Use the following information to calculate the standard deviation of Pirate Corporation’s projected returns.

State of Economy Probability of State Occurring Rate of Return
Strong 0.3 20%
Normal 0.4 10%
Weak 0.3 5%

Standard deviation = 7.59

Explanation:

Standard deviation is the sum of the  squared deviation of the individual return from the mean return under different scenarios

The mean  return = ∑R×P

r- return under circumstance,  P- probability

Mean return =(0.3×20%) + (0.4×10%) + (0.3×5%)

        = 11.5%

Outcome   R         (R- r )^2                    P×(R- r )^2

Strong     20     0.3×(20-11.5)^2            21.67        

Normal       10      0.4×(10-11.5)^2              23.4

Weak          5       0.3×(5%-11.5)^2             2.67

                                                                  57.75

Standard deviation =   √57.75 = 7.59

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