Skip to main content
The Aggregate PD is a portfolio-level metric reflecting average credit risk across a defined entity set. The goal is to produce an index on a moving pool of entities that captures genuine bank opinion changes — filtering out moves caused purely by entities entering or leaving the universe. It is built using a back-calculation approach — anchoring to the most recent month as a baseline, then working backwards through time using only month-on-month PD changes validated by the Opinion Change Indicator (OCI). This ensures the time series stays consistent with the current portfolio view and filters out noise from contributor population shifts.
The back-calculation approach means the most recent month always reflects the full current entity universe. Historical values are derived from that baseline — so the series never distorts when entities join or leave.

​
Mathematical Process

1

Logarithmic Transformation

Transform the PD for each entity ii at time tt into log space:LogPD⁡i,t=log⁡ ⁣(PD⁡i,t)\operatorname{LogPD}_{i,t}=\log\!\bigl(\operatorname{PD}_{i,t}\bigr)
2

Difference in Log PD

Compute the month-on-month change in log PD for each entity:ΔLogPD⁡i,t=LogPD⁡i,t−LogPD⁡i,t−1\Delta\operatorname{LogPD}_{i,t} = \operatorname{LogPD}_{i,t}-\operatorname{LogPD}_{i,t-1}
3

OCI Adjustment

Retain only changes where the OCI confirms a genuine shift in bank opinion. If the sign of the OCI does not match the sign of the log PD change, set the difference to zero:Adj⁡ΔLogPD⁡i,t={ΔLogPD⁡i,t,if sign(OCIi,t)=sign ⁣(ΔLogPD⁡i,t)0,otherwise\operatorname{Adj}\Delta\operatorname{LogPD}_{i,t}= \begin{cases} \Delta\operatorname{LogPD}_{i,t}, & \text{if }\mathrm{sign}(\mathrm{OCI}_{i,t}) = \mathrm{sign}\!\bigl(\Delta\operatorname{LogPD}_{i,t}\bigr)\\[4pt] 0, & \text{otherwise} \end{cases}
4

Average Log Difference

Average the adjusted log differences across all nn entities for month tt:ΔLogPD⁡‾t=1n∑i=1nAdj⁡ΔLogPD⁡i,t\overline{\Delta\operatorname{LogPD}}_{t} = \frac{1}{n}\sum_{i=1}^{n}\operatorname{Adj}\Delta\operatorname{LogPD}_{i,t}
5

Baseline — Most Recent Month

Establish the baseline by averaging raw log PDs across all entities at tlatestt_{\text{latest}}:AggLogPD⁡tlatest=1n∑i=1nLogPD⁡i,tlatest\operatorname{AggLogPD}_{t_{\text{latest}}} = \frac{1}{n}\sum_{i=1}^{n}\operatorname{LogPD}_{i,t_{\text{latest}}}This is the starting point for all back-calculation.
6

Back-calculate Previous Months

Derive each prior month by subtracting the average log difference:AggLogPD⁡t−1=AggLogPD⁡t−ΔLogPD⁡‾t\operatorname{AggLogPD}_{t-1} = \operatorname{AggLogPD}_{t}-\overline{\Delta\operatorname{LogPD}}_{t}Repeat iteratively for all months prior to tlatestt_{\text{latest}}.
7

Convert Back to PD

Exponentiate to return to the probability scale:AggPD⁡t=exp⁡ ⁣(AggLogPD⁡t)\operatorname{AggPD}_{t}=\exp\!\bigl(\operatorname{AggLogPD}_{t}\bigr)

​
Output Views

The Aggregate PD can be expressed three ways:
The absolute probability of default for the segment — the direct output of the back-calculation:AggPD⁡t=exp⁡ ⁣(AggLogPD⁡t)\operatorname{AggPD}_{t} = \exp\!\bigl(\operatorname{AggLogPD}_{t}\bigr)
Relative change from a chosen base date t0t_0, showing directional risk movement:RelChanget(%)=AggPD⁡t−AggPD⁡t0AggPD⁡t0×100\text{RelChange}_t(\%) = \frac{\operatorname{AggPD}_{t}-\operatorname{AggPD}_{t_0}}{\operatorname{AggPD}_{t_0}} \times 100
The aggregate PD mapped to the CB rating scale:Rating=f(AggPD⁡t)\text{Rating} = f(\operatorname{AggPD}_{t})Where ff is the CB PD-to-rating mapping function; see the Rating Scale.