Question

If the economy booms, RTF, Incorporated, stock is expected to return 13 percent. If the economy goes into a recessionary period, then RTF is expected to only return 4 percent. The probability of a boom is 80 percent while the probability of a recession is 20 percent. What is the variance of the returns on RTF, Incorporated, stock?

Answer 1

The variance of the returns on RTF, Incorporated, stock, considering the probabilities and potential returns in different economic scenarios, is calculated to be 0.114048%, or 0.00114048 when expressed as a proportion.

Step-by-step explanation:

To calculate the variance of the returns on RTF, Incorporated, stock, we need to use the expected returns and the probabilities of the different economic scenarios. We first determine the expected return by multiplying each possible return by its respective probability, then summing these products:

• Expected return during a boom = 13% * 80% = 10.4%
• Expected return during a recession = 4% * 20% = 0.8%

The combined expected return is 10.4% + 0.8% = 11.2%.

Next, we calculate the variance by looking at the squared deviations of each return from the expected return, weighted by their respective probabilities:

• Variance during a boom = (13% - 11.2%)^2 * 80% = 1.296% * 80% = 1.0368%
• Variance during a recession = (4% - 11.2%)^2 * 20% = 51.84% * 20% = 10.368%

The combined variance is 1.0368% + 10.368% = 11.4048%.

The calculation above represents the variance in percentage terms; to convert this into the actual variance, we must divide by 100^2, resulting in a variance of 0.114048%, or 0.00114048 when expressed as a proportion.