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%

Expert's answer

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%.

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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