Internal ratings and master scales · RiskAtoms Academy

By the end you will be able to

1Describe how a rating model turns a borrower's information into a score, a PD and a grade.
2Read a master scale: grades, PD bands, central PDs and their mapping to agency-style ratings.
3Explain why grades cover bands of PDs, and the cliff effects and overrides that follow.
4Measure what a change of grade does to a loan's expected loss and to the book's grade profile.

Why it matters

The analysis of L3.3.02: Analysing a company's credit ended with a judgement: Larkhollow Freight Ltd is weaker than Thornvale Engineering Ltd. A bank cannot price, approve, provision or hold capital on a judgement. It needs one number per borrower, comparable across a German energy company, a UK haulier and a Dutch software firm, and checkable against what actually defaults. That number is the internal grade, and every grade on RiskAtoms Bank's scale means a PD twice as high as the one before.

Core explanation

From a credit file to a grade

L1.4.07: Credit ratings and credit spreads introduced ratings from the agencies' side. Banks also rate every borrower themselves, external rating or not. An internal rating has three parts: a rating model that produces a score and a PD; a master scale that turns the PD into a grade; and a credit officer who checks the result and can override it.

Illustrative dataRiskAtoms Bank plc's credit book

One made-up lending book, in pounds, at one made-up year end: twelve invented corporate borrowers (exposure at default £587m, expected loss £2.81m a year), 152,100 retail accounts in mortgages, personal loans and cards (exposure £4.485bn), a ten-grade master scale and an illustrative rating transition matrix. No firm or person in it is real. The same book runs through every lesson in Module 3.3, so the figures agree from lesson to lesson.

The model

For large companies the model is usually a scorecard mixing financial ratios with an analyst's scores for management, market position and industry. RiskAtoms Bank's illustrative model uses four inputs: net debt / EBITDA, EBITDA interest cover, size (turnover) and a 1-to-5 qualitative score. Each adds to a score, read as the log-odds of default. Fed Thornvale Engineering Ltd's ratios, it gives a model PD of 0.230%; Larkhollow Freight Ltd gets 1.684%. (Real models are fitted to default data; that is M6.4: Credit risk modelling.) Retail models are different in scale, not in kind: an application scorecard scores millions of applicants automatically (L3.3.14: Retail credit portfolios).

The grade describes the borrower, not the loan. A secured loan and an unsecured one to the same company have the same obligor grade and PD; the security changes the LGD, which some banks capture in a separate facility rating.

Sort itDoes it move the borrower's grade?

Facts from Larkhollow Freight Ltd's file. Which ones belong in its obligor rating (PD), and which affect only the loss if it defaults?

Net debt is 3.49 times EBITDA.
The founder's son, with ten years in the business, takes over as chief executive.
The bank's loan is secured on £18m of lorries.
EBITDA covers interest 4.5 times.
The facility has £4m undrawn that the company could draw before a default.

The master scale

The master scale is the bank's common language. Ten performing grades from “Exceptional” to “Watchlist”, plus default, each with a PD band and one central PD. From grade 2 to grade 8 each band's upper edge is twice its lower edge, so on a log scale the bands are equal steps and the central PD doubles from grade to grade. The agency-style column is only a rough guide (L3.3.05: External ratings in practice maps the two properly).

Grade	Name	PD band	Central PD	Agency-style
1	Exceptional	0.00% to 0.05%	0.03%	AAA to AA
2	Very strong	0.05% to 0.10%	0.07%	AA− to A+
3	Strong	0.10% to 0.20%	0.14%	A to A−
4	Good	0.20% to 0.40%	0.28%	BBB+ to BBB
5	Satisfactory	0.40% to 0.80%	0.57%	BBB−
6	Adequate	0.80% to 1.60%	1.13%	BB+ to BB
7	Fair	1.60% to 3.20%	2.26%	BB− to B+
8	Weak	3.20% to 6.40%	4.53%	B
9	Vulnerable	6.40% to 20.00%	11.31%	B− to CCC+
10	Watchlist	20.00% to 100%	30.00%	CCC to C

Why bands, not exact PDs?

A model PD to three decimals looks precise, but it is an estimate with wide error. Pooling borrowers into grades does four things. It makes PDs checkable: a grade with 400 borrowers has a default rate you can observe; one borrower does not. It makes them stable: a grade does not move every time a ratio wobbles, so pricing and limits do not either. It makes them comparable: grade 5 means the same PD in the corporate, bank and SME models. And it makes them usable: delegated authority (L3.3.01: The credit lifecycle), pricing grids and reports are all built on grades.

The price is the cliff effect at band edges. A model PD rising from 0.30% to 0.38% leaves Thornvale Engineering Ltd in grade 4 at 0.28%; a further rise to 0.41% moves it to grade 5, and its expected loss jumps from £45.6k to £92.8k. That is why the credit officer may override a grade by a notch with a documented reason, and why overrides are counted and reviewed: a model that is overridden often is a model that needs fixing.

The formal version

The rating chain and the geometric scale

The illustrative model, with net leverage $\ell$ , interest cover $\kappa$ , turnover $S$ in £m and qualitative score $q$ :

s = -4.90 + 0.55\,\ell -0.60\ln\kappa -0.25\ln\frac{S}{100} -0.35\,(q - 3)

For Larkhollow Freight Ltd:

\begin{aligned} s &= -4.90 + 0.55 \times 3.4921 -0.60 \ln 4.50 -0.25 \ln 2.10 -0.35 \times 0 \\ &= -4.900 + 1.921 -0.902 -0.185 = -4.067 \\ \mathrm{PD}^{\text{model}} &= \frac{1}{1 + e^{4.067}} = 1.684\% \in [1.60\%,\ 3.20\%) \;\Rightarrow\; \text{grade } 7,\ \mathrm{PD} = 2.26\% \end{aligned}

The geometric scale. With upper edges $\overline{p}_k = 0.05\% \times 2^{k-1}$ for grades 1 to 8, each band from grade 2 to 8 is $[\overline{p}_{k-1},\ 2\,\overline{p}_{k-1})$ , and its central PD is the geometric mean:

\begin{aligned} \mathrm{PD}_k &= \sqrt{\overline{p}_{k-1}\cdot 2\,\overline{p}_{k-1}} = \sqrt{2}\;\overline{p}_{k-1} = 0.05\% \times 2^{k-2}\sqrt{2} \\ \mathrm{PD}_4 &= 0.05\% \times 4 \times 1.4142 = 0.28\% \text{ (rounded)} \\ \ln \mathrm{PD}_k &= \ln(0.05\%\sqrt{2}) + (k-2)\ln 2 \quad\Rightarrow\quad \frac{\mathrm{PD}_{k+1}}{\mathrm{PD}_k} = 2 \end{aligned}

Two consequences. Any PD in a doubling band is within a factor $\sqrt{2} = 1.414$ of the central PD, so the rounding error from using grades is at most about 41% either way. And because EL = PD × LGD × EAD, one grade worse doubles a loan's expected loss. Grades 1, 9 and 10 are set by hand: grade 1 has no lower edge, grade 9 stretches from 6.4% to 20% and grade 10 covers everything above.

Try it

The tool opens on Larkhollow Freight Ltd. Push its leverage to 4.4 and its cover down to 2.7, the stress of L3.3.02: Analysing a company's credit: which grade? Then load Thornvale Engineering Ltd and see how far its ratios can move before it leaves grade 4.

Try itRate a company

Net debt / EBITDA3.5×

EBITDA / interest4.5×

Turnover£210m

Management and market position3.0 of 5

Credit officer's override

Intercept−4.900

Leverage1.921

Interest cover−0.902

Size−0.185

Qualitative0.000

Score = ln(PD / (1 − PD))−4.067

Model PD1.684%

Model grade7

Position in its band (0 = best edge)0.07

Final grade7 (Fair)

PD used by the bank2.26%

The weights are invented for this module and chosen so that the two companies of L3.3.02 land in their book grades. Every override must be written down with its reason and is tracked.

Worked example

Grading the book

RiskAtoms Bank's corporate book by grade

Step 1 of 5

1

The grade profile

EAD and expected loss in each grade:

Grade	Borrowers	EAD	Share of EAD	EL a year
2	1	£45.0m	7.7%	£12.6k
3	1	£70.0m	11.9%	£39.2k
4	2	£97.5m	16.6%	£84.4k
5	2	£150.0m	25.6%	£151.3k
6	2	£120.3m	20.5%	£482.9k
7	2	£68.0m	11.6%	£421.3k
8	1	£24.3m	4.1%	£604.2k
9	1	£12.0m	2.0%	£1,017.9k

Ratings drive everything downstream

One grade on Larkhollow Freight Ltd moves its expected loss by £231.1k a year, its approval route, its price and, under the IRB approach, its capital. That is why rating models are validated every year and their grades are compared with what actually defaults (L3.3.06: Probability of default).

Regulatory lens

Banks that use the internal ratings-based (IRB) approach must meet the Basel Committee's minimum requirements (Basel Framework, CRE36). Among them: at least seven grades for borrowers not in default and one for those in default; no excessive concentration in one grade; ratings refreshed at least once a year, more often for weaker borrowers; overrides identified and their performance tracked; and each grade's PD estimated as a long-run average of one-year default rates, from at least five years of data. Capital itself is in M4.2: Credit risk capital.

Spark Atoms

Spark AtomA floor under the best grade

RiskAtoms Bank's grade 1 has a central PD of 0.03%. A bank using the IRB approach could not use it for capital: the Basel Framework (CRE32) sets a floor of 0.05% on the PD of corporate exposures. No borrower is treated as safer than five defaults in ten thousand a year.

Spark AtomTwice as risky, one step down

Doubling bands are a common design because default rates in published agency studies rise roughly geometrically down the scale. On a log axis, a scale like RiskAtoms Bank's is a ruler with equal marks.

Key takeaways

An internal rating has three parts: a model that gives a score and PD, a master scale that gives a grade, and a credit officer who can override.
Scores are log-odds: PD = 1 / (1 + e^(−s)).
The master scale gives each grade a PD band and one central PD; on RiskAtoms Bank's scale the PD doubles from grade 2 to 8.
Bands make PDs checkable, stable, comparable and usable; their cost is cliff effects at band edges.
Obligor grades drive PD; collateral and seniority drive LGD. One grade worse doubles a loan's EL.

Reaction

Check what stuck

Question 1 · objective 2

On RiskAtoms Bank's master scale, which grade does a model PD of 0.90% get?

Question 2 · objective 2

A grade's band runs from 1.6% to 3.2%. What is its central PD as the geometric mean, in % (two decimals)?

%

Question 3 · objective 1

A rating model gives a score (log-odds) of −3.5. What is the model PD, in % (two decimals)?

%

Question 4 · objective 4

Larkhollow Freight Ltd is downgraded from grade 7 to grade 8. By what factor does its expected loss multiply (two decimals)?

×

Question 5 · objective 3

Why does the bank give every borrower in a grade the same PD, instead of each borrower's own model PD?

ABecause models cannot produce a PD for one borrowerBBecause one PD per grade can be checked against default rates, is stable, and is used the same way across all portfoliosCBecause regulators forbid model PDsDBecause it makes PDs higher

Glossary

Internal rating: A bank's own assessment of a borrower's chance of default, expressed as a grade on its master scale.
Rating model: A scorecard or statistical model that turns a borrower's financial and qualitative information into a score and a PD.
Master scale: A single table of grades used across the whole bank, each grade with a band of one-year PDs and one central PD.
PD band: The range of PDs that belong to one grade. A borrower whose PD falls inside it gets that grade.
Central PD: The one PD the bank uses for every borrower in a grade, here the geometric mean of the band's edges.
Obligor grade: A rating of the borrower: how likely it is to default on anything. It drives PD.
Facility rating: A rating of one loan, taking in its security and seniority. It drives LGD.
Override: A credit officer's decision to set a grade different from the model's, with a written reason.
Log-odds: The natural log of PD / (1 − PD). It runs from minus to plus infinity, which suits a weighted sum of inputs.
Cliff effect: The jump in PD, and so in pricing, capital and provisions, when a small change carries a borrower across a band edge.

Deep Dives & Origins

Deep Dives

W. F. Treacy and M. S. Carey, “Credit risk rating at large US banks”, Federal Reserve Bulletin 84(11), November 1998, pp. 897–921. Intermediate.
B. Engelmann and R. Rauhmeier (eds), The Basel II Risk Parameters, 2nd ed., Springer, 2011. Advanced.

Origins

Basel Committee on Banking Supervision, The Basel Framework, CRE36: IRB approach: minimum requirements to use IRB approach, Bank for International Settlements.
Basel Committee on Banking Supervision, The Basel Framework, CRE32: IRB approach: risk components, Bank for International Settlements.

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