If I find an indicator (e.g. an earthquake happening) that is almost always followed by a VaR breach the next day. That means the probability of breach conditional on the indicator is too
(high/low). I should adjust the VaR
(higher/lower) the next time I see the indicator.

Question

If I find an indicator (e.g. an earthquake happening) that is almost always followed by a VaR breach the next day. That means the probability of breach conditional on the indicator is too 
 (high/low). I should adjust the VaR 
 (higher/lower) the next time I see the indicator.

BlackTom AI · Accepted Answer

In this scenario, you are looking at the relationship between an indicator (like an earthquake) and a subsequent VaR breach. If the indicator is almost always followed by a VaR breach the next day, then the conditional probability of a breach given the indicator, P(breach | indicator), is high, not low.

Option 1 analysis: choosing high vs. low. Since the empirical pattern shows frequent breaches after the indicator, the appropriate description of P(breach | indicator) is 'high.' Selecting 'low' would contradict the observed rare occurrence and would imply the indicator is a poor predictor, which it is not in this case.

Option 2 analysis: choosing higher vs. lower. If the indicator reliably precedes breaches, risk guidance should become more conservative, meaning you should raise the VaR to account for the higher tail risk when that indicator appears. Therefore, 'higher' is the logical adjustment, whereas 'lower' would understate risk and could lead to underestimation of potential losses.

Putting it together, the sentence should read: the probability of breach conditional on the indicator is high, and I should adjust the VaR higher the next time I see the indicator. This aligns with risk management principles that increase capital reserves or risk thresholds when a predictor signal indicates greater tail risk.

If I find an indicator (e.g. an earthquake happening) that is almost always followed by a VaR breach the next day. That means the probability of breach conditional on the indicator is too (high/low). I should adjust the VaR (higher/lower) the next time I see the indicator. 多项填空题

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