medium · FRM Part 2 Credit Risk
An analyst calculates a 5-year cumulative PD by raising a 1-year transition matrix to the 5th power: M^5.
If the underlying rating system is strictly Point-in-Time (PIT), how will the resulting cumulative PD likely behave over a full business cycle compared to a system using Through-the-Cycle (TTC) ratings?
- The PIT-based cumulative PD will exhibit much higher volatility and procyclicality, overstating long-term risk in a recession.
- The two approaches will converge to the same 5-year PD because the Markov property enforces long-run mean reversion to the same steady state.
- The PIT-based cumulative PD will be more stable because the matrix already incorporates the current macro-economic state.
- The TTC-based cumulative PD will always be higher because it is calibrated to a 'downturn' scenario by definition.
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