Movement between delinquency states

Figure 01 / 12

Separate probability, severity, and exposure

The simplified one-year expected loss is PD × LGD × EAD = $210,759.12. PD is 16.56%, LGD is 71.50%, and EAD is $1,780,000. 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	16.56	Percent over one year
LGD	71.5	Percent of exposure lost conditional on default
EAD	1,780,000	USD at default
Expected loss	210,759.12	USD over the stated horizon

An account’s current state and its path through prior states both matter. Roll rates require a defined starting population and transition window.

Refinanced accounts disappear from the delinquency denominator.

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 $1,780,000 of exposure. Its stated one-year PD and LGD imply $210,759.12 of expected loss, while the cover analysis leaves $1,331,500.00 of stress exposure. Monthly cash coverage is 0.66×. 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%	8,900	17,800	26,700
5%	22,250	44,500	66,750
10%	44,500	89,000	133,500
20%	89,000	178,000	267,000

Figure 03 / 12

Recorded collateral and eligible cover

The collateral record is $470,000, but a 45% illustrative haircut leaves $258,500.00 eligible in this scenario. Reserve cover adds $190,000. The resulting uncovered exposure is $1,331,500.00. Eligibility also needs enforceability and operational access; this arithmetic does not establish either.

Figure data and text version

Measure	USD
Recorded collateral	470,000
Eligible collateral	258,500
Recorded reserve	190,000
Combined usable cover	448,500
Uncovered exposure	1,331,500

Figure 04 / 12

Cash available for the period’s debt service

Defined cash available is $57,040.00 against $86,000.00 of debt service, for a 0.66× 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	57,040	After the expenses included in this illustration
Debt service	86,000	Principal and interest due in the same period
Cash after debt service	-28,960	Negative means a modeled shortfall

Figure 05 / 12

A constant-hazard illustration

The curve converts the stated one-year PD of 16.56% 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	97.03
M4	94.14
M6	91.35
M8	88.63
M10	86
M12	83.44

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	37,828.52
M4	74,532.66
M6	110,145.85
M8	144,700.5
M10	178,228.08
M12	210,759.12

Figure 07 / 12

Expected loss sensitivity to PD

Exposure stays at $1,780,000 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%	12,727
3%	38,181
5%	63,635
8%	101,816
12%	152,724
20%	254,540

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
servicing transition policy — primary	712,000
Independent group B	534,000
Independent group C	356,000
Independent group D	178,000

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	39,928	86,000
M2	48,484	86,000
M3	62,744	86,000
M4	51,336	86,000
M5	74,152	86,000
M6	65,596	86,000

Figure 10 / 12

Terms belong in the decision record

This record concerns watch movement between states. 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	Movement between delinquency states
exposure_usd	1,780,000
horizon	One year for PD; one month for cash coverage
pd_percent	16.56
lgd_percent	71.5
review_trigger	Refinanced accounts disappear from the delinquency denominator.

Figure 11 / 12

One cause can affect several loss components

The stress path connects servicing transition policy 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	Refinanced accounts disappear from the delinquency denominator.
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 ($210,759.12), uncovered exposure ($1,331,500.00), and monthly cash gap ($28,960.00) 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	210,759.12
Uncovered stress exposure	1,331,500
Monthly cash gap	28,960

Connect the result to the system

Preserve transition lineage and distinguish cure, refinancing, default, and closure.

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.