Solvency and capital in insurance

An insurer collects premiums today in exchange for uncertain obligations in the future. Technical reserves cover the expected value of those obligations plus a risk margin; solvency capital covers what reserves cannot: unexpected losses. That is why modern regimes split the balance sheet into three layers: assets backing reserves, own funds backing the capital requirement, and a surplus that gives management room to maneuver.

Mexico adopted a risk-based regime with the Ley de Instituciones de Seguros y de Fianzas (LISF), published in the DOF (Official Gazette) on April 4, 2013 and in force since April 4, 2015, together with the Circular Única de Seguros y Fianzas (CUSF) issued by the CNSF (National Insurance and Surety Commission). Its architecture closely follows Solvency II: a market-consistent balance sheet, a solvency capital requirement (RCS) calibrated to 99.5% over one year, corporate governance with an actuarial function and integrated risk management, and market disclosure.

For the actuary, solvency is where liability valuation, asset modeling, reinsurance and ruin theory converge. Understanding how the RCS is built makes it possible to design reinsurance programs, investment policies and underwriting strategies that use capital efficiently.

The starting point is an economic balance sheet: assets at market value and liabilities valued as a best estimate plus a risk margin. The difference is own funds. The capital requirement is defined as the loss in own funds that would be exceeded only with a probability of 0.5% over a one-year horizon, that is, the value at risk (VaR) at 99.5%. If the institution holds at least that amount of own funds, the probability that an adverse year leaves it with assets below its liabilities is, according to the model, at most 1 in 200.

The LISF states it explicitly: the RCS calculation must consider unforeseen losses at a 99.5% confidence level over a one-year horizon, except for risks whose nature requires a different period (Article 235, section III). It also requires assuming continuity of underwriting (a going concern) and considering all relevant risks: life, accident and health, and property and casualty underwriting, market, mismatch, liquidity, credit, concentration and operational risk.

VaR is not the only possible measure. TVaR (the expected loss given that VaR is exceeded) is coherent and subadditive, and is used in other regimes such as the Swiss Solvency Test. VaR at 99.5% dominates in Europe and Mexico because it reads directly as an annual probability of insolvency, although it is blind to what happens beyond the quantile, which matters for heavy-tailed risks such as earthquake or pandemic.

Solvency II (Directive 2009/138/EC, applicable since January 1, 2016) organizes supervision into three pillars: quantitative requirements (valuation, own funds and capital), governance and supervision (including the ORSA, the own risk and solvency assessment) and disclosure (reporting to the supervisor and the public). It sets two thresholds: the SCR, calibrated to a one-year 99.5% VaR, and the MCR, a lower floor whose breach can lead to withdrawal of authorization; the MCR moves within a corridor of 25% to 45% of the SCR.

The standard formula computes charges by module (market, counterparty default, life, health, non-life and intangibles) using stress scenarios or factors and aggregates them with prescribed correlation matrices. Operational risk is added to the basic SCR (BSCR), and the adjustment for the loss-absorbing capacity of technical provisions and deferred taxes is subtracted. Undertakings may use full or partial internal models, subject to supervisory approval.

Directive (EU) 2025/2 reformed the regime: more proportionality for small and non-complex undertakings, technical recalibrations (interest rates, spread risk, risk margin) and greater weight on sustainability risks. Member States must transpose it by around January 2027. For Mexico, Solvency II remains the conceptual benchmark, although the local calibration and calculation mechanics are different.

The LISF requires the RCS to be calculated monthly (Article 233), either with the general formula issued by the CNSF (Article 236) or with an approved internal model (Article 237). Provision 6.2.1 of the CUSF breaks the general formula into six requirements that are added together: for technical and financial insurance risks, for risks based on probable maximum loss (PML), for technical and financial risks of pension insurance, for technical and financial surety risks, for other counterparty risks and for operational risk.

The core component, RC_TyFS, is obtained not with stress scenarios but with stochastic simulation: the CUSF (Provision 6.3.2) defines the change in the value of adjusted own funds over one year and takes the 99.5% VaR of the loss. Asset losses (interest rate, equity, spread, currency, credit and concentration) and liability losses (mortality, lapse, disability, longevity, property and casualty and accident and health claims, reinsurance default) are generated jointly, so diversification between them is captured inside the simulation rather than through an explicit correlation matrix.

The earthquake, hurricane and other hydrometeorological risks, agricultural and livestock, and mortgage credit lines have their own requirement based on the retained PML, from which the catastrophe risk reserve and the protection from excess of loss contracts are deducted (see catastrophe risk). Institutions compute everything with the RCS calculation system provided by the CNSF (Provision 6.2.2), which makes the market homogeneous but limits the ability to reflect an atypical risk profile. That is what internal models are for (Chapter 6.9 of the CUSF); they can also include strategic and reputational risks, which Article 235 excludes from the general formula.

Not all book equity counts toward covering the RCS. The LISF defines eligible own funds (Fondos Propios Admisibles, FPA) as the excess of assets over liabilities that, under Articles 241 to 244, may be used to cover the requirement. Certain investments and assets are excluded (for example, treasury shares), and the CNSF classifies them into three tiers according to their nature, maturity, liquidity and marketability: Tier 1 includes paid-in capital, capital reserves and retained earnings; Tiers 2 and 3 admit lower-quality instruments subject to eligibility limits. In addition, FPA can never be lower than the minimum paid-in capital (Article 243).

The difference between FPA and the RCS is the solvency margin (reported as a surplus or shortfall), and the ratio is the coverage ratio. A ratio below 1 triggers the measures in Article 320 of the LISF, which include remediation plans. In practice, boards set a risk appetite with a target ratio well above 1 to absorb the monthly volatility of the calculation.

The RCS coexists with another constraint that comes first in the order of priority: the investment base (Base de Inversión), defined in Article 2 of the LISF as the sum of technical reserves plus premiums on deposit and other funds. It must be covered by investments that comply with the regime in Articles 247 to 255 and Title 8 of the CUSF (limits by asset type, issuer, rating and currency). Assets covering the investment base cannot count as FPA at the same time, so the balance sheet is split into layers with no double counting.

When risk charges are calculated separately, adding them up assumes the worst scenarios happen at the same time, which overstates capital. Aggregation with a correlation matrix is exact if losses follow an elliptical distribution (for example, multivariate normal) and the requirement is proportional to the standard deviation. With heavy tails or dependence that is stronger in the extremes than in the center, linear correlation understates joint capital; that is why internal models use copulas (Student t, Clayton, Gumbel) or joint simulation, as the CNSF does for RC_TyFS.

The diversification benefit is the difference between the simple sum and the aggregated capital. Allocating it to lines of business matters for pricing and for measuring risk-adjusted profitability. Euler allocation splits total capital into contributions that add up exactly to the total and that reward the lines least correlated with the rest; it underpins metrics such as RORAC by line of business.

A valid correlation matrix must be symmetric and positive semidefinite. When it is built module by module using expert judgment, it is worth checking its eigenvalues: a matrix that is not semidefinite can produce square roots of negative numbers or absurd contributions.

The RCS is a one-year snapshot. The LISF complements it with two forward-looking exercises. Dynamic Solvency Testing (Prueba de Solvencia Dinámica, PSD), required by Article 245, must be performed at least annually to assess whether FPA will continue to cover the RCS under a range of prospective scenarios: a base scenario consistent with the business plan and adverse underwriting, market, reinsurance and combined scenarios. Under Article 246, the board of directors is responsible for having it performed, and it must be signed by an actuary holding a cédula profesional (professional license) and current certification from the professional association (see certification), registered with the CNSF.

The institutional own risk and solvency assessment (Autoevaluación de Riesgos y Solvencia Institucionales, ARSI) is part of the integrated risk management system required by Article 69. It must cover compliance with risk policies, overall solvency needs given the risk profile and approved tolerance limits, ongoing compliance with investment, reserve, reinsurance, RCS and minimum capital requirements, and the extent to which the risk profile departs from the assumptions underlying the general formula. It is the Mexican version of the European ORSA.

The practical difference between the two is one of purpose. The PSD projects financial statements and requirements over several years under defined scenarios; the ARSI is a governance process that uses the PSD, the RCS and internal analyses to make decisions on capital, reinsurance and strategy. A useful ARSI documents decisions, not just figures: for example, which earthquake retention is chosen and how much capital it frees up or consumes.

The Mexican regime was built between the publication of the LISF in 2013 and its entry into force in April 2015, with the CUSF as secondary regulation (published in the DOF in December 2014 and amended continually). The CNSF supervises with a risk-based approach: institutions report the RCS and its coverage monthly, and quarterly regulatory information that feeds early warning indicators. Reserve valuation uses a best estimate plus a risk margin calculated with a net cost of capital of 10% on the FPA needed to back the RCS (Chapter 5.4 of the CUSF), whereas Solvency II uses 6%.

Disclosure takes the form of the Solvency and Financial Condition Report (Reporte sobre la Solvencia y Condición Financiera, RSCF), which each institution publishes annually with its RCS by component, FPA by tier, coverage of the investment base and minimum capital, and a qualitative description of its risk profile, reinsurance and governance. It is an excellent resource for students: it lets you compare how the RCS of a motor insurer, a life insurer or a pension insurer is made up.

The actuary has regulated functions throughout the cycle: the actuarial function within corporate governance, signing technical notes and reserve valuations, signing the PSD and the independent actuarial opinion. The standards of practice of CONAC (Colegio Nacional de Actuarios) and professional certification are the framework against which that work is assessed.