In: Finance
Malone Imports stock should return 12 percent in a boom, 10 percent in a normal economy, and 2 percent in a recession. The probabilities of a boom, normal economy, and recession are 5 percent, 85 percent, and 10 percent, respectively. What is the variance of the returns on this stock? Please explain your answer.
Expected return=Respective return*Respective probability
=(0.05*12)+(0.85*10)+(0.1*2)=9.3%
probability | Return | probability*(Return-Expected Return)^2 |
0.05 | 12 | 0.05*(12-9.3)^2=0.3645 |
0.85 | 10 | 0.85*(10-9.3)^2=0.4165 |
0.1 | 2 | 0.1*(2-9.3)^2=5.329 |
Total=6.11% |
Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)
=(6.11)^(1/2)
=2.47%(Approx).
Variance=Standard deviation^2
=6.11%