302

Standard Deviation

Standard Deviation = (Variance) ^{1 / 2} [ Under root of Variance ]

or, Standard Deviation = (203.015025%²) ^{1 / 2} = 14.2483341131% or 14.25%

Cofficient of Variation (CV)

CV = Standard Deviation / Expected return = 14.2483341131% / 13.035% = 1.0930827858 or 1.09