Question

A stock will have a loss of 10.8 percent in a bad economy, a return of 10.6 percent in a normal economy, and a return of 24.5 percent in a hot economy. there is 30 percent probability of a bad economy, 39 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

O 0.01446
O 0.01928
O 0.13886
O 0.03857
O 0.02892

Answer 1

This stock's volatile! Bad times bring losses, normal times tick up, and hot markets see fireworks. With 30% chance of each, its spread of returns dances to a tune of 0.01928, a measure of its unpredictable sway. So, The correct answer is O) 0.01928.

Here's how to calculate the variance of the stock's returns:

Calculate the expected return:

Expected return = (probability of bad economy * bad economy return) + (probability of normal economy * normal economy return) + (probability of hot economy * hot economy return)

Expected return = (0.3 * -0.108) + (0.39 * 0.106) + (0.31 * 0.245) ≈ 0.062

Calculate the squared deviations from the expected return for each scenario:

Bad economy: (-0.108 - 0.062)^2 ≈ 0.0484

Normal economy: (0.106 - 0.062)^2 ≈ 0.0184

Hot economy: (0.245 - 0.062)^2 ≈ 0.2916

Calculate the weighted variance:

Variance = (probability of bad economy * bad economy variance) + (probability of normal economy * normal economy variance) + (probability of hot economy * hot economy variance)

Variance = (0.3 * 0.0484) + (0.39 * 0.0184) + (0.31 * 0.2916) ≈ 0.01928

Therefore, the variance of the stock's returns is approximately 0.01928.

The correct answer is O) 0.01928.