# Consulting memo — Motor & household portfolio review

**To:** Risk Committee, Client Insurer plc  
**From:** Dr. Sarah Okonkwo, Horizon Risk Consulting  
**Date:** August 2026  
**Prepared by:** Horizon trainee (worked example), Actuarial Analyst  

## Executive summary

Motor expected loss cost (pure premium) is about **£331** per policy-year at λ ≈ **0.13** claims and mean severity ≈ **£2,547**. Age relativities peak in **25–39** at **~2.18×** the 40–59 base. Chain-ladder IBNR on the paid triangle is about **£0.77m**, mostly from immature **2023**. A surface-water flood stress produces **~£7.6m** of loss versus **~£2.9m** normal-year planning (**~2.6×**). Priority actions: hold more flood / catastrophe capacity than 1.5× normal-year loss, review mid/young age pricing, and book the IBNR honestly.

## 1. Motor loss model

Our compound model estimates average claim frequency λ ≈ **0.13** per policy-year (about **88%** of policies have zero claims, close to \(e^{-\lambda}\)). Mean severity is **£2,547** (median **£1,749** — the right tail pulls the mean up). Pure premium ≈ **£331** per policy-year. Simulation of 1,000 policy-years centres near that mean but the 95th percentile is roughly **£2,800** — a reminder that one year can be far worse than the average.

![Frequency](../outputs/charts/module1_frequency.png)

## 2. Pricing by driver age

With 40–59 as base (relativity 1.00), loss-cost relativities are approximately **2.07** (18–24), **2.18** (25–39), and **0.55** (60+). Indicative premiums with 25% loading run from about **£172** (60+) to **£686** (25–39).

**Recommendation:** Treat **25–39** and **18–24** as the priority monitoring bands — confirm the elevated loss cost is stable before any competitive discounting, and avoid cutting mid-age rates toward 40–59 levels without expense or selection offsets.

![Relativities](../outputs/charts/module2_relativities.png)

## 3. Reserves (IBNR)

Simple average age-to-age factors project total IBNR of about **£773k** across accident years 2019–2023. **2023** contributes the largest share (~**£455k**) because only lag_1 is observed. 2019 is fully developed (IBNR ≈ 0).

![IBNR](../outputs/charts/module3_ibnr.png)

## 4. Enterprise flood stress

Under the agreed deterministic scenario (scores ≥70: 15% loss; 50–69: 5%), portfolio stress losses total about **£7.58m** against a normal-year assumption of **£2.93m** (**~2.6×** uplift). Capital equal to **1.5×** normal-year loss (**~£4.4m**) would **not** cover this stress. Regional stress is fairly even; **South** is slightly highest in this draw.

![Flood stress](../outputs/charts/module4_flood_stress.png)

## 5. Recommended actions

- Increase catastrophe / flood capital or reinsurance so a stress near **£7–8m** is retained within appetite — 1.5× normal year is insufficient on this scenario.  
- Do not cut **25–39** / **18–24** premiums for growth until loss-cost relativities are re-checked on a later period.  
- Book IBNR near **£0.77m** (subject to actuarial review) and explain that **2023** drives most of the gap.  
- Reduce concentration in high flood-score risks or price them more sharply where regulation allows.

## 6. Limitations

- Synthetic / simplified data and methods throughout.  
- Chain-ladder ignores inflation, large claims and process change; factors are simple averages.  
- Flood scenario is deterministic, not a full probabilistic catastrophe model; no reinsurance recoveries modelled here.  
- No correlation between motor and household lines.  
- Severity simulation uses the empirical sample with replacement — thin tails if rare large claims are under-represented.

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*This memo is for training purposes and does not constitute professional advice.*