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Joint loss and tail allocation record

A combined loss measure needs joint probabilities, not just separate marginal tables.

Omni Finance AcademyBy Omni Finance Academy
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Read the original independence assumption

Each component has 4% probability of loss 100 and 96% probability of zero. The CSV states independence and lists the four joint events. It then groups equal combined losses and records the selected 95% ES allocation.

Check the event total

Neither event occurs with probability 92.16%; only A and only B each have 3.84%; both have 0.16%. The total is 100%. Combined loss 100 therefore has 7.68% probability and loss 200 has 0.16%.

Inspect the grouped worst 5%

Include all 0.16% at loss 200 and 4.84% from the 7.68% at loss 100. Their weighted loss is 5.16 and their selected mass 0.05, giving ES 103.2. The grouping does not claim a unique allocation between equal-loss event labels.

Retain a supported dependence model

If independence is not justified, replace the joint distribution with appropriate evidence or explicit assumptions. The worksheet does not infer dependence from separate records, forecast a real loss or certify an investment allocation.

Further references