Portfolio analytics

The business problem

The risk-profiling and standalone-pricing applications each lived inside a single deal: the post-model report characterised one cedent’s losses; the pricing application judged one program’s premium. Both deliberately ignored the rest of Helios Re’s portfolio. This page zooms all the way out to the questions the portfolio manager is paid to answer — not about any one contract, but about everything Helios Re has written:

What is the risk posture of the whole portfolio — how much can it lose, where is that risk concentrated, and is it earning enough premium for the risk it carries?

Answering them is not only reporting. The portfolio manager also plays a strategic role: advising underwriters about gaps and opportunities in the portfolio, and running proforma analyses of speculative future business to see how the portfolio would respond.

That is portfolio analytics: it produces the metrics, views, and quantified relationships from which the business makes informed strategic and tactical decisions. Its prerequisite is the roll-up — the mechanical task that reduces the portfolio to one loss distribution. The pipeline starts with that roll-up; the analytics built on it are the objective. Standalone pricing also left a promissory note: a program that looks underpriced in isolation may be perfectly fine once it sits beside uncorrelated business, because it adds far less to the portfolio’s capital than it needs alone. Here, that note comes due: we roll the six contracts into one portfolio, measure it, slice it, and settle whether the portfolio — not any single deal — earns its keep.

In Practice

At some reinsurers “Portfolio Manager” is a job title in its own right; at others the work sits with the Head of Cat Modelling or the Head of Exposure Management. The CRO and CUO rarely do the operational work, but they own the responsibility for the portfolio and steer it strategically — with the portfolio manager as their executive and enforcer. What all these arrangements share is the scope: the portfolio’s aggregate risk and return, not individual placements. The personas chapter draws the org chart; this page is one slice of the job.

The pipeline

Portfolio analytics runs as a pipeline of five steps, and every one reuses machinery from the earlier chapters — only the scope is new. The pipeline is deliberately generic: nothing in it is specific to Helios Re, and a slice of the portfolio runs through it exactly as the whole does.

Step	What happens	Built in
1. Select the constituents	Define the portfolio: choose contracts — by business unit, line of business, binding status — at the reinsurer’s participations	Portfolios
2. Roll up	Sum the participated losses per occurrence and per trial into the portfolio’s loss distribution	Portfolios
3. Measure the risk posture	EL, VaR, TVaR, capital on the portfolio distribution — the diversification the portfolio view carries implicitly	Metrics
4. Slice	Repeat the pipeline on narrower selections to find concentrations	this page
5. Weigh risk vs opportunity	Expected loss and capital cost against booked premium — per portfolio	this page

Step 1: select the constituents

A portfolio is a selection, and to start with we select everything: Helios Re’s whole enterprise portfolio — the six base contracts, each written at a participation share placed alongside a panel of other reinsurers. A narrower selection — one business unit’s contracts, one line of business, only bound deals — would run the same pipeline unchanged. The risk-profiling and standalone-pricing applications worked the three SunCoast layers in detail; here they are three of six, sitting beside Pacific Mutual, Baltica, and Atlas Cat Fund:

Contract	Cedent	Peril · region	Participation	Booked premium
C1	SunCoast	Hurricane · US (FL)	14.5%	$2.90M
C2	SunCoast	Earthquake · US (CA/AZ)	20%	$1.00M
C3	SunCoast	All-US backstop (net of C1, C2)	10%	$1.30M
C4	Pacific Mutual	Earthquake · US (CA)	25%	$3.25M
C5	Baltica	Windstorm · EU	30%	$5.10M
C6	Atlas Cat Fund	Earthquake · Japan	15%	$3.30M
Portfolio				$16.85M

The premium is Helios Re’s own share — the 100% layer premium scaled by the participation, just as the losses will be. The portfolio earns $16.85M for carrying its slice of these six contracts. What the portfolio carries in return for that premium is the subject of the remaining steps — starting with the roll-up, which produces the loss distribution everything else reads.

Step 2: roll it up

The roll-up is one operation: for each trial, take every contract’s gross loss — the amount ceded to Helios Re — at its participation and add them together. Do it across all 20 trials of the demo tier and the portfolio becomes a single loss distribution.

C1 · SunCoast FL hurricane C2 · SunCoast CA/AZ quake C3 · SunCoast All-US backstop C4 · Pacific CA quake C5 · Baltica EU windstorm C6 · Atlas JP quake

Helios Re's portfolio rolled up trial by trial. Each bar stacks the six contracts' ceded loss at their participation shares; the full height is the portfolio's ceded loss in that trial. Hover a segment or a legend entry to follow one contract across all trials. The peaks land in different trials — SunCoast's Florida hurricane (C1) tops out in trials 9 and 19, Baltica's European windstorm (C5) in trial 5, Atlas's Japanese quake (C6) in trial 14 — so no single trial stacks every contract's worst. That staggering is the diversification the metrics below put a number on.

The staggering is the point of this picture. The portfolio’s worst trial — trial 9, at $24.9M — is dominated by Florida hurricane: C1 tops out at its $8.7M capped share and Baltica’s windstorm contributes a further $7.7M, while the SunCoast All-US backstop does not contribute at all. Trial 4, by contrast, is driven by C6 (a $7.0M Japanese-quake share) with only a small loss from C1. No single trial stacks every contract’s worst. That is not luck: Atlantic hurricane, European windstorm, and Japanese earthquake are uncorrelated perils, so the probability that each peril’s rare large events fall in the same trial is very small — and the simulation reflects it, with no trial containing every peril’s worst.¹ Step 3 quantifies this staggering as a capital number.

Step 3: the risk posture

With the portfolio reduced to one distribution, its EP curve and metrics follow by exactly the machinery the Toolkit built — a portfolio distribution is another loss distribution:

AEP (trial aggregate) OEP (largest occurrence)

The portfolio's EP curves from the roll-up; hover for the metrics at any return period. AEP is the trial-aggregate view the capital metrics below read from: the 1-in-10-year loss is $22.08M, and the dotted line marks the expected loss — the AEP curve spends most of its width above it. OEP is the largest single occurrence per trial — its 1-in-10 loss is $5.00M.

Portfolio metric (AEP)	Value	What it says
Expected loss (EL)	$14.59M	The losses the portfolio covers in an average year
Probability of a loss	100%	Every trial produces a claim — this portfolio pays every year
$P(L \geq \text{EL})$	60%	A worse-than-average year, in 12 of 20 trials
VaR(90%)	$22.08M	The 1-in-10 year — exceeded one year in ten
TVaR(90%)	$23.51M	The average of the worst 10% of years
Capital $K = \text{TVaR} - \text{EL}$	$8.92M	The unexpected loss capital must stand behind

The capital row deserves unpacking, because it is where the risk posture reaches the balance sheet. As the standalone pricing application established, a well-priced contract covers its expected loss with premium — so a portfolio of well-priced contracts should earn enough premium to cover the portfolio’s EL. Losses beyond the expected are what the reinsurer’s own capital must absorb, and at the house 90% confidence level that means holding $K = \text{TVaR}(90\%) - \text{EL}$ — the average excess over expected loss across the worst 10% of trials.

This is the risk posture of the portfolio: it expects to pay $14.6M in claims a year — and a worse-than-average year is not rare, arriving in 12 of 20 trials. A 1-in-10 year runs to $22M, and against the tail beyond the expected the reinsurer must hold $8.9M of capital. Every one of these is read off the portfolio EP curve above — the same read the risk-profiling and standalone-pricing applications did on a single cedent, now on the whole portfolio.

Watch Out

With only 20 trials, VaR(90%) is the second-worst trial and TVaR(90%) averages the worst two — a thin tail, one storm away from noise, as the standalone pricing application flagged. The roll-up method is exact at any trial count; the numbers here are as trustworthy as 20 trials allow. A production portfolio rolls up hundreds of thousands of trials, which smooths that noise out across many more tail trials. The demo data’s 1,000-trial tier shows the effect in miniature.

helios_re/portfolio_rollup.py Python

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The diversification, carried implicitly

The standalone pricing application found diversification within SunCoast’s program — $32.7M of capital the three layers saved by not peaking together — and promised the same effect operates between programs, across the whole portfolio. The portfolio numbers above already contain it. To make it visible once, compare them against the same six contracts measured standalone, each on its own participated losses:²

Metric: TVaR(90%) EL

Contract, standalone Naive sum Portfolio, combined

Each contract's standalone value at its participation, the sum of those values, and the portfolio's own. On the TVaR(90%) view the portfolio ($23.5M) sits $13.0M below the sum of the standalone tails ($36.5M) — a 35.6% diversification benefit, because the contracts do not reach their worst losses in the same trials. Toggle to EL and the two summary bars are identical ($14.59M): expected loss adds exactly, so the entire reduction lives in the tail.

The six standalone tails sum to $36.54M; the portfolio’s tail is $23.51M. The portfolio carries $13.02M less tail risk than the sum of its parts — a 35.6% reduction — for exactly the reason the roll-up chart showed. The contracts reach their worst losses in different trials, so the portfolio’s worst trial is milder than the sum of each contract’s worst trial. The same comparison in capital, with the numbers filled in:

$$\begin{aligned} K^{\text{portfolio}} &= \text{TVaR} - \text{EL} &&= 23.51 - 14.59 &&= 8.92 \\ \textstyle\sum_i K_i &= \textstyle\sum_i \text{TVaR}_i - \textstyle\sum_i \text{EL}_i &&= 36.54 - 14.59 &&= 21.94 \end{aligned}$$

The EL term is the same $14.59M in both lines, because expected loss adds exactly — so the capital difference equals the tail difference: $21.94 - 8.92 = 13.02$. Put as a multiplier, $21.94 / 8.92 = 2.46$: per dollar of required capital, the diversified portfolio supports 2.46× the business the same contracts would support standalone — its capital efficiency.

In practice nobody runs this comparison deal by deal. Adding up standalone TVaRs is exactly the mistake the roll-up exists to avoid, and once a contract is written, its standalone performance is close to irrelevant — the desk watches the portfolio facts: premium income, expected loss, capital at risk, return on capital, and each contract’s contribution to them. The diversification is not a step in the pipeline; it is a property the portfolio view carries implicitly. It is made explicit here once because it is the reason the portfolio view and the standalone view disagree — and the reason the marginal pricing application will price new deals against the portfolio.

Key Insight

Diversification lowers the capital, never the expected loss. The portfolio still expects $14.59M of claims whether the contracts sit on one portfolio or are split across six reinsurers; what combining them changes is the tail, and with it the capital behind it. This is the mechanical reason a reinsurer values an uncorrelated risk more highly than a correlated one of the same expected loss: it adds less to the portfolio’s tail, ties up less capital, and clears a lower price. Step 5 applies the effect to Helios Re’s premium arithmetic.

Step 4: slice the portfolio

A single tail number is a summary; the portfolio manager’s next question is where the risk lives. In the pipeline above, a slice is nothing new: it is a narrower selection — include or exclude whole contracts by business unit, line of business, or binding status, at the same participations, and roll up again. And because the portfolio YELT preserves occurrence detail, a slice can also cut within contracts by peril or region. Each subportfolio produced this way gets its own metrics and its own risk-versus-opportunity verdict, which is how reinsurers actually manage: business units, lines of business, and capital sources are steered individually, each against its own objectives as well as the enterprise’s.

The simplest slice is expected loss along the contracts’ tags. EL is additive, so it slices cleanly — region, peril, cedent — and the slices always sum back to the portfolio’s $14.59M:

Slice by: Region Peril

Where the portfolio's expected loss lives. Expected loss is additive, so every slice sums back to the portfolio's $14.59M — no diversification credit hides inside EL. By region the portfolio is roughly half US ($6.99M), a third European windstorm ($4.80M), a fifth Japanese quake ($2.81M); by peril, earthquake is the largest single exposure at 43%. The tail concentrates differently from EL, which is why a portfolio manager slices both.

The portfolio is roughly half US exposure, a third European windstorm, a fifth Japanese quake; by peril, earthquake is the single largest line at 43%, spread across three cedents and two continents. This is where a portfolio manager earns the title. A portfolio that looks diversified by cedent can still be concentrated by peril — Helios Re’s earthquake exposure spans SunCoast, Pacific Mutual, and Atlas, so a rethink of earthquake pricing or retro touches three placements at once. Slicing the same EL two ways surfaces exactly that kind of hidden concentration.

Slices are portfolios, so they get more than an EL bar: each is rolled up and measured on its own. The code below cuts the portfolio by region and by peril and reads EL, TVaR, and capital per subportfolio — and it surfaces a subtlety. Slice ELs sum to the enterprise EL along any axis, but slice TVaRs do not: by region they sum to $30.92M against the enterprise’s $23.51M, because measuring slices apart keeps the diversification within each slice but widens it across slices.

helios_re/portfolio_slices.py Python

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Consider

Expected loss slices exactly because it is a mean, but the tail does not slice the same way. The portfolio’s worst trials are dominated by hurricane and windstorm, so US and EU exposure contribute more to the tail than their EL share suggests, and Japan less. Attributing the portfolio’s TVaR back to its contracts — a fair split of the diversified tail, not the additive EL — is a genuinely harder problem (Co-TVaR / Euler allocation), and it is what the next layer of portfolio analytics is built on. This page slices EL, which is honest and additive; the tail attribution is its own subject.

Step 5: risk versus opportunity

Now the portfolio manager can weigh the portfolio’s risk against what it earns. Three ratios, all read off numbers already in hand:

Ratio	Value	Reading
Loss ratio ($\text{EL} / \text{premium}$)	86.6%	Expected loss takes 87 cents of every premium dollar
Booked premium − EL − expenses	$1.53M	What the reinsurer earns for providing capital, after expected loss and an $\epsilon = 5\%$ expense load
RAROC	17.1%	Risk-adjusted return on the portfolio’s $8.92M of required capital

One caveat carries over from the standalone pricing framework: the booked premium is treated as fully earned revenue — no brokerage, ceding commission, or premium taxes are netted out — so these ratios share that framework’s illustrative scope. Their levels also inherit the demo portfolio’s arithmetic-convenience premiums, which run far richer than real placements.

The RAROC is the number that decides it:

$$\begin{aligned} \text{RAROC} &= \frac{\text{premium} - \text{EL} - \epsilon\,\text{EL}}{K} \\ &= \frac{16.85 - 14.594 - 0.730}{8.917} \approx 17.1\% \end{aligned}$$

Against a cost of capital of 10%, a portfolio returning 17.1% on its required capital is creating value — comfortably. The contrast with the standalone verdict is the lesson. Priced alone, SunCoast’s program earned 6.9% on capital that costs 10% — value-destroying, because a standalone deal stands behind its whole tail with its own capital and cannot lever capital already deployed for other business. Inside the portfolio, the same program’s worst trials overlap little with the Japanese earthquake and European windstorm business beside it. It shares the portfolio’s capital with other business and consumes less than it needs alone — and the identical premium now contributes to a 17.1% return. The premium did not change; the capital basis did. Helios Re’s portfolio clears a hurdle its deals cannot clear alone.

The contrast is the conclusion; the levels are not. Both returns read off a 20-trial tail — the 17.1% stands on the same two-trial TVaR the Watch Out in Step 3 flagged — so this page demonstrates how a desk reads its book; a real desk would compute the same returns from a production-scale roll-up before steering by them.

helios_re/portfolio_analytics.py Python

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From the Field

A reinsurer once ran two desks that each priced their own line to a standalone hurdle and quietly rejected anything that missed it. Both desks were individually disciplined and the combined portfolio was leaving money on the table — each was walking away from risk that was underpriced alone but accretive to the portfolio, because neither desk could see the other’s diversification. The fix was not better standalone models; it was moving the hurdle to the portfolio, where the marginal contract is judged against the portfolio it joins, not the empty room it imagines. That move is marginal pricing — and portfolio analytics is its prerequisite: you cannot price at the margin until you can measure the portfolio. The same argument makes the broader case for efficient portfolio management: a live, enterprise-level portfolio that every business unit prices and steers against, rather than each desk navigating by its own slice.

At production scale

Portfolio roll-up and analytics are arithmetic; what changes at scale is the bookkeeping around them.

Rows and trials. Six contracts across 20 trials is a toy. A real portfolio is thousands of contracts across hundreds of thousands to millions of trials, and the roll-up is a group-by-trial sum over a column that no longer fits in memory. The operation is still a sum — it moves into a query engine or a chunked, columnar aggregation, partitioned by trial and reduced. Nothing about the shape of the computation changes; the data volume does.

Alignment. The one real subtlety is that every contract’s losses must be aligned to the same trials before they are summed — the roll-up is a sum within a trial, so a mismatched trial index silently corrupts the tail. At occurrence resolution the same requirement applies to the full occurrence key, (trial_id, timestamp, event_id), and everything gets harder with it. The alignment is finer, and the key starts to dictate how the data is laid out on disk and whether a roll-up can query it or must scan it. Shared trial identity across every cedent’s YELT (the demo data’s locked trial ids) is what makes the sum meaningful. In production this is a join key you validate at every boundary.

Reproducibility. The chapter’s standing principle holds unchanged: the portfolio distribution is a pure function of (the contracts, their participations, the YELT). Same inputs, same portfolio, same capital — to the cent.³ Re-run it after a participation change and the whole portfolio reprices deterministically, with no analyst stitching spreadsheets together.

Remember

The portfolio is not a report you generate at quarter-end; it is a live object whose YELT you keep rolled up so that the next question — what does one more contract do to it? — is cheap to answer. A portfolio you can roll up in milliseconds is a portfolio you can price at the margin in milliseconds. Build the roll-up to be fast and pure, and marginal pricing is the same function called twice.

What carries forward

Portfolio analytics is the pipeline this page ran: select the constituents, roll up (participation, then sum), measure, slice, and weigh risk against opportunity. The roll-up reduces the portfolio to a single loss distribution; the analytics read from it the numbers the business steers by. For Helios Re those numbers are a $14.59M expected loss, an $8.92M capital requirement, a capital efficiency of 2.46× — the same contracts would need $21.94M measured standalone — and a 17.1% return on required capital, comfortably above the 10% hurdle. Those figures demonstrate the pipeline at demo scale; the pipeline itself, run at production trial counts, is what carries forward.

Two threads run out of this application. First, retrocession: the portfolio YELT can serve as a retro contract’s subject loss, so Helios Re can buy protection on its own portfolio — or free up the capital it ties up to write more business. Either way, the roll-up is what a retro layer attaches to. Second, and the flagship the chapter has been building toward, marginal pricing: once the portfolio is a live, rolled-up object, the value of one new contract is what it adds to the portfolio’s capital — the roll-up run twice, with and without it, and differenced. Standalone pricing asked whether a deal clears alone; marginal pricing asks whether it clears here, against this portfolio. This page built the “here.”

Footnotes

1. A European windstorm is not entirely independent of the Atlantic weather systems that drive hurricanes, but the correlation is small enough to ignore for simplicity. ↩

2. Everything in this chart is at Helios Re’s participations; the standalone pricing application worked C1–C3 at the 100% layer, so its figures are larger than the ones here. ↩

3. “To the cent” takes care: with monetary values as floating point, the order of summation affects the result — floating-point addition is not associative — so a reproducible roll-up fixes its reduction order, or uses fixed-point or decimal arithmetic. ↩