An amount at a certain probability losses will be less than is known as the

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When evaluating the concept described, we must map each option to its formal meaning in risk measurement.
Option 1: 'value at risk' — VaR is defined as the threshold loss value such that the probability of losses exceeding this amount is at a specified level. This description directly matches the idea of a loss amount tied to a confidence probability, so it aligns with the given statement.
Option 2: 'expected value' — This term refers to the mean or average outcome of a random variable, not a threshold tied to a probability level for potential losses. It does not describe a quantile or cutoff loss. 
Option 3: 'variance' — Variance measures the dispersion of outcomes around the mean, capturing volatility, not a specific loss threshold at a probability. It is about spread, not a probabilistic bound on losses. 
Option 4: 'the expected shortfall' — Also known as conditional value at risk (CVaR), this metric gives the average loss given that the loss exceeds the VaR threshold. It describes tail-average losses beyond the VaR, not the single threshold itself. 
Thus, comparing the definitions, the statement most consistent with a fixed probabilistic loss threshold is the value at risk, while the other options refer to related but distinct risk measures or statistics.

ERMCPS5350_006_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 8. Quiz for Class 8

An amount at a certain probability losses will be less than is known as the

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