Expected Return, Variance, Std. Deviation and Cofficient of Variation: Magee Inc

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.

Probability of State Occurring

Stock's Expected Return

30%

26.10%

50%

16.05%

20%

–14.10%

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:

Explanation / Answer

Expected return

Expected return = sum of (ProbabilitiesState x ReturnState)

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

Variance

Variance = sum of [ (ReturnState - 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

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