A stock will have a loss of 9.9 percent in a bad economy, a return of 9.7 percent in a normal economy, and a return of 23.6 percent in a hot economy. There is 21 percent probability of a bad economy, 48 percent probability of a normal economy, and 31 percent probability of a hot economy. What is the variance of the stock's returns? Multiple Choice .01054 .02811 .01405 .02108 .11855

.01405

Explanation:

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

= (Expected return of the bad economy × weightage of bad economy) + (expected return of the normal economy × weightage of normal economy) + (expected return of the hot economy × weightage of hot economy)

= (-9.9% × 0.21) + (9.7% × 0.48) + (23.6% × 0.31)

= -2.079% + 4.656% + 7.316%

= 9.893%

Now the variance would equal to the

= Weightage × (Return - Expected Return) ^2

For bad economy:

= 0.21 × (9.9% - 9.893%)^2

= 0.21 × (-0.099 - 0.09893)^2

= 0.21 × (-0.19793 )^2

= 0.21 × 0.39176285

= 0.00822702

For normal economy:

= 0.48 × (9.7% - 9.893%) ^2

= 0.48 × (0.097 - 0.0983) ^2

= 0.00

For hot economy:

= 0.31% × (23.6% - 9.893%) ^2

= 0.31% × (0.0236% - 0.0983%) ^2

= 0.005824337

So, the total variance would be

= 0.00822702  + 0.00 + 0.005824337

= 0.014051357

or

= 0.01405