What an Event Loss Table Records
A catastrophe model may generate thousands of possible events, each with a modeled annual occurrence rate and an estimated loss to an insured portfolio. An event loss table (ELT) organizes those results so that each event remains identifiable and its rate stays paired with its loss. That pairing matters: the table is not merely a list of loss amounts, because the same loss amount may arise from events with different rates.
For this tutorial, assume each event row represents one modeled occurrence, and its loss is the portfolio loss for that occurrence after the applicable policy terms have been applied. The annual occurrence rate is the expected number of occurrences of that event per year. It is not automatically the probability that the event occurs during a year. If the model represents each event type as a Poisson process, its annual rate is the Poisson frequency parameter; other annual occurrence models require their own probability interpretation.
An event identifier is essential even when two rows have identical losses. The rows may have different annual rates, belong to different perils, or represent separate modeled events that can each occur. Combining them into one row without adding their rates and retaining the relevant labels can destroy information needed for later analysis.
Build the Table in a Controlled Sequence
A reliable construction process starts by defining what the loss represents, then aligns the event-level rate and loss on a consistent event key. If the model output is at location level, first apply or receive the applicable policy-level calculations, then aggregate the location losses within each event. Do not sum losses across different events: those are alternative possible occurrences, not components of one occurrence.
Specify the portfolio, coverage, peril, currency, and whether event loss is gross or net of the relevant policy terms and inuring recoveries.
Use the model's event identifier, together with any necessary event-set or version identifier, to distinguish separate modeled occurrences.
Join each event's annual rate to its loss on the same key. Confirm that rates use the same time basis and that losses use consistent units.
Where records are location-level, sum the relevant location losses for that event and loss basis. Retain separate event rows even if their aggregated losses are equal.
Check event counts, missing rates or losses, duplicate keys, nonnegative values where appropriate, and summary totals. Keep enough labels to reproduce the selected table.
A zero-loss event can be meaningful: the event is in the catalog, but it produces no loss to the stated portfolio on the stated basis. Keeping it may be useful for catalog completeness and reconciliation. For loss-weighted calculations it contributes zero, but it still contributes to modeled event frequency if its rate is included in the table's frequency scope.
Why the Rate Weights the Loss
Let event \(j\) have annual occurrence rate \(\lambda_j\) and event loss \(L_j\). If each event type occurs according to a Poisson process, the expected annual number of occurrences of event \(j\) is \(\lambda_j\). Each occurrence contributes \(L_j\), so the expected annual loss contribution is \(\lambda_jL_j\). Summing contributions gives the table's expected annual loss.
The same weighting constructs a severity distribution conditional on an event occurrence from the table's event set. The total event rate is \(\Lambda=\sum_j\lambda_j\); the share of occurrences represented by event \(j\) is \(\lambda_j/\Lambda\). Thus an event's loss is sampled with its rate share, not with equal weight merely because it occupies one row.
This conditional average is not the expected annual loss. It is average loss per occurrence under the table's rate-weighted event distribution. The expected annual loss has units of currency per year; the conditional average has units of currency per occurrence. The identity between them is \(\operatorname{E}[\text{annual loss}]=\Lambda\operatorname{E}[L\mid\text{occurrence}]\) under the stated event-frequency interpretation.
Worked Table Construction
Worked Example: Build a Rate-Weighted Event Summary
A hypothetical portfolio has three modeled wind events. Losses are in thousands of dollars and are already stated on the desired portfolio basis. Construct the basic ELT and calculate its total event rate, rate-weighted mean loss per occurrence, and expected annual loss.
| Event ID | Annual rate | Event loss ($000) |
|---|---|---|
| W-11 | 0.20 | 0 |
| W-24 | 0.30 | 100 |
| W-38 | 0.10 | 400 |
Step 1: Total rate. Add the annual occurrence rates: \(0.20+0.30+0.10=0.60\) occurrences per year.
Step 2: Rate-weighted loss total. Multiply each loss by its rate: W-11 contributes \(0.20(0)=0\), W-24 contributes \(0.30(100)=30\), and W-38 contributes \(0.10(400)=40\), all in thousands of dollars per year. The total is \(70\) thousand dollars per year, or \(\$70,000\) per year.
Step 3: Mean loss per occurrence. Divide the rate-weighted loss total by the total rate: \(70/0.60=116.6667\) thousand dollars per occurrence. Rounded only at the final step to the nearest dollar, this is \(\$116,667\).
Check. The total rate times the unrounded mean is \(0.60(116.6667)\approx70.0000\) thousand dollars per year, agreeing with the direct sum. The zero-loss event affects the total frequency but not the loss total. The common mistake is to average the three losses equally, which would give \(166.6667\) thousand dollars and ignores that their occurrence rates differ.
Worked Example: Aggregate Location Losses by Event
A hypothetical model export gives two location losses for each event. The location losses are already net of the applicable policy terms, in thousands of dollars. Each event has one annual rate. Construct one row per event, then calculate expected annual loss and the rate of events whose total loss exceeds \(\$250,000\).
| Event ID | Annual rate | Location A ($000) | Location B ($000) |
|---|---|---|---|
| C-4 | 0.08 | 120 | 80 |
| C-9 | 0.12 | 50 | 150 |
| C-12 | 0.05 | 0 | 300 |
Step 1: Aggregate within event. C-4 has \(120+80=200\) thousand dollars; C-9 has \(50+150=200\) thousand dollars; C-12 has \(0+300=300\) thousand dollars. These sums form the event losses. Do not add losses from C-4 and C-9 together: they are separate event occurrences.
Step 2: Calculate expected annual loss. The contributions are \(0.08(200)=16\), \(0.12(200)=24\), and \(0.05(300)=15\) thousand dollars per year. The sum is \(55\) thousand dollars per year, or \(\$55,000\) per year.
Step 3: Record threshold rate. Only C-12 has event loss strictly greater than \(\$250,000\). Its event rate is \(0.05\) per year. This is an exceedance rate for the event losses in this table, not by itself a probability of at least one such event in a year.
Check. The total rate is \(0.08+0.12+0.05=0.25\) per year. The rate-weighted mean loss per occurrence is \(55/0.25=220\) thousand dollars; multiplying \(220\) by \(0.25\) returns \(55\) thousand dollars per year. The common mistake is to treat the two \(\$200,000\) events as one event because their losses match; their identifiers and rates must remain distinct.
Worked Example: Preserve Threshold and Identity Information
A hypothetical event catalog has the following post-term event losses, in thousands of dollars. Construct a compact ELT summary and calculate both the rate for losses strictly greater than \(\$250,000\) and the rate for losses at least \(\$250,000\). Also calculate the expected annual loss.
| Event ID | Annual rate | Event loss ($000) |
|---|---|---|
| R-03 | 0.15 | 300 |
| R-17 | 0.20 | 250 |
| R-22 | 0.05 | 500 |
Step 1: Calculate the loss contributions. R-03 contributes \(0.15(300)=45\), R-17 contributes \(0.20(250)=50\), and R-22 contributes \(0.05(500)=25\), all in thousands of dollars per year. Their sum is \(120\) thousand dollars per year, or \(\$120,000\) per year.
Step 2: Apply the threshold wording literally. For loss strictly greater than \(250\), R-03 and R-22 qualify, so the rate is \(0.15+0.05=0.20\) per year. For loss at least \(250\), all three qualify, so the rate is \(0.15+0.20+0.05=0.40\) per year.
Step 3: Check the summary. Total event rate is \(0.40\) per year. Mean loss per occurrence is \(120/0.40=300\) thousand dollars. Then \(0.40(300)=120\) thousand dollars per year, matching the direct calculation. The common mistake is to include the \(\$250,000\) row in a strictly-greater-than threshold.
Checks, Scope, and Common Traps
A well-built ELT makes later frequency, severity, and exceedance calculations reproducible. It should preserve the event-level observations and their rate weights rather than presenting only a single summary number. Useful checks include:
- Key integrity: each row has a valid event identifier, and duplicate identifiers are investigated rather than silently removed.
- Rate integrity: rates are nonnegative, expressed on the same annual basis, and attached to the intended event records.
- Loss integrity: losses use consistent units and a clearly stated gross or net basis; missing values are not silently interpreted as zero.
- Aggregation integrity: location or coverage amounts are combined within the event and portfolio definition, not across separate events.
- Reconciliation: calculate \(\sum_j\lambda_j\), \(\sum_j\lambda_jL_j\), and selected threshold-rate sums directly from the retained rows.
An event rate, an event probability, and an exceedance probability are different quantities. For example, under independent Poisson event processes, the probability of at least one occurrence from a set of event types with total rate \(\Lambda\) is \(1-e^{-\Lambda}\). That conversion depends on the Poisson assumption; do not label a rate as a probability or apply this conversion automatically when the model uses a different annual occurrence construction.
An ELT also does not, by itself, specify which events occur together in a simulated year. Event-level losses and rates can support occurrence-based summaries, but an annual aggregate loss calculation requires a model for annual event counts, event dependence, and any additional uncertainty. Preserve the catalog identity and rate information so those assumptions can be applied in the appropriate subsequent analysis.
Check Your Understanding
For each problem, use the stated loss basis and units. Treat an event rate as an annual occurrence rate, not as an annual probability unless the problem explicitly states otherwise.
- A hypothetical ELT has events with rates \(0.12, 0.08,\) and \(0.05\) per year and losses of \(\$0,\$200,000,\) and \(\$600,000\), respectively. Find the total event rate and expected annual loss. (Answer: \(0.25\) occurrences per year; \(\$46,000\) per year.)
- Three distinct event IDs have rates and losses \((0.10,\$80,000)\), \((0.20,\$80,000)\), and \((0.05,\$400,000)\). Find the rate-weighted mean loss per occurrence and expected annual loss. (Answer: \(\$125,714.29\) per occurrence; \(\$44,000\) per year.)
- A hypothetical event export gives two location losses, in thousands, for each event: A has rate \(0.06\) and losses \(40,60\); B has rate \(0.04\) and losses \(250,50\). Aggregate by event, then find expected annual loss and the rate for event losses strictly greater than \(\$200,000\). (Answer: event losses \(\$100,000\) and \(\$300,000\); expected annual loss \(\$18,000\) per year; exceedance rate \(0.04\) per year.)
- Event P has rate \(0.03\) and loss \(\$500,000\); Q has rate \(0.06\) and loss \(\$200,000\); R has rate \(0.01\) and loss \(\$700,000\). Find the rates for losses strictly greater than \(\$500,000\) and at least \(\$500,000\). (Answer: \(0.01\) and \(0.04\) occurrences per year, respectively.)
- Two independent Poisson event types have annual rates \(0.20\) and \(0.30\), with losses \(\$100,000\) and \(\$400,000\) per occurrence. Find their total expected annual loss and the probability of at least one occurrence of either type in a year. (Answer: \(\$140,000\) per year; \(1-e^{-0.50}=0.3935\).)