Value at Risk (VaR) at a 95% confidence level for a one-day horizon of $2 million means:

Question

BlackTom AI · Accepted Answer

Value at Risk (VaR) at a 95% confidence level for a one-day horizon of $2 million is interpreted as: on 95% of days, losses do not exceed $2 million, and on the remaining 5% of days, losses exceed $2 million.
Option A: 'There is a 95% probability that losses will not exceed $2 million in one day' is true, because VaR 95% is defined as the cutoff below which losses fall with 95% confidence.
Option B: 'There is a 5% probability that losses will exceed $2 million in one day' is also true, since the remaining tail beyond the VaR cutoff corresponds to the 5% worst days where losses surpass $2 million.
Option C: 'The expected loss on a typical day is $2 million' is incorrect. VaR at a confidence level describes a threshold for a distribution, not the mean or expected loss on a typical day; the expected loss could be less than, equal to, or greater than the VaR depending on the loss distribution.
Option D: 'Both A and B are correct' combines the correct statements from A and B, aligning with the definition of VaR at 95% for a one-day horizon.
In summary, A correctly reflects the 95% non-exceedance threshold, B correctly reflects the 5% tail exceedance, C misstates the meaning of VaR as an average or expected loss, and D is a consolidation of the true points from A and B. The coherence of A and B with the VaR concept is what validates the combined claim.

Value at Risk (VaR) at a 95% confidence level for a one-day horizon of $2 million means:单项选择题

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