Sector and Geographic Credit Concentration

Why Sector and Geographic Concentration Matter

A portfolio may have many separate borrowers yet still be exposed to a limited set of economic conditions. For example, borrowers in different industries may depend on the same regional housing market, while firms in the same industry may operate in different countries but remain sensitive to a common commodity price. Sector and geographic concentration analysis helps identify these shared exposures.

A concentration share is a descriptive measure of how much of a portfolio is assigned to a category. It does not, by itself, estimate default probability, loss severity, or portfolio loss volatility. Its value depends on the exposure measure and classification rules used. For credit analysis, exposure at default (EAD) is often a useful basis when the objective is to compare amounts potentially exposed to loss. A different question may require a different basis, but the basis should be stated and applied consistently.

Definition: For a portfolio with total exposure $E$, the share assigned to category $c$ is $s_c=E_c/E$, where $E_c$ is the exposure in that category. If the categories form a complete, nonoverlapping classification of the portfolio, their shares sum to 1. Sector shares classify exposures by economic activity; geographic shares classify them by a stated location rule, such as borrower domicile or location of collateral.

Sector and geography are two different views of the same portfolio. They are not usually mutually exclusive with each other: a loan can belong to both a sector and a geographic region. Therefore, sector shares sum to 100% within the sector classification and geographic shares sum to 100% within the geographic classification. Adding the two sets together would count the portfolio twice.

Classification rules matter. A lender might classify a commercial real estate loan by the borrower’s primary business, by the property’s use, or by the collateral type. Geographic location might refer to the borrower’s headquarters, the location of the insured property, or the country generating most of the borrower’s revenue. Any of these conventions can be appropriate for a stated purpose; switching conventions within a calculation makes the resulting shares hard to interpret.

Calculating and Interpreting Exposure Shares

The calculation is simple once the exposure basis and categories are defined. First aggregate the exposures in each category. Then divide each category total by the portfolio total. A portfolio can be described at more than one level: broad sectors may reveal a large concentration, while a sector-by-region table can show whether that exposure is concentrated in a particular location as well.

Worked Example: Sector and Geographic Shares

Method. Aggregate EAD separately by sector and by geography, then divide each total by portfolio EAD. A hypothetical lender has these five positions, all in millions of dollars:

Commercial real estate: $28 million, of which $22 million is coastal and $6 million is inland.
Residential mortgages: $22 million, of which $20 million is coastal and $2 million is inland.
Energy: $18 million, of which $8 million is coastal and $10 million is inland.
Agriculture: $12 million, all inland.
Transport: $20 million, of which $10 million is coastal and $10 million is inland.

Step 1: Check the portfolio total. Total EAD is $28+22+18+12+20=100$ million dollars. The coastal subtotal is $22+20+8+0+10=60$ million dollars, and the inland subtotal is $6+2+10+12+10=40$ million dollars. The two geographic subtotals reconcile to total EAD: $60+40=100$.

Step 2: Calculate sector shares. The commercial real estate share is $28/100=28\%$; residential mortgages are $22/100=22\%$; energy is $18/100=18\%$; agriculture is $12/100=12\%$; and transport is $20/100=20\%$. These shares sum to $28\%+22\%+18\%+12\%+20\%=100\%$.

Step 3: Calculate geographic shares. The coastal share is $60/100=60\%$, and the inland share is $40/100=40\%$. These also sum to 100%.

Step 4: Interpret a joint category. Coastal commercial real estate represents $22/100=22\%$ of total portfolio EAD. It represents $22/28=78.57\%$ of commercial real estate EAD. The first percentage answers “what share of the whole portfolio is coastal commercial real estate?” The second answers “what share of the commercial real estate exposure is coastal?”

Check and common mistake avoided. The sector totals and geography totals each reconcile to $100 million. Do not add 28% commercial real estate to 60% coastal and call the result a 88% portfolio concentration: these categories overlap, and the same exposures can appear in both.

A large share is a signal for further investigation, not a conclusion that losses will be large. The same share can have different risk implications depending on borrower quality, collateral, contractual terms, default likelihood, and recovery. Conversely, moderate shares in several categories can still be vulnerable if those categories respond to the same economic driver.

How Common Drivers Cluster Credit Losses

A shared economic driver can make defaults more likely to occur together. For instance, a downturn could affect multiple borrowers in one region, or a commodity-price decline could affect several firms across related sectors. The important distinction is between borrowers’ individual default probabilities and the dependence between their default outcomes. The dependence affects the distribution of aggregate losses even when the expected loss of each exposure is unchanged.

The following simplified model makes this point. Let $Z=1$ denote a downturn and $Z=0$ denote no downturn. Assume a downturn has probability 0.2000. Two borrowers each have a $10 million loss if they default and no loss otherwise. Conditional on the state of the economy, their defaults are independent. Each borrower’s default probability is 0.3000 in a downturn and 0.0500 otherwise. This is a hypothetical model, not a claim about observed default rates.

Model assumption: Conditional independence means the borrowers’ default indicators are independent after the common economic state $Z$ is specified. Unconditionally, their defaults need not be independent, because both outcomes respond to $Z$.

Worked Example: Measuring the Effect of a Common Downturn

Method. Find the marginal default probability and joint default probability by conditioning on the common state. Use their difference from the independent case to compare aggregate loss variance. The common mistake to avoid is treating conditional independence as unconditional independence.

Let $I_1$ and $I_2$ equal 1 if borrower 1 or borrower 2 defaults, respectively, and 0 otherwise. For either borrower, the marginal default probability is

$$ P(I_j=1)=0.2000(0.3000)+0.8000(0.0500)=0.0600+0.0400=0.1000. $$

Thus each borrower has expected loss $10(0.1000)=1.0000$ million dollars, and the expected aggregate loss is $2.0000 million.

Conditional independence gives a joint default probability of $0.3000^2=0.0900$ in a downturn and $0.0500^2=0.0025$ without a downturn. Therefore,

$$ P(I_1=1,I_2=1)=0.2000(0.0900)+0.8000(0.0025)=0.0180+0.0020=0.0200. $$

The covariance of the default indicators is

\operatorname{Cov}(I_1,I_2)=E[I_1I_2]-E[I_1]E[I_2]=0.0200-(0.1000)(0.1000)=0.0100.

Each indicator has variance $0.1000(1-0.1000)=0.0900$. Aggregate loss in millions is $L=10I_1+10I_2$, so

\operatorname{Var}(L)=10^2(0.0900)+10^2(0.0900)+2(10)(10)(0.0100)=20.0000

million dollars squared. The standard deviation is $\sqrt{20.0000}=4.4721$ million dollars. If the defaults instead were independent unconditionally with the same marginal probability 0.1000, the covariance term would be zero and the variance would be $100(0.0900)+100(0.0900)=18.0000$ million dollars squared, with standard deviation $\sqrt{18.0000}=4.2426$ million dollars.

Check and common mistake avoided. Both models have the same expected aggregate loss of $2.0000 million, but the common-driver model has greater variance. Conditional independence does not permit dropping the covariance term in the unconditional aggregate-loss variance.

The variance identity used above follows directly from expanding the square. For two loss amounts $X_1$ and $X_2$, subtract their means and expand:

\operatorname{Var}(X_1+X_2) =E\left[((X_1-E[X_1])+(X_2-E[X_2]))^2\right] =\operatorname{Var}(X_1)+\operatorname{Var}(X_2)+2\operatorname{Cov}(X_1,X_2).

The cross-product inside the square has expectation $2\operatorname{Cov}(X_1,X_2)$, which explains the final term. Positive covariance increases aggregate variance; negative covariance decreases it. For more than two exposures, the variance is the sum of individual variances plus twice the sum of covariances over all distinct pairs. Consequently, exposure shares alone cannot determine the variability of portfolio credit losses: assumptions about joint outcomes are also needed.

Combining Sector and Geography in Stress Analysis

A sector-by-geography table can locate overlapping exposure concentrations. It is especially useful for a hypothetical stress scenario that specifies which cells are affected and by how much. Such a scenario is a conditional calculation: it estimates losses under the stated assumptions, not the probability that the scenario will occur. If categories form a complete partition, each exposure should appear in one cell only, so the scenario loss can be calculated without counting any exposure twice.

Worked Example: A Sector-by-Region Stress Scenario

Method. Build a mutually exclusive sector-geography table, apply each scenario loss rate to its specified cell, and add the cell losses. The common mistake to avoid is applying a sector loss rate and a geographic loss rate to the same exposure as if they were separate losses.

A hypothetical $120 million portfolio is allocated as follows, in millions of dollars:

Sector	Coastal	Inland	Total
Commercial real estate	40	10	50
Manufacturing	20	15	35
Agriculture	0	20	20
Utilities	10	5	15
Total	70	50	120

The sector shares are commercial real estate $50/120=41.67\%$, manufacturing $35/120=29.17\%$, agriculture $20/120=16.67\%$, and utilities $15/120=12.50\%$. They sum to 100.01% because the displayed percentages are rounded; the unrounded shares sum to 100%. The coastal share is $70/120=58.33\%$, and the inland share is $50/120=41.67\%$.

Suppose a hypothetical stress scenario assigns a 12% loss rate to coastal commercial real estate, 8% to coastal manufacturing, 15% to inland agriculture, and 2% to all utilities. All other cells have zero incremental loss in this scenario. The cell losses are:

Coastal commercial real estate: $40(0.12)=4.80$ million dollars.
Coastal manufacturing: $20(0.08)=1.60$ million dollars.
Inland agriculture: $20(0.15)=3.00$ million dollars.
Utilities: $(10+5)(0.02)=0.30$ million dollars.

The total scenario loss is $4.80+1.60+3.00+0.30=9.70$ million dollars. Relative to total EAD, this is $9.70/120=8.0833\%$, or 8.08% when rounded to two decimal places.

Check and common mistake avoided. The table’s row totals sum to $120 million, and its column totals also sum to $120 million. The $9.70 million result counts each stressed cell once; it is a scenario loss, not a probability-weighted expected loss. Do not add separate sector and geography “losses” if both calculations include the same exposures.

Practical Interpretation and Common Traps

Sector and geographic analysis is most useful when its assumptions are explicit and its results are linked to plausible economic drivers. A concentration report should make clear what exposure measure it uses, how the categories are defined, and whether location refers to a borrower, asset, collateral, or source of revenue. Those choices can change the distribution of exposures across categories.

Confusing exposure count with exposure share. Ten small loans do not necessarily represent more credit exposure than two large loans. A share based on EAD weights positions by amount.
Mixing denominators. A share of total portfolio EAD and a share of one sector’s EAD answer different questions. Label the denominator when reporting a percentage.
Assuming labels imply independence. Borrowers in different sectors or regions can still share an economic driver. Classification helps investigate dependence; it does not prove that exposures are independent.
Adding overlapping views. Sector categories and geographic categories are separate classifications of the same exposures. Do not add their shares or losses without accounting for overlap.
Treating a stress result as a forecast. A scenario loss follows from its stated loss rates and affected exposures. It is not an expected loss unless scenario probabilities and the other relevant outcomes are incorporated.

Sector and geographic shares complement name-level concentration measures: the name-level view focuses on individual obligors, while these classifications help reveal common economic sensitivities across obligors. Together with an explicit dependence model or a clearly stated stress scenario, they provide a more informative view of how credit losses could cluster. This treatment is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus.

Check Your Understanding

For each problem, state the exposure basis and show how the category totals reconcile before interpreting the result.

A hypothetical portfolio has EAD of $18 million in equipment finance, $12 million in retail lending, and $30 million in home loans. Calculate each sector’s share of total EAD and identify the largest sector share. (Answer: 30.00%, 20.00%, and 50.00%, respectively; home loans are largest.)
A $80 million portfolio has $50 million of coastal exposure and $30 million inland. Of the coastal amount, $32 million is commercial property; of the inland amount, $8 million is commercial property. Calculate the coastal share of total EAD and the commercial-property share of total EAD. (Answer: Coastal $50/80=62.50\%$; commercial property $(32+8)/80=50.00\%$.)
Two borrowers each have a $5 million loss if they default. Their default probabilities are each 0.1000, and their joint default probability is 0.0250. Calculate the covariance of their default indicators and the variance of aggregate loss, in million-dollars squared. (Answer: Covariance $=0.0250-0.1000^2=0.0150$; variance $=25(0.09)+25(0.09)+2(5)(5)(0.0150)=5.25$ million-dollars squared.)
A $60 million portfolio contains $20 million of coastal energy exposure and $10 million of inland energy exposure. A scenario applies a 10% loss rate to coastal energy and a 4% rate to all inland exposures, including the inland energy. No other exposure is stressed. What is the scenario loss? (Answer: $20(0.10)+10(0.04)=2.40$ million dollars.)
A common downturn has probability 0.2500. Conditional default probabilities for two borrowers are each 0.2000 in a downturn and 0.0400 otherwise; defaults are conditionally independent. Find each marginal default probability and their unconditional joint default probability. (Answer: Marginal probability $=0.2500(0.2000)+0.7500(0.0400)=0.0800$; joint probability $=0.2500(0.2000^2)+0.7500(0.0400^2)=0.0112$.)

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