Reader’s Guide

A plain-English companion to The Decreasing-Term Anachronism — explainers, regulations, and a glossary, written for brokers, journalists, and board members.

Part 1. How to read the paper

What the paper is about, in one paragraph

In Ireland, mortgage protection life cover is sold and priced using a method that has barely changed in thirty years. The sum insured falls in a straight, predictable line based on a fixed 6 per cent interest rate. Mortgage balances, in the real world, fall along a different line — they are driven by whatever rate the borrower is actually paying, which today is rarely 6 per cent and which moves around over the term of the loan. The two lines do not match. The paper measures the gap between them, shows how big it is in euros, and asks whether the product could be re-designed so the cover follows the real loan more closely. It does not say the industry is doing anything wrong; it asks whether the design assumptions still serve borrowers and insurers best.

The headline numbers

These are not anybody's fault. They are the arithmetic consequence of a design choice — a sensible choice when interest rates last sat near 6 per cent, less sensible now.

Who this guide is for, and how to navigate it

If you are a broker, the most useful sections of the paper are §3 (failure modes), §6 (results — what the gap looks like), and §8 (the redesign options). If you are a journalist or commentator, start with §1 (the modernisation question), §6 (the numbers), §7 (mechanisms), and §10 (conclusion). If you are a board member or executive in a life office, the priority sections are §3 (the three failure modes), §7 (system-level vs firm-level distinction), §8 (spectrum of responses), and §9 (limitations). If you are a policy or regulatory reader, §1, §3, §8, §9 and §10. If you are a curious customer, read this Part 1, then the maths explainers in Part 2, then dip into §6 of the paper for the numbers.

What the paper is not

It is not a customer-redress argument. The paper acknowledges several legitimate reasons the current convention persists: it gives borrowers a prudential cushion if rates rise, it covers the estate if death occurs near the end of term, it is operationally simple to administer, and it interacts cleanly with the capital regime under which life offices operate. The paper sets the gap out honestly and lets the reader weigh the trade-offs.

A note on integrity

Every figure in the paper traces back to a single workbook (MWP-03-Workbook.xlsx). The interest-rate model and the simulation results were independently diagnosed in Annex B. The 6 per cent convention was verified directly against the Key Features Documents of all five major Irish life offices. The regulatory dates and citations were checked against the original Official Journal entries. Where the analysis depends on a judgement call — for example, how to split the in-force book by remaining term — that judgement is disclosed and the answer is given as a range, not a point estimate.

Part 2. Plain-English maths explainers

Nine short boxes, one concept each. The equations can be skipped.

Box 1 · Decreasing term vs. level term

A level-term life insurance policy pays the same amount whenever a claim is made — €300,000 today, €300,000 in fifteen years' time. The premium reflects the fact that, on average, the policyholder is more likely to die in year fifteen than in year one. A decreasing-term policy is designed to mirror a falling mortgage balance: the amount paid out drops over time according to a schedule fixed at the start of the policy, and the premium is lower because the average payout is lower. The question the paper asks is whether the schedule that determines how the sum insured falls actually matches the way the mortgage balance falls. When mortgage rates and policy assumptions match, yes. When they diverge — as they have for most of the last decade — the policy can pay more than the loan balance on the day of death; that excess goes to the estate, which is not nothing, but it is not what the customer thought they were buying.

If you want the maths. A decreasing-term policy has payout S(t) following an amortisation schedule fixed at issue. The paper compares S(t) — the insured amount — against B(t) — the actual outstanding loan — and measures the gap S(t) − B(t).

Box 2 · Amortisation and the 6 per cent convention

A mortgage is paid off through a sequence of monthly instalments, each part interest and part capital. In the early years most of the payment is interest; in the late years most is capital. The exact split at any point depends on the interest rate the borrower is paying. If you assume a 6 per cent rate you get one amortisation curve; at 3 per cent you get a flatter curve where more of each early instalment is capital, so the balance falls faster early on. Irish life offices set the decreasing-term schedule using a fixed 6 per cent assumption — verified directly against the Key Features Documents of Irish Life, Royal London, Zurich Life, New Ireland, and Aviva. It is a market convention; none of these firms invented it, and none can move unilaterally without commercial risk. When the borrower's actual rate is below 6 per cent (which it has been for most of the last decade), their loan balance falls more slowly than the insurance schedule, especially in the middle years — that is where the gap opens up.

If you want the maths. Outstanding balance at month t under monthly rate r and original principal P over n months is B(t) = P · [(1 + r)^n − (1 + r)^t] / [(1 + r)^n − 1]. The insured amount S(t) uses the same formula with r fixed at 6%/12.

Box 3 · Present value and discounting

A euro today is worth more than a euro in twenty years' time. To compare cashflows across time you bring them all back to today's terms — this is discounting. At a 4 per cent discount rate, €1,000 received in five years is worth roughly €822 today; the same €1,000 in twenty-five years is worth roughly €375. When the paper says the "30-year present value of excess premium is €345 million," it means: take all the excess premium being paid each year across the Irish market for the next thirty years, discount each year's amount back to today, and the total in today's money is €345 million.

If you want the maths. Present value of a cashflow C(t) over horizon T at discount rate d is PV = Σ C(t) / (1 + d)^t for t = 1 to T.

Box 4 · The Vasicek interest-rate model in one paragraph

To say anything about what mortgage rates might do over a thirty-year horizon, you need a model of how rates behave. The paper uses the Vasicek model — the actuarial workhorse. It says rates tend to drift back toward a long-run average over time (mean reversion) but wobble randomly around that drift. The model has three parameters — the long-run mean, the speed of reversion, and the volatility — calibrated to historical Irish mortgage data. It is intentionally simple; it does not capture regime changes or fat-tailed crises. The paper uses it because the alternative — pretending the rate stays constant — is worse.

If you want the maths. The Vasicek short-rate dynamics are dr(t) = κ (θ − r(t)) dt + σ dW(t), where κ is the mean-reversion speed, θ the long-run mean, σ the volatility, and W a Brownian motion.

Box 5 · Monte Carlo simulation — what 50,000 paths actually mean

If interest rates are random, there is no single answer to "what will the gap be in year twelve?" — only a distribution of possible answers. Monte Carlo simulation handles this by simulating many possible rate paths (the paper uses 50,000), computing the gap under each, and reporting the distribution. When the paper says "the 30-year present value of excess premium is €345 million, with a 5th–95th percentile range of €100 million to €587 million," it means: across the 50,000 simulated worlds, the median outcome was €345 million; 5 per cent came in below €100 million; 5 per cent above €587 million. The median is the best single-number summary; the range tells you how confident to be. Annex B includes convergence checks confirming that running more paths does not materially change the answer.

Box 6 · Sensitivity analysis and the 50bps step

A model's answer depends on its inputs; sensitivity analysis is the discipline of varying them deliberately to see how much the answer moves. The paper varies the central interest-rate assumption in 50-basis-point steps (a basis point is one-hundredth of a percentage point). For each step it re-runs the calculation; the slope it finds — roughly €224,000 of nominal excess premium per 100bps near the 4 per cent centre — tells you how steep the relationship is. The choice of 50bps is deliberate: large enough to produce a visible effect, small enough to feel realistic against actual rate moves, and aligned with the granularity at which lenders set fixed-rate products.

Box 7 · The prudential cushion — what over-insurance really buys

The paper does not claim the excess sum insured is wasted. It acts as a prudential cushion in case rates rise: if a borrower's mortgage rate spikes, their actual balance falls more slowly than expected and they need more cover for longer, and the decreasing-term schedule — with its 6 per cent built in — anticipates a high-rate world. The paper stress-tests this. Under a +200bps step at year five — holding the contractual six-per-cent notional schedule fixed and shocking the actual borrower rate from 4 per cent to 6 per cent — the mean over-cover cushion shrinks from €14,332 to €5,032 (roughly two-thirds), the peak falls from €22,292 to €8,394, and critically the policy never falls under-cover at any month. That is the point of the cushion: it absorbs shocks the borrower did not see coming. The corollary is that in the world we have actually been living in, the cushion has been larger than needed, and the borrower has paid for cover they did not end up using. The paper surfaces both facts honestly.

Box 8 · SCR, capital, and why pricing reflects more than mortality

When a life office sells a policy it sets aside capital against the risk that things go wrong. The amount is set by Solvency II rules and is called the Solvency Capital Requirement (SCR). Mortality is one component but not the only one. A redesigned product that more closely tracks the actual mortgage balance is, on the face of it, smaller — less sum insured, less mortality exposure — but it can also be more sensitive to interest-rate movements, which feeds a different SCR component. The paper shows that for design module M2, SCR_mort goes up 27 per cent relative to legacy under the D3 (term-extension) scenario; in steady state the picture is much more nuanced. Pricing a new product is not just a matter of cutting the sum insured; it has to be reset against the full capital model.

Box 9 · Break-even expense loading — the commercial reality check

A life office has fixed costs per policy regardless of size: an underwriter's time, the systems to administer it, the broker's commission, the medical evidence. If you redesign the product so each policy is smaller, the fixed costs do not shrink in proportion, and there is a floor below which the policy becomes unprofitable. The paper calculates this floor explicitly at the canonical premium-per-mille of €1.2336 per €1,000 SA/yr (€397.20 base annual premium). For module M1 the break-even expense loading is €10.61 per policy per year (about 2.7 per cent of base premium); for M2, €13.01 (3.3 per cent); for M3, €11.87 (3.0 per cent). The share-of-premium ratio (2.7–3.3 per cent) is invariant to the premium-per-mille assumption. These are not absurdly high — most current expense allowances would cover them — but they constrain how aggressively any single firm could move without losing money, which is one of the main reasons the paper argues against a unilateral move by any one office and frames the question as a market-wide design conversation.

Part 3. Industry rules and regulations

Mortgage protection in Ireland — the regulatory frame

Mortgage protection in Ireland is shaped by three overlapping bodies of rules. First, the Central Bank's Consumer Protection Code sets standards for how insurance is sold, how advice is given, and how disclosures are made. Second, the Consumer Credit Act 1995 historically made mortgage protection a quasi-compulsory product for residential mortgages — the lender requires it. Third, the Consumer Insurance Contracts Act 2019 rewrites the duties of disclosure between insurer and customer, away from the old "utmost good faith" doctrine toward a more proportionate, fairer duty for the consumer to answer honest questions honestly.

Solvency II in one page

European life insurers operate under the Solvency II regime, in force since January 2016, with three pillars. Pillar 1 — quantitative: the Solvency Capital Requirement (SCR), the minimum capital required, calibrated so a firm has at least a 99.5 per cent probability of remaining solvent over a one-year horizon. Pillar 2 — governance and risk management: the Own Risk and Solvency Assessment (ORSA), board-level risk oversight, and the actuarial function. Pillar 3 — disclosure and reporting: the Solvency and Financial Condition Report (SFCR) and the Regular Supervisory Report (RSR). For mortgage protection the Pillar 1 mortality risk module is where the action sits: a redesigned product changes the mortality cashflow profile and therefore the capital required.

The Solvency II Review (Regulation (EU) 2026/269), adopted 29 October 2025, published in the Official Journal on 18 February 2026, entering into force 10 March 2026 and applying from 30 January 2027, updates parts of the regime — proportionality, the risk margin, long-term equity, and the supervisory framework. It does not change the underlying logic of how mortgage-protection capital is computed but eases some constraints on smaller and less-complex undertakings.

The Key Features Document and the 6 per cent convention

Every life insurance product sold in Ireland carries a Key Features Document (KFD) — a standardised summary specifying the assumptions used. For mortgage protection the KFD specifies the assumed interest rate used to construct the decreasing-term schedule. Across all five major Irish life offices — Irish Life, Royal London, Zurich Life, New Ireland and Aviva — that rate is 6 per cent. The figure dates to a period (broadly the mid-1990s) when Irish mortgage rates ran in that range; it also gives a prudent margin. The question the paper raises is whether prudence calibrated to a 1990s rate environment is the right calibration today.

Distribution channels and commercial incentives

Mortgage protection in Ireland is distributed through three channels: tied agents (selling one firm's product only — typically bank-owned channels), multi-agency intermediaries (offering a panel of providers), and independent brokers (advising across the market). Commission is a percentage of premium, which means brokers earn more when premiums are higher. This is a known commercial reality the paper does not moralise about — but it matters for any redesign discussion, because a product that cuts premiums also cuts commissions, which affects distribution willingness to recommend it.

Actuarial standards — best-estimate vs. prudential

The best-estimate is the actuary's central, unbiased view of future cashflow, with no padding; the prudential view layers margins on top to cover uncertainty. Solvency II requires firms to report on a best-estimate basis (with the SCR providing the prudential margin separately). The paper uses best-estimate assumptions throughout, with sensitivities to show how the answer moves. The Society of Actuaries in Ireland (SAI) issues practice guidance through Actuarial Standards of Practice (ASPs) — ASP LA-8 covers reserving for life insurance liabilities; ASP LA-6 covers the Head of Actuarial Function role.

Consumer Insurance Contracts Act 2019

The CICA 2019 is one of the most significant pieces of Irish insurance law in a generation. Two effects are most relevant. First, it shifts the duty of disclosure: the customer must answer honest questions honestly but is no longer required to volunteer information the insurer did not ask about. Second, it limits the insurer's ability to repudiate claims for innocent non-disclosure or minor inaccuracies.

The Central Bank, fair value, and the Differential Pricing Review

The Central Bank of Ireland's Differential Pricing Review (concluded in 2022 for motor and home insurance) established the principle that loyal customers must not pay materially more than equivalent new customers — the "loyalty penalty." While that review focused on motor and home, the underlying fair-value framework — the requirement that customers receive value commensurate with what they pay — applies across the regulated retail insurance space and is increasingly read into supervisory expectations for mortgage protection.

Reinsurance and the capital model

Life offices typically reinsure a large portion of their mortality risk. The reinsurer takes most of the mortality exposure; the cedent retains a margin. This means the SCR for the direct writer is materially smaller than the gross mortality exposure suggests, and a redesigned product affects the reinsurance treaty terms — which in turn affects pricing and capital. The paper does not model the reinsurance leg explicitly but flags it as a constraint on how fast any market-wide change could move.

Part 4. Glossary

Part 5. What this guide is not

This guide does not summarise the paper's argument so completely that the paper becomes unnecessary — the point of a companion is to enable, not replace. If a reader wants to know whether to trust the numbers, they should read §4 (data and methods) and §9 (limitations) in the paper itself; if they want to know whether the redesign is feasible, §8. This guide also does not advocate. The paper is deliberately neutral on what the industry should do — it offers a spectrum of responses (§8) ranging from no change to a full market-wide redesign, and lays out the trade-offs for each. The companion follows the same posture.