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Finance 432Spring 2008Class Exercise #3Value-at-Risk1. A financial institution has $30 million invested in stocks. The company uses a model to simulate the portfolio’s annual return. The results of running this simulation for 100 iterations, ranked by the change in value of the portfolio, are listed on the back page. What is the 5% Value-at-Risk for this portfolio based on a one year holding period?$9,975,605This illustrates a problem when mathematicians are dealing with the terminology of financial economics. VaR is a number that will be exceeded in value only x% of the time, in this case 5%. A mathematician would say, based on these simulation results, the value would be $11,964,744-ε, but the purpose of VaR was to explain risk to non mathematicians, so the ε is out. Therefore the best approach is to multiply 5% times the number of iterations and add one to determine which value to select. For this case, since we are dealing with assets, VaR would be the sixth lowest value. (If we were evaluating losses we would have taken the sixth highest value. Generally simulations are run for thousands of iterations, so whether youtake the 5% value or the 5% plus one would not make much difference. 2. Explain, in terms that a board member without a background in financewould understand, what the value you listed above means.The best answers were:Based on the historical simulation method, 5% of the time (during a year) the company’s loss will exceed $9,975,605. (The problem with this answer is that the approach was based on Monte Carlo simulation, not historical simulation. You would also need to explain this approach to the board member.)Based on our simulation 5% of the time we will lose a value greater than or equal to $11,964,744. (This uses the wrong value and an incorrect definition, but is in terms the board member could understand. VaR is the level that losses will exceed (not equal or exceed) only x% of the time, but don’t use x% when talking to


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UIUC FIN 432 - Value-at-Risk

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