Question

Kurt's Adventures, Inc. stock is quite cyclical. In a boom economy, the stock is expected to return 30% in comparison to 12% in a normal economy and a negative 20% in a recessionary period. The probability of a recession is 15%. There is a 30% chance of a boom economy. The remainder of the time the economy will be at normal levels. What is the standard deviation of the returns on Kurt's Adventures, Inc. stock

Answer 1

Answer:

15.83%

Explanation:

Calculation to determine is the standard deviation of the returns on Kurt’s Adventures, Inc. stock

First step is to determine l E(r)

E(r) = (.30 *.30) + (.55 *.12) + (.15 *-.20)

E(r)= .09 + .066 -.03

E(r)= .126

Second step is to determine Var

Var = .30 *(.30 -.126)^2 + .55 *(.12 -.126)^2 + .15 *(-.20 -.126)

Var=0090828 +.0000198 + .0159414

Var= .025044

Now let determine the Std dev

Std dev = √.025044 = .15825

Std dev= 15.83 percent

Therefore the standard deviation of the returns on Kurt’s Adventures, Inc. stock.is 15.83 percent