Answer to Question #207012 in Statistics and Probability for Baker Naja

Question

Use the following information to calculate the standard deviation of Macadam Corp.'s returns.

StateProbability

Return

Boom20%

40%

Normal60%

15%

Recession20%

(20%)

a.

19.8%

b.

19.2%

c.

8.6%

d.

11.4%

Answer 1

Solution

Step one

To calculate the standard deviation of the the above scenario, we have to compute the expected return first.

For Boom Phase

p1=20%, r1=40%

Expected return(p1r1)=0.08

Normal phase

p2=60%, r2=15%

Expected return(p2r2)=0.09

Recession phase

p3=20% , r3=-20%

Expected return(p3r3)= -0.04

Total expected return = 0.13 = 13%

Step two

The next step will be to compute the deviations from the expected return

Boom phase = 13-40 =-27.000%, Square of deviations = 0.0729

Normal Phase= 13-15 = -2.000%, square of the deviation = 0.0004

Recession Phase = 13--20 = 33.00%, square of deviation = 0.1089

Probability x Square of deviations

0.2 x 0.0729 = 0.01458

0.6 x 0.0004 = 0.00024

0.2 x 0.1089 = 0.02178

The sum of the above gives;

0.01458 + 0.00024 + 0.02178 =Variance = 0.0366

standard deviation =$\sqrt{0.0366} = 0.191311 = 19.13$%

from the choices we can choose $19.2$ %