What is the 95% for a portfolio consisting of both investments A and B? (Hint: write out the probabilities of all possible portfolio outcomes.) Is the summation of the 95% VaRs of the individual investments greater or smaller than the 95% VaR of the portfolio? If we measure the risk of an investment or portfolio using VaR, does this suggest that diversification must decrease risk? (Intuitively, putting A and B in a portfolio is a form of diversification.)

EBK CONTEMPORARY FINANCIAL MANAGEMENT
14th Edition
ISBN:9781337514835
Author:MOYER
Publisher:MOYER
Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 20P
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(Portfolio VaR) Suppose there are two investments A and B. Either investment
A or B has a 4.5% chance of a loss of $15 million, a 2% chance of a loss of $2
million, and a 93.5% change of a profit of $2 million. The outcomes of these
two investments are independent of each other.
Transcribed Image Text:(Portfolio VaR) Suppose there are two investments A and B. Either investment A or B has a 4.5% chance of a loss of $15 million, a 2% chance of a loss of $2 million, and a 93.5% change of a profit of $2 million. The outcomes of these two investments are independent of each other.
What is the 95% for a portfolio consisting of both investments A and B?
(Hint: write out the probabilities of all possible portfolio outcomes.)
Is the summation of the 95% VaRs of the individual investments greater
or smaller than the 95% VaR of the portfolio? If we measure the risk of
an investment or portfolio using VaR, does this suggest that diversification
must decrease risk? (Intuitively, putting A and B in a portfolio is a form
of diversification.)
Transcribed Image Text:What is the 95% for a portfolio consisting of both investments A and B? (Hint: write out the probabilities of all possible portfolio outcomes.) Is the summation of the 95% VaRs of the individual investments greater or smaller than the 95% VaR of the portfolio? If we measure the risk of an investment or portfolio using VaR, does this suggest that diversification must decrease risk? (Intuitively, putting A and B in a portfolio is a form of diversification.)
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