The 11% cost of equity threshold reflects current market conditions. Using CAPM — risk-free rate ~4.5%, equity risk premium 5–6%, beta ~1.0 for a P&C insurer — the cost of equity falls in the range of 9.5–10.5%, rising to 11–13% for more volatile or specialist books. Most insurance boards and institutional investors are currently applying hurdles of 11–12% or above, reflecting both the higher risk-free base and the premium demanded for insurance earnings uncertainty.
Capital is modelled as the SCR (40% of GWP) held at 175% coverage, giving £70m of required capital on £100m of premium — consistent with a well-capitalised mid-market insurer. The P/B multiple is anchored at 1.0× when ROE equals the cost of equity, rising to 1.10× at the base ROE. On capital structure: roughly 75–80% equity and 20–25% subordinated or hybrid debt is typical for a P&C insurer; ROE should always be benchmarked against the cost of equity — not WACC — since equity holders bear the residual risk after debt obligations are met.
This page sets out the thinking behind the interactive model — the assumptions, derivations, and the key conceptual points raised in building it. It is intended as a teaching companion to the tool, explaining not just what the model shows but why each mechanism works the way it does.
Most analysts and non-specialists treat a loss ratio revision as a simple one-line P&L adjustment: premiums stay the same, losses go up, profit goes down. The magnitude is understood. What is widely missed is that a revision to the loss ratio assumption is not a current-year event — it is a statement about the adequacy of reserves across all open accident years, and about the future pricing and capital requirement of the business.
This produces a compounding cascade of four distinct hits, each building on the last. The tool is designed to make that cascade visible in a way that a static spreadsheet cannot.
The most straightforward impact. On £100m of gross written premium, each 1 percentage point rise in the loss ratio costs £1m of underwriting profit directly. With an expense ratio of 40% and a base loss ratio of 50%, the combined ratio starts at 90% and the underwriting profit is £10m. At 60% loss ratio the combined ratio hits 100% and underwriting profit is zero.
This is the hit most people miss. Incurred But Not Reported (IBNR) reserves are the provision held for claims that have occurred but not yet been fully reported or settled. At any given point an insurer is carrying reserves across multiple open accident years — the model uses four, which is conservative for many long-tail commercial lines.
When you revise the loss ratio assumption upward, you are not just saying "this year will be worse." You are saying "all years we priced at 50% were actually worse, and our reserves for those years are inadequate." Every open year gets restated simultaneously. This is a balance sheet charge that flows through the income statement in the year of recognition.
Higher expected losses mean a fatter loss distribution and a larger 1-in-200 year tail event — the standard on which Solvency II SCR calculations are based. Rating agencies apply similar logic. The required capital base therefore increases alongside the loss ratio assumption, compressing ROE from both directions: the numerator (profit) falls while the denominator (capital) rises.
The model applies a sensitivity of £2m of additional capital per 1pp increase in the loss ratio. This is a simplification; in practice the SCR is a non-linear function of the full loss distribution, but the directional effect is robust.
The share price is affected by two simultaneous forces: the book value (NAV) is depleted by the Year 1 IBNR charge, and the market re-rates the earnings multiple downward as it prices in the lower steady-state ROE. Both effects move in the same direction, producing an equity return that is highly leveraged relative to the underlying loss experience.
See Section 5 for the P/B multiple derivation.
The following table summarises the key assumptions and the reasoning behind each choice. Several of these were refined during the development of the tool based on analytical challenges raised in review.
| Parameter | Value | Rationale |
|---|---|---|
| Gross Written Premium | £100m | Round number for illustrative clarity; all outputs scale linearly |
| Base Loss Ratio | 50% | Representative of a well-performing commercial P&C or specialty book |
| Expense Ratio | 40% | Covers acquisition costs, management expenses and Lloyd's levies; revised upward from an initial 25% to better reflect realistic combined ratios |
| IBNR Development Years | 4 | Conservative assumption for commercial lines; casualty or liability lines may carry 6–10+ years |
| Investment Income | £3m (fixed) | Simplified; in a full model this would be a yield applied to the total asset base (reserves + capital). At 3% on ~£100m of assets this is approximately correct at base |
| SCR as % of GWP | 40% | Typical for a diversified P&C insurer under Solvency II standard formula; specialist or mono-line books may be higher |
| SCR Coverage Ratio | 175% | Representative of a well-capitalised insurer; ratings agencies (A.M. Best, S&P) typically expect 150–200%+ for strong ratings |
| Required Capital (base) | £70m | £100m × 40% SCR × 175% coverage = £70m. This replaced an earlier £50m assumption which produced an unrealistically high base ROE |
| Capital Sensitivity | +£2m per 1pp LR | Linear approximation; actual SCR sensitivity is non-linear and line-of-business dependent |
| Cost of Equity (Ke) | 11% | See Section 4 |
| Base P/B Multiple | 1.10× | Modest premium to book value, consistent with a business earning a small excess return above cost of equity |
| Tax | Not modelled | Excluded for simplicity; post-tax ROE at ~25% corporate tax would reduce all ROE figures by approximately 25% |
An initial version of the model used 10% as a round-number cost of capital threshold. With UK risk-free rates at ~4.5%, this deserves proper derivation.
For an insurance ROE model, the relevant hurdle rate is the cost of equity, not WACC. ROE measures return on the equity capital base, so it should be compared to what equity investors require — not to the blended cost of the whole capital structure.
The model uses 11% as a pragmatic mid-point, which is appropriate for a diversified P&C book. Most insurance CFOs and institutional investors are currently applying hurdles of 11–13%, reflecting the higher rate environment and the premium demanded for earnings volatility. The old near-zero rate era compressed these toward 8–9%, and those thresholds are now outdated.
A typical P&C insurer funds itself with approximately 75–80% equity and 20–25% subordinated or hybrid debt. Sub debt is currently priced at risk-free plus 150–250bps, giving a gross cost of ~6–7% and a post-tax cost of ~4.5–5%. Blending these produces a WACC of approximately 9–10% — close to the 11% equity threshold. However, using WACC to benchmark ROE would understate the required return, because equity holders bear the residual risk after debt is serviced. The correct comparison is always ROE vs cost of equity.
The price-to-book (P/B) multiple for an insurance company is fundamentally driven by the spread between ROE and cost of equity. When ROE exceeds Ke, the business is creating value and should trade above book; when ROE falls below Ke, value is being destroyed and the market will re-rate toward or below book.
The model uses a linear approximation calibrated to the existing cost-of-equity variable, rather than introducing new parameters:
This approach has the correct qualitative properties: the multiple is anchored at 1.0× when the business earns exactly its cost of capital, falls below book when it destroys value, and rises above book when it creates value. The 1.10× starting multiple reflects a business that earns a modest premium above its hurdle rate — typical for a well-run insurer in a hard market.
The share price impact in Year 1 combines two simultaneous effects:
NAV depletion: The IBNR strengthening charge flows through the income statement and reduces retained earnings, directly lowering book value per share. This is not a future liability — it is a current-year P&L charge.
Multiple compression: The market simultaneously re-rates the earnings multiple downward as it prices in the new steady-state ROE. Both forces act together.
The equity leverage ratio expresses how many pounds of market capitalisation are destroyed per pound of additional annual claims. It captures the full compounding effect of the cascade in a single number.
This leverage arises from three compounding sources: the IBNR multiplier (4× the annual hit), the multiple compression (re-rating on lower earnings), and the capital dilution (larger denominator reduces ROE further). None of these would appear in a naive single-year P&L analysis.
This model is intentionally simplified for teaching purposes. The following limitations should be understood before applying the framework to a real-world situation:
Tax: All figures are pre-tax. At a 25% corporate tax rate, post-tax ROE would be approximately 75% of the figures shown. The cascade direction and magnitude are unaffected; only the scale changes.
Variable investment income: Investment income is treated as a fixed £3m. In reality it is a function of the total asset base (reserves + capital), the asset allocation, and prevailing yields. As reserves grow with higher loss ratios, investment income would increase modestly — partly offsetting the underwriting deterioration. This is the "silver lining" of a worsening loss ratio that is excluded here.
Pricing response: The model assumes premium volume and pricing are fixed. In practice, a loss ratio deterioration would trigger a pricing review; a re-underwriting of the portfolio would shift the loss ratio back over time, at the cost of volume. The model can be read as a "before repricing" snapshot.
Non-linear SCR: The capital sensitivity is linear at £2m per 1pp. Solvency II SCR is a non-linear function of the full loss distribution; large loss ratio moves would generate non-linear capital demands, particularly in the tail.
Recapitalisation dynamics: When the Year 1 IBNR charge depletes NAV significantly, the company may be unable to sustain the required SCR coverage without raising new capital. A rights issue at a distressed multiple would be further dilutive to existing shareholders — an effect not modelled here.
Multiple model linearity: The P/B multiple formula is linear in ROE, anchored at 1.0× when ROE = Ke. In practice, the relationship is non-linear and also depends on growth expectations, franchise value, and market sentiment. The linear model captures the key direction and order of magnitude but should not be used for precise valuation work.
Obvious enhancements to this framework would include: adding a tax rate slider; making investment income dynamic (linked to reserve size and a yield assumption); introducing a growth rate into the P/B model via the Gordon Growth framework; modelling the recapitalisation scenario; and extending to multiple lines of business with different development tails and SCR charges.
| Term | Definition |
|---|---|
| Loss Ratio | Incurred claims as a percentage of earned premium. The primary measure of underwriting performance. |
| Expense Ratio | Operating expenses (acquisition + management) as a percentage of earned premium. |
| Combined Ratio | Loss ratio + expense ratio. Below 100% indicates underwriting profit; above 100% indicates underwriting loss. |
| IBNR | Incurred But Not Reported. Reserves held for claims that have occurred but have not yet been fully reported or settled. Open across multiple accident years simultaneously. |
| SCR | Solvency Capital Requirement under the Solvency II regulatory regime. The amount of capital an insurer must hold to survive a 1-in-200 year loss event with 99.5% confidence. |
| SCR Coverage Ratio | Actual capital held as a multiple of the SCR. Regulators require >100%; ratings agencies and boards typically target 150–200%+. |
| ROE | Return on Equity. Net profit as a percentage of shareholders' equity (capital base). The primary shareholder value metric in insurance. |
| Cost of Equity (Ke) | The return required by equity investors to hold the stock. Derived via CAPM as risk-free rate + beta × equity risk premium. The hurdle rate against which ROE is benchmarked. |
| P/B Multiple | Price-to-Book ratio. Market capitalisation divided by book value (net asset value). Reflects the market's assessment of whether the business earns above or below its cost of equity. |
| Equity Leverage Ratio | The multiple by which a change in underlying annual losses is amplified into a change in equity market capitalisation. Driven by IBNR compounding, multiple re-rating, and capital dilution. |
| WACC | Weighted Average Cost of Capital. The blended cost of equity and debt, weighted by their proportions in the capital structure. Appropriate for investment decisions but not for benchmarking ROE. |