Question

If the economy booms, rtf, incorporated, stock is expected to return 10 percent. If the economy goes into a recessionary period, then rtf is expected to only return 2 percent. The probability of a boom is 66 percent while the probability of a recession is 34 percent. What is the variance of the returns on rtf, inc., stock?

1) .037897
2) .000460
3) .036400
4) .001436
5) .000948

Answer 1

The variance of the returns on rtf, Inc. stock is 0.000948.

Step-by-step explanation:

To calculate the variance of the returns on rtf, Inc. stock, we first need to calculate the expected return. The expected return is found by multiplying the probability of each outcome by its corresponding return and summing the results. So for a boom, the expected return is 0.66 * 0.10 = 0.066, and for a recession, the expected return is 0.34 * 0.02 = 0.0068.

Next, we calculate the squared deviation of each return from the expected return. For a boom, it is (0.10 - 0.066)^2 = 0.001296, and for a recession, it is (0.02 - 0.0068)^2 = 0.00002848.

Finally, we calculate the variance by multiplying the squared deviation of each return by its corresponding probability and summing the results. So the variance of the returns on rtf, Inc. stock is 0.001296 * 0.66 + 0.00002848 * 0.34 = 0.000948.