FIN.13:5.4 - A percentile leaves both a tail and a funding question

For a constructed one-period loss distribution, loss is 0 with probability 90%, 10 with probability 8% and 40 with probability 2%. Define the 95th-percentile loss as the smallest amount with cumulative probability at least 95%. It is 10: cumulative probability is 90% at 0 and 98% at 10. Expected loss is 0.90 × 0 + 0.08 × 10 + 0.02 × 40 = 1.60.

The largest loss within these three modeled cases is 40, and the 95th percentile does not remove its 2% probability. Averaging the worst 5% of this distribution gives (0.03 × 10 + 0.02 × 40) / 0.05 = 22. Because the distribution has discrete probabilities, that tail average includes part of the probability mass at 10; averaging only losses strictly greater than 10 would instead give 40 and answer a different question.

These are three summaries of the same stipulated model. Its probabilities require evidence before actual reliance, and unmodeled outcomes can exceed 40. If a case also requires cash collateral before its final gain or loss is realized, neither the expected loss 1.60 nor the percentile 10 supplies the intervening funds. Return the actual payment sequence to FIN.2.