There are two states of the economy. If the economy is normal, Charleston Freight stock is expected to return 16.5 percent. If the economy falls into a recession, the stock's return is projected at a negative 11.6 percent. The probability of a normal economy is 80 percent while the probability of a recession is 20 percent. What is the variance of the returns on this stock

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Business

Keegan

16 October, 18:19

There are two states of the economy. If the economy is normal, Charleston Freight stock is expected to return 16.5 percent. If the economy falls into a recession, the stock's return is projected at a negative 11.6 percent. The probability of a normal economy is 80 percent while the probability of a recession is 20 percent. What is the variance of the returns on this stock

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Alexa Riley · Answer 1

0.012634

Explanation:

Mean return is the expected value, or mean, of all the likely returns of investments comprising a portfolio.

Mean return E (r) = (probability of a normal economy * return of a normal economy) + (probability of economy in recession * return of economy in recession)

Therefore, the mean return E (r) = (0.80 * 0.165) + (0.20 * -0.116) = 0.1088

Variance = 0.80 (0.165 - 0.1088) ^2 + 0.20 (-0.116 - 0.1088) ^2 = 0.012634

The variance of the returns on this stock is 0.012634