Question

The rate of return on the common stock of Flowers by Flo is expected to be 15 percent in a boom economy, 7 percent in a normal economy, and only 3 percent in a recessionary economy. The probabilities of these economic states are 20 percent for a boom, 70 percent for a normal economy, and 10 percent for a recession. What is the variance of the returns on this stock?

Answer 1

Answer:

the Expected rate of return will be 8.2%

the variance will be 0.001296

Explanation:

We will calculate the Expected Rate of Return which is the sum of the wieghted return based on their probabilities:

return of 0.15 probability 20%  =  0.03

return of 0.07 probability 70% =  0.049

return of 0.03 probability 10% =   0.003

              expected return        =   0.082 = 8.2%

Now to calculate the variance we do:

∑(rk-ERR)^2 x pk

The sum of the difference between the expected rate and the escenario rate, power two, and multiply by their posibility

$(0.15-0.082)^{2}\times0.20+(0.07-0.082)^{2}\times0.70+(0.03-0.082)^{2}\times0.10$

the variance will be: 0.001296