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%	22.05%
Normal	55%	15.45%
Recession	15%	–14.15%

11.77%

14.71%

10.00%

12.94%

13.53%

Answer 1

Answer :

Standard deviation of estimated returns is $ 11.77 %

State of the Economy	Probability of State Occurring (I)	Stock's Expected Return (II)	Expected Return (III) = [(I)×(II)]	Deviation(d) (IV) = [(II) - TOTAL (III)]	Squared Deviation (d2) (V)=(IV)^2	Variance (V) × (I)
Boom	0.30	0.2205	0.06615	0.09060	0.00821	0.00246
Normal	0.55	0.1545	0.08498	0.02460	0.00061	0.00034
Recession	0.15	-(0.1415)	-(0.02123)	-(0.27140)	0.07366	0.01105
Total			0.12990			0.01385

Portfolio variance = 0.01385

Therefore, Standard deviation = Sq. Root of Variance

= (0.01385)^^1/2 = 0.1177 = 11.77 %