9. The 10?Q report of ABC Bank states that the monthly Value at Risk of ABC Bank is USD 10 million at 95% confidence level. What is the proper interpretation(s) of this statement?

A. If we collect 100 monthly gain/loss data of ABC Bank, we will always see 5 months with losses larger than USD 10 million.

B. There is a 95% probability that the company will lose less than USD 10 million over a month.

C. There is a 5% probability that the company will gain less than USD 10 million each month.

D. There is a 5% probability that the company will lose less than USD 10 million over a month.

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A is incorrect because it uses the word "always" as VaR is an expected value and actual gain/loss frequency often deviate from the expected value in practice.B is correct.  Per Jorion's definition, VAR summarizes the expected maximum losses (or worst loss) over a target horizon within a given confidence interval.  As a "confidence interval" represents a percentile point on the probability distribution, this can be phrased in probability terms.

C is incorrect since VaR is a measure of "maximum loss" not "minimum gain".

D is incorrect because the 95% confidence level is on the left tail of the probability distribution and there is only 5% losses greater then the VaR number.

Reference: Philippe Jorion, Value at Risk, 2nd Edition (ffice:smarttags" />New York: McGraw?Hill, 2001), Chapter 5.

Type of Question: Market Risk