(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. (a) What is the 95% VaR of investment A? How about investment B? (b) What is the 95% for a portfolio consisting of both investments A and B? (Hint: write out the probabilities of all possible portfolio outcomes.) (c) 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.)
(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. (a) What is the 95% VaR of investment A? How about investment B? (b) What is the 95% for a portfolio consisting of both investments A and B? (Hint: write out the probabilities of all possible portfolio outcomes.) (c) 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.)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Please answer all three question.

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.
(a) What is the 95% VaR of investment A? How about investment B?
(b) What is the 95% for a portfolio consisting of both investments A and B?
(Hint: write out the probabilities of all possible portfolio outcomes.)
(c) 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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