Answer to Question #58608 in Finance for abdiaziz

Question #58608
Stock W has the following returns for various states of the economy: State of the Economy Probability Stock W's Return Recession 10% -30% Below Average 20% -2% Average 40% 10% Above Average 20% 18% Boom 10% 40% Stock W's standard deviation of returns is A) 10%. B) 14%. C) 17%. D) 20%
1
Expert's answer
2016-03-22T11:32:03-0400
State of the Economy Probability Stock W's Return
Recession 10% -30%
Below Average 20% -2%
Average 40% 10%
Above Average 20% 18%
Boom 10% 40%
Firstly, let's calculate the weighted average of the stock return at different states of the economy:
X(avg) = (10*(-30) + 20*(-2) + 40*10 + 20*18 + 10*40)/100 = 8.2%
Then Stock W's standard deviation of returns is:
SD = ((10*(-30 - 8.2)^2 + 20*(-2 - 8.2)^2 + 40*(10 - 8.2)^2 + 20*(18 - 8.2)^2 + 10*(40 - 8.2)^2)/100)^0.5 = 16.98% = 17%
So, the right answer is C) 17%.

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