P5. Through-the-Cycle vs Point-in-Time PD Explained

Risk: From Market Risk to Expected Credit Loss, Part 5. Previously: PD, LGD and EAD.

Through the cycle PD and point-in-time PD are two answers to what looks like one question. Both are legitimate. They differ by a factor that can exceed two in the same year on the same borrower, and a bank that runs one model for both purposes will be wrong twice.

The two philosophies

Point-in-time (PIT) asks: what is this borrower’s default probability over the next year, given everything we know today, including current economic conditions? It rises in downturns and falls in recoveries. It is a forecast.

Through-the-cycle (TTC) asks: what is this borrower’s default probability averaged over a full economic cycle? It strips out where we happen to be in the cycle and reports a long-run average for borrowers of this type. It is deliberately stable.

A concrete illustration. A mid-sized manufacturer, rated internally as investment-grade equivalent:

Same borrower, same credit quality in any fundamental sense. The TTC figure never moves. The PIT figure moves by a factor of five.

Why regulation wants both

The split is not academic preference. Two different regimes demand two different answers, for coherent reasons.

Basel capital wants stability. If capital requirements tracked current conditions exactly, they would fall in booms and spike in downturns — forcing banks to raise capital or shrink lending precisely when the economy needs credit most. That procyclicality is the same defect identified in VaR two posts ago, transplanted to credit. TTC estimation dampens it.

IFRS 9 wants a forecast. Accounting provisions are meant to reflect expected credit losses on the balance sheet date, incorporating reasonable and supportable forward-looking information. A long-run average would be a poor answer to that question. IFRS 9 therefore needs PIT, and explicitly requires forward-looking macroeconomic input.

The expensive mistake

The failure mode is predictable: a bank builds a Basel-compliant rating model, then reuses its output directly for IFRS 9 provisioning because the model already exists and rebuilding is costly.

The consequence is systematic. In good years, TTC-based provisions exceed what conditions warrant, depressing reported earnings. In bad years, they fall short, and provisions jump sharply when loans migrate between stages — producing exactly the cliff effect IFRS 9 was designed to avoid.

Auditors increasingly catch this. The defence that “our Basel model is approved” does not address the question, since the two regimes are asking different things.

Converting between the two

Rebuilding from scratch is not the only option. The standard approach keeps the TTC rating model and applies a scalar adjustment driven by macroeconomic variables.

1. Keep the existing rating model, which ranks borrowers by relative creditworthiness.
2. Estimate the long-run average default rate per grade — the TTC PD.
3. Build a model linking observed system-wide default rates to macro variables such as GDP growth, credit growth and interest rates.
4. Use that relationship to produce a scalar for current and forecast conditions.
5. Apply the scalar to the TTC PD to obtain a PIT PD for each grade.

The rating model’s ordinal power — its ability to rank borrowers correctly — is preserved. Only the level shifts. This is substantially cheaper than a parallel model, and it is what most banks in practice do.

The weak point is step 3. It needs a default-rate series long enough to span at least one full cycle. For many Vietnamese institutions that series is short, and the relationship is estimated on a handful of annual observations. That is a real constraint, and it should be disclosed rather than hidden behind a confident-looking coefficient.

Hybrid reality

In practice no model is purely one or the other. A rating model using current financial statements already absorbs some cyclical signal, since a borrower’s leverage and margins deteriorate in a downturn. A model using only structural factors sits closer to TTC.

Most internal models therefore land somewhere in between, and the useful question is not “which type is this” but “how much does the output move with the cycle, and is that the amount we intended?” Measuring that cyclicality explicitly — regressing model output against a macro index — is a validation step worth doing, and one many banks skip.

Frequently asked questions

What is through the cycle PD?

It is a default probability averaged over a full economic cycle, deliberately stable and independent of current conditions. Basel capital uses it to avoid procyclical capital requirements.

Why does IFRS 9 need point-in-time PD?

Because provisions must reflect expected losses at the reporting date using forward-looking information. A long-run average would ignore the conditions actually prevailing.

Can a bank use its Basel model for IFRS 9?

Not directly. The output needs a macro-driven scalar adjustment to convert TTC estimates into point-in-time ones, otherwise provisions are too high in booms and too low in downturns.

How do you convert TTC PD to PIT PD?

Keep the rating model’s ranking, estimate the long-run default rate per grade, then scale it using a relationship between system default rates and macroeconomic variables.

Try it yourself

Measure how cyclical a model actually is, in this order:

1. Take a rating model’s output across several years of the same portfolio.
2. Build a simple macro index from GDP growth and credit growth over the same period.
3. Regress average model-implied PD against that index.
4. Read the slope — a steep slope means the model is closer to point-in-time.
5. Ask whether that slope matches the use the model is actually being put to.

Step five is the one that matters. A model behaving as point-in-time while feeding capital calculations, or the reverse, is a finding worth raising before a validator raises it for you.

Next in this series: building a rating model when you don’t have enough defaults.