Limits on a changing exposure stock

Figure 01 / 12

Separate probability, severity, and exposure

The simplified one-year expected loss is PD × LGD × EAD = $73,673.60. PD is 9.20%, LGD is 71.50%, and EAD is $1,120,000. This is a teaching expected-value calculation, not an accounting allowance method or a capital standard.

Figure data and text version

Input	Value	Unit
PD	9.2	Percent over one year
LGD	71.5	Percent of exposure lost conditional on default
EAD	1,120,000	USD at default
Expected loss	73,673.6	USD over the stated horizon

A processing limit controls one source of new exposure, while existing obligations continue to mature. The limit needs the right aggregation key and observation period.

Several related accounts each receive the full limit despite one shared loss driver.

All amounts, rates, capacity limits, and outcomes in this case are synthetic. The three conditions are separate assumptions for comparison. A better result in the response condition is not measured proof that the proposed control causes that improvement. The figures expose the calculation and its limits; a real deployment needs its own evidence.

Read the result

The case has $1,120,000 of exposure. Its stated one-year PD and LGD imply $73,673.60 of expected loss, while the cover analysis leaves $812,500.00 of stress exposure. Monthly cash coverage is 0.82×. These are separate measures: one describes an average under probability assumptions, one describes available cover, and one describes a period’s funding capacity.

Figure 02 / 12

Probability and severity move the result together

Each cell is the same exposure multiplied by the row default probability and the column loss severity. The grid makes joint stress visible. A downturn can affect both factors; the calculation does not assume that the two causes are independent.

Figure data and text version

PD	LGD 25%	LGD 50%	LGD 75%
2%	5,600	11,200	16,800
5%	14,000	28,000	42,000
10%	28,000	56,000	84,000
20%	56,000	112,000	168,000

Figure 03 / 12

Recorded collateral and eligible cover

The collateral record is $250,000, but a 45% illustrative haircut leaves $137,500.00 eligible in this scenario. Reserve cover adds $170,000. The resulting uncovered exposure is $812,500.00. Eligibility also needs enforceability and operational access; this arithmetic does not establish either.

Figure data and text version

Measure	USD
Recorded collateral	250,000
Eligible collateral	137,500
Recorded reserve	170,000
Combined usable cover	307,500
Uncovered exposure	812,500

Figure 04 / 12

Cash available for the period’s debt service

Defined cash available is $40,300.00 against $49,000.00 of debt service, for a 0.82× ratio. The ratio uses one period and one defined cash measure. It does not establish affordability, suitability, or a required underwriting threshold.

Figure data and text version

Component	USD	Meaning
Cash available	40,300	After the expenses included in this illustration
Debt service	49,000	Principal and interest due in the same period
Cash after debt service	-8,700	Negative means a modeled shortfall

Figure 05 / 12

A constant-hazard illustration

The curve converts the stated one-year PD of 9.20% to a constant monthly hazard using h = 1 − (1 − PD)^(1/12). Survival after 12 months is therefore 1 − PD. Constant hazard is an assumption; seasonality and changing exposure are omitted. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Months since start	Survival %
M0	100
M2	98.4
M4	96.83
M6	95.29
M8	93.77
M10	92.27
M12	90.8

Figure 06 / 12

Cumulative expected loss at comparable age

This curve multiplies cumulative modeled default probability by a fixed EAD and LGD. It is useful for separating observation age from the chosen assumptions. It omits amortization, recoveries over time, prepayment, and changing utilization. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Age	Expected USD
M0	0
M2	12,777.95
M4	25,352
M6	37,725.42
M8	49,901.4
M10	61,883.09
M12	73,673.6

Figure 07 / 12

Expected loss sensitivity to PD

Exposure stays at $1,120,000 and LGD stays at 71.50% while PD changes. The linear relationship follows the simplified expected-loss formula. It is not evidence that real-world losses respond linearly to economic stress. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

One-year PD	Expected USD
1%	8,008
3%	24,024
5%	40,040
8%	64,064
12%	96,096
20%	160,160

Figure 08 / 12

A shared dependency can dominate exposure

The four amounts are disjoint portions of this case’s exposure. The largest bucket represents one shared supplier, funding source, or other specified dependency. Counting customers alone would not reveal this common loss driver.

Figure data and text version

Dependency bucket	Exposure USD
related merchant group — primary	448,000
Independent group B	336,000
Independent group C	224,000
Independent group D	112,000

Figure 09 / 12

A weak month can disappear inside an average

The six-month path applies explicit seasonal factors to the defined monthly cash amount and compares it with fixed debt service. These are constructed cash assumptions, not a forecast. A negative month needs a funding or terms response even when the average ratio looks comfortable. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Month	Cash available	Debt service
M1	28,210	49,000
M2	34,255	49,000
M3	44,330	49,000
M4	36,270	49,000
M5	52,390	49,000
M6	46,345	49,000

Figure 10 / 12

Terms belong in the decision record

This record concerns use limits to bound exposure. A binary approval omits the amount, observation horizon, cover assumptions, and review trigger. Retaining those terms makes the decision reproducible and identifies when changed facts require another assessment.

Figure data and text version

Field	Illustrative value
entity	Limits on a changing exposure stock
exposure_usd	1,120,000
horizon	One year for PD; one month for cash coverage
pd_percent	9.2
lgd_percent	71.5
review_trigger	Several related accounts each receive the full limit despite one shared loss driver.

Figure 11 / 12

One cause can affect several loss components

The stress path connects related merchant group to repayment cash, default probability, recovery, and funding needs. Arrows state the scenario’s assumed causal chain. They are hypotheses to test with evidence, not proof that every affected customer will default.

Figure data and text version

Stage	Mechanism
Dependency shock	Several related accounts each receive the full limit despite one shared loss driver.
Cash pressure	Receipts fall or essential payments move earlier
Default and severity	Repayment probability and recovery can both worsen
Response	Reassess terms, usable cover, and exposure within the approved process

Figure 12 / 12

Expected loss, uncovered exposure, and cash gap

Expected loss ($73,673.60), uncovered exposure ($812,500.00), and monthly cash gap ($8,700.00) answer different questions. The bars are deliberately separated measures and must not be added. A low expected value can coexist with a large stress exposure.

Figure data and text version

Measure	USD
Expected one-year loss	73,673.6
Uncovered stress exposure	812,500
Monthly cash gap	8,700

Connect the result to the system

Aggregate relevant exposure and enforce reservations before new commitments are accepted.

Check the population, evidence, permitted action, and actual effect together. A balanced calculation can still use the wrong population; a successful response can still leave an unknown financial outcome. The case’s numerical result applies only to its stated assumptions.