Consider a portfolio comprised of four risky securities. Assume the economy has three states with varying probabilities of occurrence. Which one of the following will guarantee that the portfolio variance will equal zero? A. The portfolio beta must be 1.0. B. The portfolio expected rate of return must be the same for each economic state. C. The portfolio risk premium must equal zero. D. There must be equal probabilities that the state of the economy will be a boom or a bust.

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Business

Alyssa Guzman

10 January, 12:26

Consider a portfolio comprised of four risky securities. Assume the economy has three states with varying probabilities of occurrence. Which one of the following will guarantee that the portfolio variance will equal zero? A. The portfolio beta must be 1.0. B. The portfolio expected rate of return must be the same for each economic state. C. The portfolio risk premium must equal zero. D. There must be equal probabilities that the state of the economy will be a boom or a bust.

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Trystan Huang · Answer 1

B. The portfolio expected rate of return must be the same for each economic state.

Explanation:

Variance formula = sum of (probability x (r - mean) ^2)

r = expected return

if the expected return would be same for each economic state then the mean would equal to expected return which ultimately will give variance zero (as r-mean would be 0).

Hence the correct option is B. The portfolio expected rate of return must be the same for each economic state.