Question

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%

Answer 1

Standard deviation = 7.59

Step-by-step 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