Demand for Product Probability of Demand Occuring Rate of return if demand occur

Question

Demand for Product Probability of Demand Occuring Rate of return
if demand occurs

Weak 0.2 -20%
Below Average 0.2 -14%
Average 0.3 18%
Above Average 0.1 32
Strong 0.2 71



a. Calculate the stock's expected return. Round your answer to two decimal places.
_________________________%

b. Calculate the standard deviation. Round your answer to two decimal places.
_________________________ %

c. Calculate the coefficient of variation. Round your answer to two decimal places.

__________________________%


*please show how to derive answer, thanks!

Explanation / Answer

a. expected return = E(X)=0.2*(-0.2)+0.2*(-0.14)+0.3*0.18+0.1*0.32+0.2*0.71=0.16 (16%)
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b. E(X^2)=0.2*(-0.2)^2+0.2*(-0.14)^2+0.3*0.18^2+0.1*0.32^2+0.2*0.71^2= 0.1327

Var(X)= E(X^2)- [E(X)]^2
= 0.1327-0.16^2
= 0.1071

So standard deviation =var= 0.1071= 0.3272614 (32.73%)

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c.coefficient of variation = s/E(X) = 0.3272614/0.16=2.045384

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