> ## Documentation Index
> Fetch the complete documentation index at: https://docs.creditbenchmark.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Rating Comparisons (Notch Differences)

> Credit Benchmark uses notch differences to compare PD estimates for peer benchmarking, portfolio analysis, and cross-entity risk reporting.

A notch difference is the numerical gap between two PD estimates once both are mapped to a rating scale.

Credit Benchmark uses notch differences in portfolio analytics, peer benchmarking, and time-series tracking — anywhere a relative credit quality comparison is needed.

By default we use the 21-category CB scale; see the [Rating Scale](/methodology/rating-scales). The same concept applies using a bank's internal rating scale — if a mapping is provided, notch differences can be calculated on the bank's own scale.

$$
\text{Notch Difference} = f(PD_i) - f(PD_j)
$$

Where:

* $PD_i$, $PD_j$ — PD estimates from two sources being compared
* $f(PD)$ — rating scale mapping function returning a notch index
* Positive values indicate $PD_i$ is the stronger credit; negative values indicate the reverse

## Applications

<AccordionGroup>
  <Accordion title="Bank vs Consensus">
    $$
    f(PD_b) - f(PD_c)
    $$

    How far a contributing bank's view sits from the market consensus for the same entity.

    * **Positive** — bank is more optimistic than consensus (lower PD)
    * **Negative** — bank is more conservative than consensus (higher PD)
  </Accordion>

  <Accordion title="Time-based">
    $$
    f(PD_t) - f(PD_{t-n})
    $$

    How credit quality on an entity has shifted over a chosen period — 1, 3, 6, or 12 months.

    * **Positive** — credit quality improved (PD decreased)
    * **Negative** — credit quality deteriorated (PD increased)
  </Accordion>

  <Accordion title="Entity Comparison">
    $$
    f(PD_A) - f(PD_B)
    $$

    Relative credit quality between two entities — used for peer benchmarking and portfolio analysis.

    * **Positive** — Entity A has stronger credit quality than Entity B
    * **Negative** — Entity A has weaker credit quality than Entity B
  </Accordion>
</AccordionGroup>