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 -0.14 Normal +0.08 Boom +0.20 What is the standard deviation of Orange?

Answer 1

State of Economy	Return(%)	Deviation form average return (D)	D^2
Recession	-14	-12.67	160.53
Normal	8	9.33	87.05
Boom	2	3.33	11.09

Average Return = Sum of Returns / No. of Returns

= (-14+8+2)/3

= -4/3

= -1.33%

Variance = $\sum$D^2/n

= (160.53+87.05+11.09)/3

= 258.67/3

= 86.22

Standard Deviation = $\sqrt{}$Variance

= $\sqrt{}$86.22

= 9.29%

*Deviation form average return = Rate of return -  average return