The actuary in banking and credit: scoring, PD/LGD/EAD, reserves and Basel

Overview of the specialty

Credit risk is the possibility of loss because a debtor fails to pay. Its structure is that of an insurance contract: there is a probability that default occurs (PD), a fraction of the exposure that is not recovered (LGD, severity) and an amount exposed at that moment (EAD). The product of the three is the expected loss, which is covered by pricing and reserves; the variability around it, the unexpected loss, is covered by capital.

Actuaries come to credit with an edge: frequency models, decrement tables that closely resemble rating transition matrices, survival analysis for time to default and valuation of contingent cash flows. The difference from insurance is that dependence between borrowers is greater, because a recession hurts many of them at once, which is why banking regulation places so much emphasis on capital and stress scenarios.

In Mexico, the CNBV (National Banking and Securities Commission) regulates loan portfolio rating and the setting of loan loss reserves in the Circular Única de Bancos (Single Banking Circular), with general methodologies by portfolio type and the option of using approved internal methodologies. Since January 1, 2022, banks have applied accounting criteria aligned with IFRS 9: reserves under an expected loss approach that classifies each loan into one of three impairment stages, as documented by Banco de México. For other entities, CINIF's NIF C-16 sets out the impairment of financial instruments receivable using the same logic.

The Mexican credit market includes commercial banks, development banks, regulated and unregulated SOFOMES (multiple-purpose financial companies), credit unions, popular financial companies and the financial technology institutions created by the 2018 Fintech Law. Each of them needs to originate with models, reserve with judgment and measure capital, and in all of them the actuary competes with economists and data scientists by bringing probabilistic rigor and a risk perspective.

Key functions

Origination models (scoring)

Builds models that rank applicants by risk using credit bureau, application and transactional behavior data. Sets cutoffs according to loss appetite and expected profitability by segment.

Estimating PD, LGD and EAD

Calibrates 12-month and lifetime probabilities of default, recovery curves for severity and credit conversion factors for undrawn lines. Separates point-in-time and through-the-cycle estimates depending on their use.

Expected loss reserves

Classifies the portfolio into stages, calculates 12-month reserves for stage 1 and lifetime reserves for stage 2, and incorporates probability-weighted macroeconomic scenarios. Reconciles the CNBV regulatory methodology with the accounting one where they differ.

Regulatory and economic capital

Calculates credit risk-weighted assets under the standardized approach or with approved internal models, plus economic capital that feeds risk-adjusted pricing and concentration limits.

Portfolio stress testing

Builds satellite models linking PD and LGD to unemployment, interest rates, inflation and growth, and projects losses and capital under supervisory and internal scenarios.

Model validation and monitoring

Measures discriminatory power, calibration and population stability, backtests against observed defaults and documents recalibrations. It is an independent function that demands both technical rigor and judgment.

Techniques, models and formulas

The technical toolkit blends classical statistics, survival analysis and dependence models. The golden rule is the same as in insurance: a model is only as good as its data and its validation, and a model that discriminates well but is poorly calibrated produces the wrong reserves.

Logistic regression and scorecards

The industry standard because of its interpretability: variables binned using weight of evidence (WoE), selection by information value and scaling to points. It is benchmarked against gradient boosting, which usually discriminates better but requires explainability.

Discrimination and calibration

The Gini coefficient, the Kolmogorov-Smirnov statistic and the AUC measure whether the model ranks well; binomial and Hosmer-Lemeshow tests check that the estimated PD matches the observed rate by group.

Transition matrices and survival

Markov chains between ratings and proportional hazards models make it possible to build lifetime PDs, a stage 2 requirement, much like a multiple decrement table.

LGD and EAD

Severity is estimated from discounted recovery cash flows on defaulted loans, including collection costs; EAD for revolving credit uses conversion factors on the undrawn portion of the line.

The Vasicek model and IRB capital

The one-factor model assumes that default depends on a common systematic factor and an idiosyncratic one. Basel uses it to derive the 99.9% loss conditional on the factor, the basis of the capital formula for internal models.

Expected loss

\[EL = PD \times LGD \times EAD\]

In CNBV notation: reserves = PI × SP × EI, that is, probability of default, loss severity and exposure at default.

Lifetime expected loss

\[ECL = \sum_{t=1}^{T} \frac{PD_t^{marg}\; LGD_t\; EAD_t}{(1+r)^{t}}\]

PD_t^marg is the (unconditional) probability of defaulting in year t, T the remaining term and r the loan's effective interest rate; for stage 1 only t = 1 is used.

Credit risk capital (IRB, retail)

\[K = LGD\left[\Phi\left(\frac{\Phi^{-1}(PD) + \sqrt{R}\,\Phi^{-1}(0.999)}{\sqrt{1-R}}\right) - PD\right]\]

Φ is the standard normal cumulative distribution function and R the asset correlation with the systematic factor; capital covers the unexpected loss at 99.9% over and above the expected loss.

Regulatory framework in Mexico

CNBV · Circular Única de Bancos

Sets out loan portfolio rating and loan loss reserves, with general methodologies by type of credit (commercial, revolving and non-revolving consumer, mortgage) and the option of internal methodologies subject to approval. The reserve is expressed as probability of default times loss severity times exposure.

Accounting criteria aligned with IFRS 9 · NIF C-16

Since January 1, 2022, bank loan portfolios have been classified into stage 1, 2 or 3 according to their impairment, with 12-month or lifetime reserves. CINIF's NIF C-16 applies the expected credit loss approach to entities that follow Mexican Financial Reporting Standards (NIF), such as many unregulated SOFOMES.

Basel III in Mexico

Banks must maintain a minimum capital ratio of 10.5% including the conservation buffer, and banks designated as domestic systemically important must hold an additional surcharge: in the 2026 designation, eight banks with surcharges of 0.60 to 1.50 percentage points. A breach triggers corrective measures by the CNBV.

CNBV · Capital Adequacy Assessment

Every year, banks carry out a capital adequacy exercise under supervisory and internal scenarios, with projections of credit losses, revenue and capital over a multi-year horizon. It is the sector's main regulatory stress exercise.

Fintech Law and SOFOMES

The 2018 Ley para Regular las Instituciones de Tecnología Financiera (Fintech Law) created electronic payment fund institutions and crowdfunding institutions, licensed by the CNBV. Regulated SOFOMES follow CNBV prudential rules; unregulated ones register with CONDUSEF (the financial consumer protection agency) and must comply with anti-money laundering rules.

Banco de México

Publishes the Financial Stability Report with system-wide stress tests and regulates credit bureaus, whose information is the core input for scoring models.

Case study: expected loss reserves for a consumer loan portfolio

A SOFOM with a personal loan portfolio of $970 million classifies $800 million in stage 1 (12-month PD of 4%, LGD of 70%), $120 million in stage 2 with a remaining term of three years and $50 million in stage 3. In stage 2, the expected exposures at the start of each year are 120, 90 and 50 million, the marginal PDs 12%, 10% and 8%, the LGD 70% and the effective discount rate 30%. In stage 3, PD is 100% and LGD 80%. For simplicity, stage 1 is not discounted.

Stage 1: 800 × 0.04 × 0.70 = $22.40 million.
Stage 2, lifetime: year 1: 0.12 × 0.70 × 120 / 1.30 = 7.754; year 2: 0.10 × 0.70 × 90 / 1.30² = 3.728; year 3: 0.08 × 0.70 × 50 / 1.30³ = 1.275. Total $12.76 million, 64.5% more than the 7.75 million under a 12-month horizon.
Stage 3: 50 × 1.00 × 0.80 = $40.00 million.
Total reserve: 22.40 + 12.76 + 40.00 = $75.16 million, coverage of 7.75% of the portfolio.
Stress: with PDs multiplied by 1.5 and LGD five points higher, stage 1 rises to 36.00, stage 2 to 20.50 and stage 3 to 42.50. The reserve reaches $99.00 million, 23.84 million (31.7%) more than in the base scenario.

Lesson: Moving a loan from stage 1 to stage 2 multiplies its reserve because the horizon changes from 12 months to the full lifetime, and that jump makes the results highly sensitive to the significant increase in credit risk criterion. Documenting that criterion and stressing the parameters is as important as estimating them.

Where they work and how they grow

Analyst (0 to 3 years)

Prepares origination and collections databases, calculates delinquency and vintage indicators, and develops models under supervision. Learns the regulatory reserving methodology.

Model specialist (3 to 7 years)

Develops PD, LGD and EAD models end to end, documents them for validation and audit, and takes part in the monthly reserve calculation and stress exercises.

Credit risk manager (7 to 12 years)

Owns the origination policy or the reserving and capital framework for a portfolio, negotiates with the business and collections teams, and presents to the risk committee.

Chief risk officer (12+ years)

Leads the credit risk function or the entity's integrated risk management, answers to the board and the regulator, and sets the loss appetite.

Typical employers in Mexico

Commercial banks (risk, models and origination)
Development banks and public development funds
SOFOMES and consumer and auto lenders
Fintech institutions and digital lending platforms
Credit bureaus
Consulting and audit firms with a risk practice
CNBV and Banco de México
Credit rating agencies

Common roles

Credit risk analystScoring modelerIFRS 9 reserving specialistModel validatorStress testing analystOrigination policy managerCredit data scientistChief risk officer

Skills and tools

Technical

Generalized linear models and logistic regressionSurvival analysisMarkov chains and transition matricesSupervised machine learningEconometrics for satellite modelsAccounting for financial instruments

Tools

Python (scikit-learn, statsmodels)RSASSQLSpark or cloud data platformsPower BI or Tableau

Personal

Healthy skepticism toward dataRigorous documentationCommunication with business teamsJudgment to balance growth and riskEthics in the use of personal data

Certification and training

FRM (GARP)

The benchmark credential in financial risk, with extensive modules on credit risk, Basel and capital measurement.

CERA

The actuarial credential in enterprise risk management, useful for those who aim for entity-wide risk roles.

SOA, Corporate Finance and ERM practice area

An FSA pathway with content on economic capital and risk that transfers well to banking.

Graduate degree in finance, risk or data science

Master's degrees in financial risk or data science are common on modeling teams and ease the move into validation and leadership.

Trends reshaping the field

Alternative data and digital lending

Fintechs originate using transactional, mobile phone and in-app behavioral data, which opens credit to people with no credit history but requires watching for bias and complying with personal data protection rules.

Model explainability

Gradient boosting models and neural networks are gaining ground, and with them techniques such as SHAP to explain decisions to customers, auditors and regulators.

Forward-looking scenarios in reserving

Expected loss requires probability-weighted macroeconomic scenarios, and the actuary becomes responsible for a judgment that did not exist under reserves based on days past due.

Climate risk in the portfolio

Banks and supervisors are starting to measure how physical events and the energy transition affect PD and collateral values in exposed sectors and regions.

Frequently asked questions

What does an actuary do in a bank that an economist does not?

Actuaries bring applied probability for default events, survival analysis, valuation of contingent cash flows and reserving experience. In practice, risk teams combine both profiles, and actuaries tend to stand out in reserving, capital and validation.

What changed with IFRS 9 in Mexico?

Reserves moved from depending mainly on observed delinquency to an expected loss approach with three stages. Loans with a significant increase in credit risk are reserved over their full lifetime, which brings forward the recognition of losses.

Do SOFOMES and fintechs need actuaries?

Yes. They originate with scoring models, must reserve on an expected loss basis and, when growing fast, need to measure vintages and stress their portfolios for their funders, who demand that analysis.

Which programming skills should I master?

SQL to extract data and Python or R to build models are indispensable; SAS is still present at large banks. Version control and model documentation are worth knowing, because every model is validated and audited.