A stock’s return has the following distribution: Demand for Products Probability

Question

A stock’s return has the following distribution:

Demand for Products                           Probability of Occurrence of Demand              Return if

Demand Occurs

Weak                                                             0.1                                                                 -40%

Below Average                                             0.2                                                                  -5

Average                                                         0.4                                                                   12

Above Average                                             0.2                                                                   21

Strong                                                            0.1                                                                   50

Calculate the stock’s expected return and standard deviation.

Explanation / Answer

Stock Expected Return P R Probability of Occurance of Demand Return if Demand Occurs Probability* Return*100 Weak 0.1 -40% -4 Below Average 0.2 -5% -1 Average 0.4 12% 4.8 Above Average 0.2 21% 4.2 Strong 0.1 50% 5 9 Stock Expected Return = 9% Standard Deviation Assume P as Probability Assume R as Return Assume X is Expected Return (R-X)^2 P*[(R-x)^2] Weak 0.1 -40.00 9.00 2401.00 240.1 Below Average 0.2 -5.00 9.00 196.00 39.2 Average 0.4 12.00 9.00 9.00 3.6 Above Average 0.2 21.00 9.00 144.00 28.8 Strong 0.1 50.00 9.00 1681.00 168.1 479.8 Standard Deviation = Square root of Probabilty * [ (Return - Expected Reurn)^2] for all lines Standard Deviation = Square root of 479.8 i.e 21.9

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