A portfolio manager reports a one-day 99% VaR of $500,000. What is the correct interpretation?
AThe portfolio will lose no more than $500,000 on any given trading day
BThere is a 1% probability that the daily loss will exceed $500,000
CThe portfolio is expected to lose $500,000 on 99% of trading days
DIn the worst-case scenario, losses will be exactly $500,000
99% VaR of $500,000 means: with 99% probability, the daily loss will be $500,000 or less — equivalently, there is a 1% chance of losing MORE than $500,000. Option A is the most dangerous misconception: VaR is not a loss cap or maximum. In the worst 1% of days, losses can be $500,001 or $50 million — VaR says nothing about that. Option C reverses the probability completely.
Question 2 Multiple Choice
Portfolio A has a 99% one-day VaR of $1 million with average tail losses of $1.1 million. Portfolio B also has a 99% VaR of $1 million but average tail losses of $10 million. What does this illustrate?
APortfolio B is better diversified because larger tail losses indicate wider exposure
BVaR fails to distinguish between portfolios with identical threshold losses but very different tail severities
CThis situation is impossible — equal VaR implies equal tail risk by definition
DPortfolio A is riskier because its tail losses are closer to the VaR figure, indicating the model underestimates losses
This is VaR's fundamental limitation: it only specifies the 1st-percentile loss threshold, not what happens beyond it. Portfolios A and B are indistinguishable by VaR, but B is catastrophically riskier — its average loss in the worst 1% of days is nearly 10× larger. Expected Shortfall (ES/CVaR) would correctly separate them: approximately $1.1M vs $10M. VaR is blind to the shape of the tail beyond the threshold.
Question 3 True / False
Two portfolios can have identical 99% VaR while one has dramatically larger expected losses in the worst 1% of scenarios.
TTrue
FFalse
Answer: True
True. VaR is a single percentile — it identifies the threshold but says nothing about the distribution of losses beyond that threshold. A portfolio of vanilla bonds and a portfolio of short deep out-of-the-money options can have the same VaR threshold while the latter has catastrophically fat tails. This is precisely why Expected Shortfall (the average loss conditional on being in the worst 1%) was adopted in Basel III/IV: it penalizes fat tails that VaR ignores.
Question 4 True / False
A 99% VaR of $2 million means that the portfolio can seldom lose more than $2 million in a single day.
TTrue
FFalse
Answer: False
False. A 99% VaR of $2 million means that in 99% of trading days, the loss will be $2 million or less — equivalently, in 1% of days, the loss will EXCEED $2 million. VaR explicitly does not cap losses. In the tail (the worst 1% of days), actual losses could be $2.1 million or $200 million; VaR provides zero information about that range. Treating VaR as a maximum loss is among the most dangerous misinterpretations in risk management.
Question 5 Short Answer
Why do risk managers compute Expected Shortfall (ES) in addition to VaR, and what information does ES provide that VaR cannot?
Think about your answer, then reveal below.
Model answer: VaR identifies the loss threshold at a given percentile but is completely silent about how large losses are beyond that threshold. Expected Shortfall is the average loss conditional on being in the worst 1% (or α%) of scenarios. ES answers the question VaR ignores: when things go very badly, how badly do they go on average? Two portfolios with identical VaR can have very different ES values, revealing very different tail risk profiles — a difference that matters enormously for capital adequacy and systemic risk.
During the 2008 financial crisis, many institutions met their VaR limits while sustaining tail losses orders of magnitude larger. A portfolio short of deep out-of-the-money options might show modest VaR because the 1% threshold stays low — but in the extreme scenarios beyond the threshold, losses are catastrophic. ES penalizes fat tails; VaR is indifferent to them. This is why Basel III/IV shifted from requiring VaR to requiring ES at the 97.5% level for regulatory capital calculations.