Capital assessment and solvency: risk-based capital, internal models and risk appetite
What the domain tests
You must explain how a general insurer sets regulatory and economic capital, how risks are aggregated, and how an internal model and risk appetite are governed.
Core rules
- Capital is the excess of eligible assets over liabilities. Regulatory capital is a minimum; economic capital reflects the insurer's own risk profile.
- The solvency capital requirement is typically calibrated to a 99.5% one-year VaR. Risks include underwriting, reserve, market, credit, operational, and liquidity risk.
- Aggregation uses variance-covariance or copulas; diversification benefit is not a free good and must be evidenced.
- Internal models need validation, documentation, use test, model governance, and sensitivity/stress testing. The ORSA links risk profile, capital needs, and business plan.
- Risk appetite is expressed as a statement, tolerances, and limits, with escalation triggers.
Worked example
Suppose underwriting capital is ₹100m and reserve risk capital is ₹60m, with correlation 0.25. Aggregated capital = √(100² + 60² + 2 × 0.25 × 100 × 60) = √(10,000 + 3,600 + 3,000) = ₹128.8m. The diversification benefit is ₹160m − ₹128.8m = ₹31.2m. If available capital is ₹180m, the solvency ratio is 180/128.8 = 140%.
Traps
Giving full capital credit for reinsurance without assessing counterparty risk; confusing one-year and ultimate horizons; ignoring correlation between reserving and underwriting risk; treating diversification as automatic; using a model without expert judgement; confusing regulatory capital with economic capital; omitting operational risk.