Use the following information on states of the economy and stock returns to calc
ID: 2718354 • Letter: U
Question
Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) State of Economy
Probability of state economy Security Return if state occurs
Recession: .40 -6%
Normal: .25 10%
Boom: .35 19%
Explanation / Answer
Probability(p) Return(r) Er(Expected Return) r-Er (r-Er)2 p * (r-Er)2
0.40 -0.06 0.0675 -0.1275 0.01626 0.00650
0.25 0.10 0.0675 0.0325 0.00106 0.00027
0.35 0.19 0.0675 0.1225 0.01501 0.00525
Variance 0.01202
Standard deviation of returns = (variance)1/2
= (0.01202)1/2
= 10.96
Note: Expected return( Er) = (0.40 * -0.06 ) + (0.25 * 0.10)+ (0.35* 0.19)
= 0.0675