Suppose you are considering investing your entire portfolio in three assets A, B and C. You expect that after you invest, four possible mutually exclusive scenarios will occur, with associated returns (in %) for each of the three assets as listed below. The probability of each scenario is given below. A B C Probabilities return 0.05 0.50% -3.60% 3.60% 0.35 0.60% 2.75% 0.15% 0.45 3.66% 1.45% 0.45% 0.15 -4.80% -0.60% 6.30% Find the expected returns and standard deviations of Asset A, B & C. (HINT: the expected return is given by the probability-weighted sum of returns in each scenario. The expected standard deviation is given by the square root of the probability-weighted sum of squared deviations from the expected return.) Is there any reason to invest in Asset A given its low expected return and high standard deviation?
Suppose you are considering investing your entire portfolio in three assets A, B and C. You expect that after you invest, four possible mutually exclusive scenarios will occur, with associated returns (in %) for each of the three assets as listed below. The probability of each scenario is given below. A B C Probabilities return 0.05 0.50% -3.60% 3.60% 0.35 0.60% 2.75% 0.15% 0.45 3.66% 1.45% 0.45% 0.15 -4.80% -0.60% 6.30% Find the expected returns and standard deviations of Asset A, B & C. (HINT: the expected return is given by the probability-weighted sum of returns in each scenario. The expected standard deviation is given by the square root of the probability-weighted sum of squared deviations from the expected return.) Is there any reason to invest in Asset A given its low expected return and high standard deviation?
Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 5P
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Question
Suppose you are considering investing your entire portfolio in three assets A, B and C. You expect that after you invest, four possible mutually exclusive scenarios will occur, with associated returns (in %) for each of the three assets as listed below. The probability of each scenario is given below.
A | B | C | |
Probabilities | return | ||
0.05 | 0.50% | -3.60% | 3.60% |
0.35 | 0.60% | 2.75% | 0.15% |
0.45 | 3.66% | 1.45% | 0.45% |
0.15 | -4.80% | -0.60% | 6.30% |
- Find the expected returns and standard deviations of Asset A, B & C. (HINT: the expected return is given by the probability-weighted sum of returns in each scenario. The expected standard deviation is given by the square root of the probability-weighted sum of squared deviations from the expected return.)
- Is there any reason to invest in Asset A given its low expected return and high standard deviation?
Expert Solution
Introduction
Expected return and standard deviation of a stock say "X" can be calculated as:
Here, i represents each state
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