The expected rate of return is based on 3 possible states; boom, normal and rece

Question

The expected rate of return is based on 3 possible states; boom, normal and recession, which have probablilties of occurrence of 20%, 75%, and 5% respectively. Which of the following statements is correct concerning the variance of the returns on this stock?
a. The variance must decrease if probablilty of occurrence for boom increases
b. variance remain constant as long as sum of the economic probablilties is 100%
c. variance can be positive, zero , or negative, depending on expected rate of return assigned to each economic state
d. variance must be positive provided that each state of economy produces a different expected rate of return
e. variance is independent of the economic probablilties of occurrence

Explanation / Answer

a. The variance must decrease if probablilty of occurrence for boom increases

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