Operational risk · loss distribution approach

Load a loss-event register — or the teaching workbook’s 1,500-event demo — and every event type gets a frequency and a severity fitted to its own events. The simulation convolves them year by year, correlates the event types, and returns expected loss, OpVaR, expected shortfall, the capital each event type consumes and a multi-year loss horizon. It runs in your browser; the register never leaves it.

1 · Loss-event register

CSV, TSV or pasted from Excel, in any of the five languages. One row per event.

Demo loss-event register · 1,500 events · 8 columns · Basel event-type codes detected

Column mapping

Guessed from the headers. The date and one loss column are required; net loss is gross − recovery when there is no net column.

Event date *Gross lossRecoveryNet lossEvent typeEvent ID

2 · The register

What the data says before any model: how often, how much, when and where.

Events

1,500

2022-04-01 – 2023-12-30

Observation window

1.75 years

21 calendar months

Events per year

857.39

per year

Net loss per year

284,002

per year

Gross loss

511,406

Recoveries

14,548

2.8% of gross

Mean / median event

331.2 / 136

a mean far above the median is a skewed severity

Largest event

12,717

2.6% of all net loss

Cell

Events and net loss by month · All cells■ events ·━ Net loss

Heat map columns

Net loss by cell and Business unit

	Finance & accounting	Business unit Guatemala	Business unit Panama	Quality & productivity	Corporate banking	Technology	Legal	Internal audit	Credit administration	Operations - Loans	Operations	Business unit El Salvador	Business unit Nicaragua	Risk management	Other
1.1 - Unauthorised activity	42				338			324	14	264	2.8K	397
1.2 - Theft and fraud	8.4K	6.3K	11.1K	6.4K	5.4K	3.5K	11.6K	12.2K	3.1K	10.2K	1.5K	4.1K	3.1K	1.3K	13.7K
2.1 - Theft and fraud	6.5K	1.5K	500	386	904	86	646	31	2K	776	1.5K	1.7K	3.7K	1K	3.1K
2.2 - Systems security	3.3K	422	1.7K	591		498	2.1K	3.8K	826	421	2.7K	30	1K	593	890
3.1 - Employee relations	893	4.6K	349	3.6K	2.7K	2.6K	1.5K	382	3.6K	572	470	1.7K	1.5K	710	3.8K
3.2 - Safe environment	1.7K	8.4K	7.7K	2.9K	5.9K	4.5K	1.3K	2.1K	888	3.6K	3K	2.4K	274	7.6K	7.5K
3.3 - Diversity and discrimination	7.9K	3.1K	973	108	3K		666	387	1.9K	546	2.1K	1.8K	480	1.5K	2.4K
4.1 - Suitability, disclosure and fiduciary	8.2K	2K	3K	1.8K	4.4K	2.5K	4.2K	4.7K	4.1K	1.5K	3.9K	3.5K	1.1K	2.7K	8.7K
4.2 - Improper business or market practices	4.7K	1.6K	3.1K	14.2K	897	409		751	3K	3.7K	379	3.2K	1.9K	660	4.1K
4.3 - Product flaws	2.5K	233	222	155	262	12.4K	2.7K	832	255	669	1.9K	171	958	729	6.3K
4.4 - Selection, sponsorship and exposure	1.3K	370		1.2K	266	40	469	486	293	83	27	590	3.3K	1.7K	2.5K
4.5 - Advisory activities	129	29	896	89			817	600	339	90	1.6K	1.9K	756	58	485
5.1 - Disasters and other events	815	3K	152	95		268		195	1.9K	515	19	725	20	1.4K	2.9K
6.1 - Systems	2.3K	4K	4K	1.3K	5K	2.2K	1.5K	1.1K	2.7K	4.1K	913	558	4.7K	536	8.5K
7.1 - Transaction capture, execution and maintenance	2.8K	2.4K	341	605	2.5K	82	1.1K	697	1.2K	187	2K	2.2K	227	1.3K	2.5K
7.2 - Monitoring and reporting	180	57				17				574				492	346
7.3 - Customer intake and documentation		7				19			2.3K					410	9
7.4 - Customer and client account management		245		80				28				127		36	28
7.5 - Trade counterparties				22				45							1.2K
7.6 - Vendors and suppliers					36		257			17	317	31

Darker is more loss. The fourteen largest columns are shown; the rest are folded into “Other”.

Ten largest events

Event date	Event type (level 3)	Business unit	Cause	Gross loss	Net loss
2022-11-24	4.2.1 - Antitrust	Quality & productivity	People	12,717	12,717
2023-03-24	4.3.1 - Product defects (unauthorised, etc.)	Technology	People	11,647	11,647
2023-01-11	3.3.1 - All discrimination types	Finance & accounting	People	7,427	7,427
2023-12-07	3.2.3 - Workers compensation	Business unit Panama	People	7,121	7,121
2023-06-29	3.2.3 - Workers compensation	Business unit Guatemala	People	6,016	6,016
2023-11-14	1.2.5 - Forgery	Operations - Loans	People	5,256	5,256
2023-01-30	1.2.8 - Account take-over / impersonation	Internal audit	People	4,897	4,897
2023-01-27	3.1.1 - Compensation, benefit, termination issues	Business unit Guatemala	People	4,369	4,369
2023-10-15	1.2.6 - Check kiting	Business unit Panama	People	4,084	4,084
2023-07-04	3.2.3 - Workers compensation	Risk management	People	3,365	3,365

3 · Cells, frequency and severity

One row per unit of measure. The values in grey come from the data; type over them to override, ↺ to go back.

Cells bySplit cells byYears observedFrom the data: 1.75. λ = events ÷ years.

Cell	Events	λ / year	Frequency	KS	Largest	E[loss] / year
	10		VMR 0.97	0.330	2.8K	2.4K
	304		VMR 0.77	0.050	5.3K	58.2K
	78		VMR 1.51	0.124	2.9K	14K
	46		VMR 1.22	0.162	2.1K	10.7K
	81		VMR 0.94	0.152	4.4K	16.6K
	120		VMR 1.28	0.091	7.1K	34.1K
	46		VMR 1.31	0.156	7.4K	15.4K
	293		VMR 0.66	0.135	2.2K	32.2K
	107		VMR 0.94	0.064	12.7K	24.4K
	68		VMR 1.39	0.091	11.6K	17.3K
	45		VMR 0.81	0.068	1.5K	7.3K
	25		VMR 1.82	0.198	1.9K	4.5K
	37		VMR 1.13	0.216	1.6K	6.8K
	124		VMR 1.66	0.149	2.9K	24.8K
	82		VMR 0.69	0.157	1.5K	11.4K
	9		VMR 0.60	0.272	346	952.3
	8		VMR 0.91	0.429	2.2K	1.5K
	7		VMR 1.30	0.248	245	310.9
	5		VMR 1.22	0.465	907	739.6
	5		VMR 1.22	0.446	317	376.1
Total	1,500	857.39				284K

Click a cell to see its fitted severities against its data.

4 · Dependence between cells

Whether bad years for different event types coincide. It does not move the expected loss — it moves OpVaR.

IndependentEmpirical (from monthly losses)Uniform ρ

Rank correlation of monthly net losses

	1.1	1.2	2.1	2.2	3.1	3.2	3.3	4.1	4.2	4.3	4.4	4.5	5.1	6.1	7.1	7.2	7.3	7.4	7.5	7.6
1.1 - Unauthorised activity	1.00	0.06	0.02	0.26	0.15	0.34		0.33	0.18				0.06	0.34	0.25
1.2 - Theft and fraud	0.06	1.00	0.23	0.01			0.25			0.31			0.19			0.31	0.61
2.1 - Theft and fraud	0.02	0.23	1.00		0.24		0.04		0.19	0.12							0.35	0.42	0.20	0.09
2.2 - Systems security	0.26	0.01		1.00	0.23		0.12	0.16			0.18		0.44		0.03
3.1 - Employee relations	0.15		0.24	0.23	1.00		0.11	0.23	0.31					0.24	0.01	0.05		0.07	0.22
3.2 - Safe environment	0.34					1.00		0.52					0.10	0.29	0.38
3.3 - Diversity and discrimination		0.25	0.04	0.12	0.11		1.00		0.11			0.22				0.17	0.38		0.24	0.13
4.1 - Suitability, disclosure and fiduciary	0.33			0.16	0.23	0.52		1.00		0.07	0.41		0.02	0.40	0.42			0.12
4.2 - Improper business or market practices	0.18		0.19		0.31		0.11		1.00			0.10		0.14	0.49		0.15	0.10	0.08	0.23
4.3 - Product flaws		0.31	0.12					0.07		1.00	0.42	0.10	0.10	0.19		0.22	0.30	0.11
4.4 - Selection, sponsorship and exposure				0.18				0.41		0.42	1.00		0.32					0.20	0.08
4.5 - Advisory activities							0.22		0.10	0.10		1.00			0.04	0.29	0.12			0.48
5.1 - Disasters and other events	0.06	0.19		0.44		0.10		0.02		0.10	0.32		1.00	0.08					0.09
6.1 - Systems	0.34				0.24	0.29		0.40	0.14	0.19			0.08	1.00	0.30
7.1 - Transaction capture, execution and maintenance	0.25			0.03	0.01	0.38		0.42	0.49			0.04		0.30	1.00			0.08		0.26
7.2 - Monitoring and reporting		0.31			0.05		0.17			0.22		0.29				1.00	0.32	0.13
7.3 - Customer intake and documentation		0.61	0.35				0.38		0.15	0.30		0.12				0.32	1.00	0.28
7.4 - Customer and client account management			0.42		0.07			0.12	0.10	0.11	0.20				0.08	0.13	0.28	1.00	0.29
7.5 - Trade counterparties			0.20		0.22		0.24		0.08		0.08		0.09					0.29	1.00	0.04
7.6 - Vendors and suppliers			0.09				0.13		0.23			0.48			0.26				0.04	1.00

Spearman correlation between cells’ monthly net losses over 21 months; only positive values are shaded. The empirical mode uses this matrix, made consistent if needed.

5 · Simulation

IterationsConfidence levelLoss horizon (years)SamplingSeed

Run the simulation to see the results.

Operational risk · loss distribution approach

1 · Loss-event registerⓘ

Column mappingⓘ

Categoriesⓘ

2 · The registerⓘ