Final answer:
The variance of the returns on the stock is calculated using the probability-weighted returns and the expected return. None of the provided options exactly match the calculated variance, but you can find the closest match by following the calculation steps.
Step-by-step explanation:
To calculate the variance of the returns on the stock, we use the expected return formula and the formula for variance in the context of probability and return. First, we need to compute the expected return (ER) by using the given probabilities and possible returns:
ER = (Probability of Normal Economy * Return in Normal Economy) + (Probability of Recession * Return in Recession)
ER = (0.78 * 10.3%) + (0.22 * (-2.9%))
ER = 7.434% + (-0.638%) = 6.796%
Next, we use the expected return to find the variance:
Variance = (Probability of Normal Economy * (Return in Normal Economy - ER)^2) + (Probability of Recession * (Return in Recession - ER)^2)
Variance = (0.78 * (10.3% - 6.796%)^2) + (0.22 * (-2.9% - 6.796%)^2)
Variance = (0.78 * 0.123204)^2 + (0.22 * 0.09696)^2
Variance = 0.009460536 + 0.001905216
Variance ≈ 0.011365752 (or 0.0114 in decimal form)
After computing the variance, we can look at the options provided to find the closest answer. The correct option based on our calculation is not directly listed. However, calculating the answer using the steps mentioned, you can find the approximate variance value for the stock returns that closest matches the provided options.