Risk profiling: the post-model report

The business problem

It is renewal season at Helios Re. SunCoast Insurance — the Florida-based cedent behind three of the five contracts in the portfolio — wants its reinsurance program renewed, and its broker has sent the submission: the package of exposure data, historical losses, and desired structure that opens every placement.

The catastrophe modeller has run SunCoast’s exposure data through the vendor models. Now comes the deliverable this story is about: the post-model report — the write-up of model output that characterizes the cedent’s exposure and subject loss for the underwriter, before any contract is applied. Names for this artifact vary by organization — modelling summary, account analytics report — but every reinsurer with a modelling team produces some version of it.

The underwriter will not rerun the models. They will read this report and decide how to structure and price the renewal. That makes the report’s job precise: answer the questions the underwriter would otherwise have to guess at.

• What arrived, and does it behave? Which loss sets, from which models, and do they reconcile?
• Where is the book exposed? The book is the set of risks SunCoast has underwritten — the policies whose losses this submission is asking Helios Re to help carry. Which perils, geographies, and lines of business carry the risk?
• What does the subject loss look like? Expected loss, volatility, and — above all — the tail.
• What drives the tail? One giant event, or many medium ones? Which peril, which geography?

Everything in this story uses tools the Analytics Toolkit already built: trials and TELTs, EP curves, and the metrics EL, VaR, and TVaR. This is the Toolkit exercised end to end on a real task — measuring the object before anything transforms it.

The pipeline at a glance

Everything left of the loss sets — exposure data preparation, geocoding, model configuration — is the catastrophe modelling process itself, and stays out of scope here (the trial worldview section sketches where trials come from; model internals are a discipline of their own). Our pipeline starts where the model output arrives: one loss set per peril, each a TELT.

This split is the normal state of affairs, not an inconvenience. Hurricane and earthquake come from different models — often different vendors — with different event catalogs. A submission covering two perils arrives as two loss sets, and nothing guarantees they agree on schema, units, or conventions until you check.

In Practice

We assume here that each loss set arrives as a TELT we can consume directly. Not every vendor obliges. Some ship only an ELT — events with rates but no trial structure — and leave you to sample it into a TELT first, drawing occurrences per trial from each event’s rate and assigning timestamps before any aggregate or portfolio metric is possible. That sampling step is its own topic, not yet covered on the site; we are tracking it for a future Toolkit addition.

Step 1: validate and reconcile the loss sets

Before any metric is quoted, the analyst answers a quieter question: do these loss sets behave? The workflow is the same everywhere, even when the tooling differs:

1. Validate each loss set at the ingestion boundary — schema, sign convention, trial range. One assert per invariant.
2. Compute standalone metrics per loss set — each peril’s distribution on its own.
3. Combine and recompute — the same metrics on the union of loss sets.
4. Reconcile — check that standalone and combined views relate the way arithmetic says they must.

The reconciliation step has teeth because expected loss and the tail metrics behave differently under combination — and only one of them gives an exact check. Expected loss is a mean, and trial by trial the combined loss simply is the hurricane loss plus the earthquake loss, so the means add exactly:

$$\text{EL}_{\text{combined}} = \text{EL}_{\text{HU}} + \text{EL}_{\text{EQ}}$$

That identity is the check: if the combined EL is anything other than the sum of the parts, something is structurally wrong — duplicated rows, a dropped trial, a join gone bad. A quantile carries no such identity. The combined $\text{VaR}_\alpha$ is not the sum of the standalone VaRs, and — as the numbers below show — the difference is not an error to chase but the first sight of diversification.

helios_re/loss_set_reconciliation.py Python

▶ Run Reset

The output, as a table:

Loss set	Rows	EL	Std	VaR(90%)	TVaR(90%)	Max
HU	400	$254.6M	$133.0M	$471.8M	$532.4M	$593.0M
EQ	1,257	$21.0M	$6.9M	$31.2M	$32.7M	$34.2M
Sum		$275.6M		$503.0M	$565.1M
Combined	1,657	$275.6M	$135.3M	$489.1M	$552.6M	$616.2M

The EL check passes exactly: $254.6M + $21.0M = $275.6M, matching the combined book and the average loss the Toolkit established for SunCoast.

The tail is the more interesting half. The standalone VaR(90%)s sum to $503.0M, but the combined VaR(90%) is $489.1M — $14M lower, and the reason is concrete. With $N = 20$ trials the 90% tail is the second-worst year ($k = 2$); hurricane’s second-worst year is trial 2, earthquake’s is trial 12 — different years. The $503.0M sum implicitly prices a year in which both perils hit their second-worst at once, which never happens in the data. The combined VaR instead reads the second-worst total year, trial 2, where earthquake contributed only $17.3M rather than its own $31.2M peak. That $14M shortfall is diversification: the perils reach their tails in different trials, so the book’s tail comes in under the sum of its parts.

The sum of standalone VaRs is worth naming, because it is the no-diversification benchmark — the tail the book would carry if the two perils always peaked together (the comonotonic case, in which VaR genuinely does add). The distance from that benchmark down to the combined tail is the first quantitative glimpse of diversification benefit; the portfolio roll-up story measures it properly, across many contracts at once. One honest caveat on the benchmark: plain VaR is not guaranteed to fall below the standalone sum the way it does here — it is the reason the site prefers TVaR, which is sub-additive and can never exceed the sum of standalone TVaRs. Here VaR behaves; the analysis can proceed.

Watch Out: diversification can raise VaR

The qualifier “the way it does here” is deliberate. Take two independent exposures, each paying $100M with probability 6% and nothing otherwise. A 6% loss sits past the 1-in-10 cutoff, so each standalone $\text{VaR}_{0.90}$ is $0 — and so is their sum. But combine them: the chance that at least one pays rises to $1 - 0.94^2 \approx 11.6\%$, which clears the 10% tail, so the combined $\text{VaR}_{0.90}$ is $100M — above the $0 sum. Nothing became riskier; pooling merely pushed a loss across the single quantile VaR reads, and VaR, blind to everything past that point, was fooled. This is the formal statement that VaR is not sub-additive, and low-frequency, weakly-correlated catastrophe risk — most of a cat reinsurer’s book — is exactly where it bites. TVaR averages the whole tail, so a loss cannot hide just beyond the cutoff, and it can never exceed the standalone sum.

From the Field

A loss set once arrived from an accounting-system extract with losses as negative values — that system’s house convention. Nothing crashed. Combining it with the other perils’ loss-positive data quietly reduced the book’s total modelled loss, and every tail metric shrank. The error surfaced weeks later, in a pricing review, as “why did the combined book get safer when we added a peril?” A one-line sign assertion at ingest — the same one in the code above — would have caught it the moment the file arrived.

Key Insight

Reconciliation is regression testing for data. Standalone metrics are the unit tests; the combined view is the integration test; the additivity of EL is the invariant that must hold exactly. But like any single assertion it is necessary, not sufficient: a matching EL catches structural breakage — duplicated rows, dropped trials, bad joins — yet says nothing about the tail or about the order of events within a trial. Two loss sets can share an expected loss and still differ where it matters — sparse, heavily-layered books can post near-identical ELs over very different tails, and EL is blind to within-trial sequencing, which aggregate contracts depend on. Treat a reconciliation failure like a failing build; treat a reconciliation pass as one green test, not a clean bill of health.

Step 2: the exposure picture

With the loss sets verified, the report turns to the book itself. The TELT’s tiv column — the total insured value each occurrence touched — lets the report characterize the book from the model-output side along three axes the underwriter will structure against:

• Concentration — which perils, geographies, and lines of business the loss falls on. We measure this as each slice’s expected annual loss: its share of the $275.6M book EL, computed by averaging the slice’s loss across the 20 trials. Summed over any one dimension, these contributions add back to the book EL, so the chart below is a decomposition of expected loss, not a pile of unrelated totals.
• Exposed value — how much insured value stands behind each slice (the TIV the events touched), which says whether a concentration of loss reflects a large book or an unusually severe one.
• Severity — how hard events damage what they touch, read as the aggregate damage ratio, $\sum \text{loss} / \sum \text{tiv}$ over the slice. Severity that is uniform across slices is reassuring; an outlier slice is where a data problem would surface.

Hurricane Earthquake

SunCoast expected annual loss by geography — each geography's mean contribution to a year's loss, the seven bars summing to the book's $275.6M expected loss. Labels show each geography's share; hover for the aggregate damage ratio. Texas — not Florida — carries the largest share.

The same view in numbers, by peril — expected annual loss is each peril’s contribution to the book EL, so these are exactly the per-loss-set ELs from the reconciliation table above:

Peril	Expected annual loss	Share	Damage ratio
Hurricane (FL, GA, MS, LA, TX)	$254.6M	92.4%	11.6%
Earthquake (CA, AZ)	$21.0M	7.6%	12.2%

Three observations carry into the report:

• This is a hurricane book. 92% of expected loss is hurricane, on an exposed value many times the earthquake book’s. The earthquake exposure is genuinely secondary — SunCoast writes it at roughly a third of market scale (the Helios Re data notes record the 0.35 scaling), and the loss sets reflect that.
• The footprint is Gulf-wide, not Florida-shaped. Texas carries 36.4% of expected loss — more than twice Florida’s 15.9%. A reader who knows SunCoast as “the Florida cedent” learns something here, and so does the underwriter renewing a Florida-only layer: most of this book’s expected loss falls outside that layer’s geography.
• Severity is homogeneous. Aggregate damage ratios sit between 10.1% and 13.4% across every peril, geography, and line of business. No slice shows the implausibly high or low severity that usually signals an exposure-data problem. For a report whose reader cannot rerun the model, this is the data-quality signal that matters.

helios_re/exposure_summary.py Python

▶ Run Reset

In Practice

A full post-model report has an exposure-input half as well: TIV by county, construction and occupancy mix, data-quality grading of the cedent’s schedule. That half is produced inside the cat modelling process, from the exposure data itself — it cannot be derived from a TELT, and this site deliberately treats it as upstream (see the TIV caution: exposed TIV is not book TIV). What a TELT supports is the model-output half you see here — and in practice that is the half the underwriter’s structuring questions hang on.

Step 3: the subject loss profile

The core of the report is the distribution itself. One chart and one table characterize the subject loss the way the Toolkit taught: per-peril and combined AEP curves, then the headline metrics with return periods.

Combined Hurricane loss set Earthquake loss set

SunCoast subject loss AEP curves per loss set (20 trials, log return-period axis). The earthquake curve hugs the bottom of the chart at this scale — that flatness is the finding: the tail of the combined book is a hurricane tail.

Metric	Value	Reading
EL	$275.6M	Mean annual loss across all 20 trials
Std (CV)	$135.3M (0.49)	Volatility around the mean
AEP VaR(80%)	$378.2M	1-in-5 annual loss
AEP VaR(90%)	$489.1M	1-in-10 annual loss
AEP TVaR(90%)	$552.6M	Average of the worst 10% of years
AEP VaR(95%)	$616.2M	1-in-20 annual loss — the worst trial
OEP VaR(90%)	$174.1M	1-in-10 largest single occurrence

With $N = 20$ trials, the VaR machinery is concrete enough to check by eye. Writing $L_{(r)}$ for the $r$-th largest annual loss (the order-statistic notation from the Toolkit), at $\alpha = 0.90$ the tail holds $k = 2$ trials, so $\text{VaR}_{0.90} = L_{(2)} = 489.1\text{M}$ — the second-largest annual loss — and $\text{TVaR}_{0.90}$ averages the worst two. At $\alpha = 0.95$ the tail is a single trial, so VaR, TVaR, and the maximum coincide at $616.2M: the 20-trial dataset has hit its resolution limit, a point the report must state rather than bury (more on this below).

Two structural findings ride on the chart:

• The tail is a hurricane tail. Toggle the earthquake curve and watch it hug the axis: its worst year is $34.2M, smaller than the average hurricane year. In the two tail trials that define TVaR(90%), hurricane losses are 96% of the total. Earthquake matters in the body of the distribution — a steady $10–34M every year — but contributes nothing material to the tail.
• Bad years are many-storm years. The 1-in-10 occurrence loss is $174.1M while the 1-in-10 annual loss is $489.1M. That $315M gap is multi-occurrence risk — the OEP vs. AEP distinction doing real work. SunCoast’s worst years are bad because several storms make landfall, not because a single storm is exceptionally large: the worst trial holds 29 occurrences. And the OEP curve’s flat top tells its own story — a single catalog event, a $174.1M Texas hurricane, recurs in 7 of 20 trials and single-handedly sets the occurrence tail.

The gap between the two curves below is the visual form of that finding — the aggregate (annual) curve sits well above the occurrence (single-largest) curve at every return period, and the distance between them is exactly the multi-occurrence risk:

OEP (peak occurrence) AEP (aggregate) Log scale

SunCoast subject loss EP curves (20 trials). Move your cursor over the chart for details. The dashed AEP curve is always at or above the solid OEP curve — the gap reflects multi-occurrence risk.

The profile itself composes the pieces the Toolkit already provides — build the AEP and OEP curves, read off the metrics, attribute the tail:

helios_re/risk_profile_report.py Python

▶ Run Reset

Watch Out

“The 1-in-20 loss is $616.2M” does not mean a worse year is impossible — it means the 20-trial sample cannot see past its largest member. Quoting VaR(95%) from 20 trials as if it had the same evidential weight as VaR(95%) from 100,000 trials is a category error. A real report quotes tail metrics only where the trial count supports them, and says so explicitly.

What the underwriter reads off this page

The report exists to drive decisions, so let’s close the loop: here is what each finding means to the person structuring the renewal.

Finding	Underwriting implication
Tail is 96% hurricane	Tail-protecting structures should attach on the hurricane book; earthquake needs no occurrence protection of its own
Bad years are many-storm years ($315M OEP–AEP gap)	A single occurrence layer will be hit repeatedly in bad years — reinstatement terms and aggregate protections are where the negotiation lives
Texas carries 36% of expected loss; Florida 16%	A Florida-only layer leaves most of the book’s expected loss outside its geography — the renewal conversation should ask whether that is intentional
One catalog event sets the OEP plateau	The occurrence tail is concentrated, not smooth — per-event terms are sensitive to a handful of catalog entries
Damage ratios homogeneous (10.1–13.4%)	No exposure-data red flags visible from model output
20 trials → resolution floor at 1-in-20	Quotes beyond VaR(90%) need a larger trial set before anyone prices off them

None of this is a structuring decision — attachment points, limits, and prices belong to the next story in this chapter, where contract terms start transforming this distribution. The post-model report’s job ends where it should: the underwriter now knows what the object looks like before anything reshapes it.

At production scale

The 20-trial walkthrough is the real workflow in miniature; three things change with the zeros.

Trial and row counts. Production loss sets run 10,000 to 1,000,000+ trials, and the row count is the trial count times the events per trial — which depends on the peril’s frequency. A hurricane book might see a handful of occurrences per trial; a high-frequency peril like earthquake can average on the order of a thousand. At a million trials, that is around 10⁹ rows for a single loss set. The metrics do not change shape — each is a groupby plus a sort, $O(\text{rows})$ and $O(N \log N)$ — and at 10⁷ rows the pandas library runs them in seconds in memory. At 10⁹ rows on one loss set, in-memory pandas is no longer the right tool: this is where columnar formats, chunked or out-of-core aggregation, and pushing the groupby into a query engine start to matter. What the extra trials buy is not speed but resolution: the 1-in-200 and 1-in-500 quotes that capital decisions need and 20 trials cannot see.

Loss-set multiplicity makes it a big-data problem. Two loss sets here, for one cedent’s submission; a reinsurer’s portfolio fans out far wider. A single reinsurer might write on the order of a thousand programs across its cedents, each program covering several peril-and-LOB combinations and modelled across multiple vendors, model versions, and climate assumptions — tens of thousands of loss sets to track across the portfolio, before any are combined. Reconciliation stops being a sanity check and becomes the backbone of the workflow: every loss set validated, every combination accounted for, and the “which loss sets entered this report?” question answered precisely. That makes loss sets named, versioned inputs, not files on a share — and it is combining dozens of them into the portfolio view, not profiling any one, where performance actually bites.

Reproducibility. This chapter’s standing principle applies with no modification: the report is a pure function of (loss sets, parameters). Same inputs, same report, byte for byte. When the vendor ships a model update and the loss sets regenerate, the report regenerates with them — automatically, not by an analyst re-running notebook cells in the right order. The moment a post-model report is hand-assembled, two reports for the same submission can disagree, and the underwriter is back to guessing which one to trust.

Consider

Post-model reporting should be a build artifact, not a document. Generate it from versioned inputs with a pipeline; render it to whatever the underwriter wants to read. Teams that hand-craft these reports spend their week formatting; teams that generate them spend it on the one thing a machine cannot do — deciding what the numbers mean.

That is the first application story: the Toolkit’s metrics, composed into the artifact that starts every deal. The next story hands this risk profile to the underwriter’s structuring problem, where financial terms begin transforming the distribution the report just measured.