Session number: [assigned by CAS] · Casualty Actuarial Society Ratemaking, Product and Modeling Seminar

Customer Lifetime Value You Can Actually File

Pramod Misra · Georgia Institute of Technology, Atlanta

This research was funded by the Casualty Actuarial Society.
Disclosure: the author is Director of Data Analytics at an insurance agency and a partner in 5G Vector Inc., which builds commercial software for insurance agencies. No proprietary agency or vendor data was used and no commercial product is evaluated or recommended in this session.
Views expressed are my own and not necessarily those of the Casualty Actuarial Society or my employer.

Where the project stands

All three contractual deliverables are assembled, and they agree with each other by construction.

Underneath all of it: 5,000 customers, 32,728 policy terms, 5,617 claims, $103,314,190 written premium, loss ratio 0.5246 — synthetic throughout.

What is left is not research. It is four routing decisions, three of which only the CAS can make.

Why you can trust the numbers on these slides

Every figure in this deck is generated from the same seeded payload the manuscript is validated against. The deck cannot drift from the paper.

• 289 tracked figures, 0 unmatched against the drift gate — 274 reproduced from the toolkit, 15 cited to primary sources.
• 122 tests pass, and they pass inside the release subset, not only in the working repository.
• Seed 42 throughout; train and test identifier sets are asserted disjoint rather than assumed so.
• One negative result is reported as a negative result — the external validation of the tenure gradient did not reproduce, and the toolkit ships accordingly.

Reproduce every figure: python docs/calls/phase6_package_review_data.py

The question this session answers

A single-term view tells you whether this policy is profitable this year. It is silent on whether the relationship is worth having.

Customer lifetime value closes that gap. Most lifetime-value work cannot survive a rate filing, because it mixes loss-based and willingness-to-pay signals, hides its estimation inside unmaintained packages, and ignores what a state actually permits.

This session is about the version that can survive one.

The claim: lifetime value earns its place in ratemaking through retention-weighted loss statistics, acquisition-cost recovery and cohort-level quotation — not by becoming a new rating variable. Two results that ran against our own expectations are what narrowed the claim to that, and both are worth your time.

Views expressed are my own and not necessarily those of the Casualty Actuarial Society or my employer.

Seven policyholders, no model at all

Two renew once. Five renew for ten years. All seven run an identical 0.66 loss ratio on $1,450 of premium, 0.40 acquisition charged once, 0.20 renewal expense thereafter.

Same loss ratio. Same premium. Same expenses. Persistence is doing all of the work.

A book written entirely of one-renewal policyholders at a “profitable” 0.66 loses money. Every cell above checks with a calculator.

Before I show you Result 1 — a show of hands

You have just seen seven policyholders, one loss ratio, and a calculator. Now suppose we measure something every book believes and most have seen: the loss ratio improves the longer a customer stays.

We fit that improvement and apply it as a classification relativity — revenue-neutrally, as a relativity must be, so the indicated rate level does not move.

Hands up: does the mean lifetime value of the ten-plus year cohort go up, or down?

Hold the thought. Most rooms split, and the majority is usually wrong — which is the reason this result is in the paper at all.

Result 1 — the tenure credit runs backwards

Loss ratios do improve with tenure here: 0.63 in year one down to 0.42 at ten years, so the obvious move is a tenure credit. But a relativity must be applied revenue-neutrally — it allocates expected loss, it cannot create rate adequacy. Normalise to a loss-weighted mean of 1.000000 and the effect inverts:

Long-tenured business has already realised its improvement; it is younger business that still has improvement ahead to credit. A tenure factor built naively from a loss-ratio-by-tenure exhibit is likely pointing the wrong way.

Why the two bases are not interchangeable

Against a flat-loss-ratio reference of $16,111,118, the filing basis (revenue-neutral) moves the book total by $0.09 — zero, to rounding. It answers how expected loss is allocated across tenure, and that arithmetic guarantee is what a reviewer looks for.

The planning basis (level effect) is +$2,615,287 — the modelled loss saving to the dollar, answering how much less loss we expect to pay.

Both are correct. Only one belongs in a classification exhibit — so every exhibit stamps its basis.

Result 2 — for ranking, it adds almost nothing

Rank the in-force book by five-year lifetime value. Rank it again by plain current-term margin. Shed the worst quintile by each rule.

This is an honest negative result, and it bounds the claim.

The value of a lifetime-value lens is proportional to how much persistence heterogeneity your model can resolve. That is a property of your book and your model, not a law of nature. Measure it before you buy it.

Where it does change the answer

A single-period view sends retention budget to the highest current margin. A lifetime view sends it to the highest value at risk — the value that walks out the door if the customer lapses.

More than a third of a margin-targeted retention budget is misdirected — toward older business, away from the cohort that has paid its acquisition cost and not yet earned it back. This, and acquisition economics, is where the lens actually earns its keep.

Acquisition cost is sunk, and that matters

Acquiring a customer costs roughly 0.40 of first-year premium against 0.20 at renewal. For a customer you already have, that cost is spent.

Run the split forward for a new customer and the proverb becomes an exhibit: year one contributes $159.22 of discounted margin against $821.26 in year two.

The recovery schedule

Breakeven by acquisition load: year 1 at 0.40, year 2 at 0.45, year 3 at 0.70.

The bright line, made structural

Every model returns two columns from one calculation:

The gap between them is an exact, auditable figure for what your growth assumptions are worth: $376.21 per customer at $150 cross-sell and $100 upsell.

A regulator can verify to the dollar that none of it is in the filing. That is compliance as architecture, not as procedure.

Cross-sell is a one-time event

Worth getting right, because getting it wrong is easy and expensive. Our own first implementation added cross-sell value to the margin of every renewal term.

A household adds a second product line once. Read cross_sell_value as the lifetime value of the secondary product, and the term as that value times the probability of the sale.

Upsell is different in kind: a coverage upgrade is a permanent step-up in annual margin, so it recurs from the upgrade year onward.

Relativities: the loss-ratio column is the whole defence

The gradient — 1.60 in the lowest segment down to 0.20 in the highest — is what makes the segmentation filing-relevant.

The relativity is indicated by the loss-ratio column, not by the lifetime-value label. It would be indicated by identical loss experience under any labelling of the segments.

Credibility belongs on claim counts

1,082 is the classical full-credibility standard for claim counts. Applied to customer counts on equal-size quantiles it produces a column that carries no information:

On claims, the segments whose relativities depart furthest from unity are exactly the ones with the claim volume to support the departure. Caught in peer review; indicated relativities are unaffected, only the weighting.

The exhibit that supports an actual rate decision

May a segment expected to persist longer be charged less, when its first-term loss ratio gives no reason to charge it less? Weight each segment's loss ratio by its own expected lifetime:

The three-plus-product segment has the worst first-term loss ratio of the three — and still indicates a credit.

A single-term exhibit ranks that segment last of three. The lifetime exhibit ranks it second, entirely on 7.92 expected years against 2.72 for mono-line. That is the multi-policy discount argument, quantified.

Is that admissible where price optimization is banned?

A fair challenge, and it deserves a direct answer rather than reassurance.

The argument that it is. What Proposition 103 and the NAIC white paper prohibit is using a customer's predicted price response to set their price. This exhibit has none. Numerator and denominator are loss and premium experience; the weights are realised survival frequencies estimated with no price variable anywhere — a property enforced by a test, not by a promise. It is the same construction as weighting by a lapse assumption.

The concession. No regulator has reviewed it. In a prior-approval state, document the retention estimate's inputs, be ready to say whether the credit survives on first-term loss experience alone — on our book it does not — and know that the exhibit degrades gracefully to unweighted segment loss ratios if the weighting is declined.

Cohort value rises steeply with tenure

The gradient across tenure is the headline most books will recognise: the longest-tenured cohort is worth several times the newest one, and it is a small share of the customers.

That is the number everyone quotes. The next slide is why quoting it alone is a mistake.

Quote cohorts, never customers

The bands are wide relative to the means. The two-to-three-year cohort's P25 and median are both exactly $0.00 — not a floor in the code, but 34.6% of that cohort having already lapsed, with negative values coexisting in the same frame.

A single customer's lifetime value is not a quotable number. A cohort with its band is.

Reported rather than smoothed away

Mean residual value rises 4.3 times across tenure while the cohort loss ratio falls 0.65 to 0.46.

Six model families, one contract

Buy-till-you-die, survival, multi-state and hybrid estimators all answer predict_clv() identically, so they can be compared rather than argued about.

They agree within about 12% at book level and disagree instructively on distribution. Model choice contributes a stable ~12% spread; scenario assumptions reach −54% — so getting the assumptions right matters more than getting the model right.

What flat loss ratios cost you

The seven-policyholder cohort held its loss ratio flat so a reader could check it by hand. Switch the measured tenure gradient on:

The gradient more than doubles the ten-year renewer's value and barely moves the short renewer, who has no future tenure over which to earn it.

Which is why the open question — does that gradient reproduce on your book? — is worth more than the choice of model. Fit it on your own experience.

What to take back to your desk

The single-term view is not wrong. It is incomplete.

Reproducibility, and where to get it

Everything on every slide comes from one seeded run. The toolkit, cas_clv, is CAS research output under the Mozilla Public License 2.0 — the reproducibility artifact for the paper, not a product. Six executed notebooks run from data exploration to a full worked example.

Where to get it: the repository is being provisioned by the Casualty Actuarial Society; the address is published with the paper, in its data-availability statement. Funding and disclosure are on the title slide.

Questions

The two results I would most like to be argued with about:

1. A tenure credit built from a loss-ratio-by-tenure exhibit is probably backwards.

2. For ranking in-force customers, five-year lifetime value adds almost nothing to current-term margin.

Neither is what we expected to find, and both would change if persistence heterogeneity on your book is larger than on ours. That is an empirical question, and the toolkit exists so you can settle it on your own data.

Pramod Misra · Georgia Institute of Technology, Atlanta