LAB · 02 / 09

Commercial insurance

Loss ratios of five commercial lines and an actuarial model that decides how much to trust a book’s history. SUSEP · Bühlmann credibility · backtest

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How it works

Visual mode: shadows, ambient occlusion, depth of field and quality that adapts to your device. Light mode: no shadows or post-processing. Each bar is one cell of the data; the full analysis is right below.

Sheet of each analysis

Objective, why, target variable, predictors, method, metric, validation and whether the objective was reached.

How big each line is and how fast it grows

Objective: Size each commercial line and find the fastest-growing.
Why: Before choosing where to underwrite you need to know where the volume is and where it is going; growth shows where gaining share costs less.
Target variable: Annual direct premium by line family.
Predictors / explanatory variables: Line family (21 grouped SUSEP codes), year.
Method: Monthly → annual sum; compound growth rate 2016–2025.
Metric: R$ bn and % per year growth (nominal).
Validation: Market total checked against the published order of magnitude (~R$ 205 bn in 2025, all lines).
Objective reached?: Yes: property is the largest; engineering grows fastest.

Loss ratio: level and volatility

Objective: Separate expensive lines from unpredictable ones.
Why: An expensive line is fixed with price; a volatile one with capital and reinsurance. Treating both the same leads to mispricing or misallocated capital.
Target variable: Annual loss ratio (incurred claims ÷ earned premium).
Predictors / explanatory variables: Line family, year.
Method: Mean and standard deviation over 10 years.
Metric: Mean loss ratio; year-to-year deviation (points).
Validation: Isolated peak checked in the raw monthly data before keeping it.
Objective reached?: Yes: liability is the most volatile; surety the cheapest.

Who competes in each line

Objective: Find out whether there is room for a mid-sized insurer.
Why: A concentrated market requires scale to enter; a dispersed one rewards underwriting and service, which is where a digital insurer competes.
Target variable: HHI and top-5 share by family, 2025.
Predictors / explanatory variables: Premium by insurer and family.
Method: Herfindahl-Hirschman index.
Metric: HHI (below 1,500 = unconcentrated).
Validation: Count of active insurers above R$ 1 m premium to skip residual books.
Objective reached?: Yes: all 5 lines stay below 1,000.

Credibility: own history or the market’s?

Objective: Forecast each insurer’s next-year loss ratio better than the market or its own history alone.
Why: A small book has a noisy history and a new book has none; credibility says how much to trust each, and it is the accepted actuarial method for that.
Target variable: The insurer’s loss ratio in the family in year t.
Predictors / explanatory variables: Own loss ratio t−5…t−1, market mean, earned premium (weight).
Method: Bühlmann-Straub: Z = P / (P + k), k = within variance ÷ between-insurer variance.
Metric: Premium-weighted mean absolute error (loss-ratio points).
Validation: Backtest 2021–2025, using only years before the forecast one; 887 forecasts.
Objective reached?: Yes, with a small gain (27.0 × 27.5 for the market); the main result is the weight-by-size rule.

SUSEP database

Monthly premiums and claims of every insurer and line, 2016–2025, from the public SES database. Five commercial line families: cargo, liability, property, engineering and surety.

Credibility

Bühlmann-Straub model: blends the insurer’s history with the market’s, with a weight that grows with book size. Tested by forecasting 2021–2025 without looking ahead.

Z = P / (P + k)

Commercial insurance in data

Cargo, liability, commercial property, engineering and surety: the lines of an insurer focused on businesses. Using SUSEP’s public database, this analysis sizes each line, measures its risk and tests a classic actuarial model to forecast each insurer’s loss ratio for the following year.

Real-world use

Pricing and underwriting: how much to trust the book’s own history versus the market’s when setting a line’s rate, especially for a small or new book.

R$ 34.1 bndirect premium in 2025 across the 5 lines

85insurers writing premium in 2025

113,486monthly rows analysed (2016–2025)

845out-of-sample forecasts tested

How big each line is and how fast it grows

QuestionWhere is the premium volume and which line grows fastest?

Decision and whyI grouped 21 SUSEP line codes into 5 families a commercial insurer sells together. Line 0171 (Miscellaneous Risks) was left out: it mixes consumer products such as phones and would inflate "property".

ResultCommercial property is the largest (R$ 15.4 bn in 2025). Engineering grows fastest: 14.8% a year since 2016, in nominal terms.

Source: SUSEP · Ses_seguros.csv (prêmio direto)

Analysis technical sheet

Objective: Size each commercial line and find the fastest-growing.
Why: Before choosing where to underwrite you need to know where the volume is and where it is going; growth shows where gaining share costs less.
Target variable: Annual direct premium by line family.
Predictors / explanatory variables: Line family (21 grouped SUSEP codes), year.
Method: Monthly → annual sum; compound growth rate 2016–2025.
Metric: R$ bn and % per year growth (nominal).
Validation: Market total checked against the published order of magnitude (~R$ 205 bn in 2025, all lines).
Objective reached?: Yes: property is the largest; engineering grows fastest.

Direct premium, 2016 × 2025

2016
2025

Loss ratio: level and volatility

QuestionWhich line is riskiest, and in what way: expensive on average or unpredictable?

Decision and whyLoss ratio = incurred claims ÷ earned premium, year by year. I split level (10-year mean) from volatility (standard deviation across years), because they are different risks: one is solved with price, the other with capital and reinsurance.

ResultLiability is the most volatile (std. dev. of 30 points), peaking at 134% in 2019: a single bad year wipes out several good ones. Cargo & transport is the most stable (std. dev. of 5 points) and surety has the lowest mean loss ratio (21%).

Source: SUSEP · Ses_seguros.csv (sinistro ocorrido, prêmio ganho)

Analysis technical sheet

Objective: Separate expensive lines from unpredictable ones.
Why: An expensive line is fixed with price; a volatile one with capital and reinsurance. Treating both the same leads to mispricing or misallocated capital.
Target variable: Annual loss ratio (incurred claims ÷ earned premium).
Predictors / explanatory variables: Line family, year.
Method: Mean and standard deviation over 10 years.
Metric: Mean loss ratio; year-to-year deviation (points).
Validation: Isolated peak checked in the raw monthly data before keeping it.
Objective reached?: Yes: liability is the most volatile; surety the cheapest.

Loss ratio by year

Cargo & transport
Liability
Commercial property
Engineering
Surety

Summary 2016–2025

family	mean loss ratio	std. dev.	commission 2025
Cargo & transport	53%	5	24%
Liability	56%	30	16%
Commercial property	54%	11	14%
Engineering	52%	18	13%
Surety	21%	6	24%

Who competes in each line

QuestionIs there room for a new or mid-sized insurer, or are the lines dominated by a few?

Decision and whyI measured 2025 premium concentration with the HHI and the top-5 share. HHI sums the squared shares: below 1,500 a market is considered unconcentrated.

ResultAll 5 lines stay below 1,000 HHI, with 23 to 44 active insurers. The top 5 hold about half of the premium. There is room to compete, and the edge becomes underwriting and price, not market access.

Source: SUSEP · Ses_seguros.csv, 2025

Analysis technical sheet

Objective: Find out whether there is room for a mid-sized insurer.
Why: A concentrated market requires scale to enter; a dispersed one rewards underwriting and service, which is where a digital insurer competes.
Target variable: HHI and top-5 share by family, 2025.
Predictors / explanatory variables: Premium by insurer and family.
Method: Herfindahl-Hirschman index.
Metric: HHI (below 1,500 = unconcentrated).
Validation: Count of active insurers above R$ 1 m premium to skip residual books.
Objective reached?: Yes: all 5 lines stay below 1,000.

family	insurers (> R$ 1 m)	HHI	top 5
Cargo & transport	26	785	53%
Liability	39	692	49%
Commercial property	44	744	52%
Engineering	23	880	54%
Surety	41	768	49%

Credibility: own history or the market’s?

QuestionTo price next year, should I use my book’s loss ratio or the market’s?

Decision and whyI used the Bühlmann-Straub model, an actuarial standard: forecast = Z × (own mean) + (1 − Z) × (market mean), with Z = P / (P + k), where P is the book’s earned premium and k comes from the data itself (within-insurer variance ÷ between-insurer variance). I compared it with using only the market or only the own history, forecasting each year from 2021 to 2025 with the previous 5 years, never looking ahead.

ResultCredibility has the lowest error overall: 27.0 loss-ratio points on average, versus 27.5 using the market and 27.7 using only the own history (1.6% better than the market). The gain is small: insurer-level loss ratios are very noisy. The value is the rule for how much to trust: in engineering, a book already earns 50% weight with R$ 115 m of premium over 5 years; in property, only at R$ 2,007 m.

Source: SUSEP · Ses_seguros.csv · analises/seguros.py

Analysis technical sheet

Objective: Forecast each insurer’s next-year loss ratio better than the market or its own history alone.
Why: A small book has a noisy history and a new book has none; credibility says how much to trust each, and it is the accepted actuarial method for that.
Target variable: The insurer’s loss ratio in the family in year t.
Predictors / explanatory variables: Own loss ratio t−5…t−1, market mean, earned premium (weight).
Method: Bühlmann-Straub: Z = P / (P + k), k = within variance ÷ between-insurer variance.
Metric: Premium-weighted mean absolute error (loss-ratio points).
Validation: Backtest 2021–2025, using only years before the forecast one; 887 forecasts.
Objective reached?: Yes, with a small gain (27.0 × 27.5 for the market); the main result is the weight-by-size rule.

Mean absolute error by family (loss-ratio points)

market only
own history only
credibility

Mean error from 2021 to 2025, weighted by each insurer’s earned premium.

Weight on own history (Z) × book size, 2025

Cargo & transport
Engineering
Commercial property

earned premium over 5 years (R$ m) (log scale) × Z

What each dataset contributed

Premium by line and year: size and growth of each market.
Incurred claims ÷ earned premium: separated expensive lines from unpredictable ones, which call for different answers (price × capital and reinsurance).
Premium by insurer: showed unconcentrated markets, where underwriting and price decide.
History by insurer and line: gave the credibility model the rule for how much to trust one’s own book.

Limits of this analysis

Data is aggregated by insurer and line, with no individual policy or claim: client-level risk cannot be modelled.
Nominal values, not adjusted for inflation.
Incurred claims include estimates (IBNR) that may be revised later.

Analysis code: analises/seguros.py