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? Group of answer choices

6.11%

Explanation:

For computing the variance, first we have to determine the expected return which is shown below:

= (Expected return of the boom * weightage of boom) + (expected return of the normal economy * weightage of normal economy) + (expected return of the recession * weightage of recession)

= (12% * 5%) + (10% * 85%) + (2% * 10%)

= 0.6% + 8.5% + 0.2%

= 9.30%

Now the variance would equal to the

= Weightage * (Return - Expected Return) ^2

For boom:

= 5% * (12% - 9.3%) ^2

= 0.3645

For normal economy:

= 85% * (10% - 9.3%) ^2

= 0.4165

For recession:

= 10% * (2% - 9.3%) ^2

= 5.329

So, the total variance would be

= 0.3645 + 0.4165 + 5.329

= 6.11%