Question

The return on shares of the Orange Company are predicted under the following states of nature. The states of nature are all equally likely, and because there are a total of three states, each state has a 33.333% chance of occurring. Recession -0.13 Normal +0.07 Boom +0.24 What is the standard deviation of Orange?

Answer 1

State	Returns	(Returns - Average)^2
Recession	-13.00%	3.61000000%
Normal	7.00%	0.01000000%
Boom	24.00%	3.24000000%
Total	18.000000%	6.86000000%

33.333% means equal chance of occuring.

n=3 (seven observations)

Average = X = Total / n

X = 18%/3

X = 6%

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Standard Deviation = ((Sum of (Return petaining to each year - Average)^2)/n)^0.5       

Standard Deviation =(6.86%/3)^0.5        

Standard Deviation = 0.151217283

Standard Deviation = 15.12%