The Loss Distribution

The Loss Distribution

VaR and expected shortfall start from a stated discrete loss distribution.

highlighted = computed this step

A stated loss distribution

Start with a stated loss distribution for one period. The losses are $-100.00, $0.00, $200.00, $500.00, and $1,500.00. Losses are signed: a negative loss is a gain, so scenario 1's $-100.00 loss is a $100.00 profit.

L∈{$−100.00,$0.00,$200.00,$500.00,$1,500.00}L\in\{\$-100.00,\$0.00,\$200.00,\$500.00,\$1,500.00\}

Exact probabilities

The probabilities are exact fractions: 3/5, 1/5, 3/20, 1/50, and 3/100. They sum to 1.

∑pi=1\sum p_i=1
Loss distributionVaR and expected-shortfall rows are recomputed from the distribution.Loss distributionScenarioLossProbabilityCumulative1$-100.003/53/52$0.001/54/53$200.003/2019/204$500.001/5097/1005$1,500.003/1001

Stated model input

The distribution is a stated model input, not an estimate from data or a forecast. In real risk work, the distribution is estimated with uncertainty, and historical outcomes need not describe the future. This is descriptive, not investment advice.

distribution is a stated input\text{distribution is a stated input}