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# FRTB P&L attribution tests and backtesting

export const productName = "Atoti FRTB";

These pages describe the implementation (that is, the cube specification and file formats) of P\&L Attribution Tests and Backtesting in {productName}.

## Supported Use Cases

The P\&L Attribution Tests and Backtesting have been designed to enable the following use cases.

1. Monitoring historical VaR and P\&L values at the desk and firm-wide [^1] levels, as required by regulation.
2. Calculating desk and firm-wide VaR values from trade level VaR P\&L vectors.
3. Customizing [^2] trade level inputs and analytics to support analysing recent exceptions/outliers.

## Definitions [^3]

| Term                                                                                                                                                   | Definition                                                                                                                                                                                                                                                                    |
| ------------------------------------------------------------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **T-1** Tthe most recent close of business. This is the **AsOfDate** in the cube. <br />**T-n**: close of business for the nth preceding business day. |                                                                                                                                                                                                                                                                               |
| **Actual P\&L \[APL]**                                                                                                                                 | As-of T-1, the daily P\&L (from T-2 to T-1) of the desk (or firm-wide) based on actual prices [^4] and including trading activity [^5].                                                                                                                                       |
| **Hypothetical P\&L \[HPL]**                                                                                                                           | As-of T-1, the daily P\&L value (from T-2 to T-1) of the desk (or firm-wide) based on actual prices for the T-2 portfolio [^6].                                                                                                                                               |
| **Risk-Theoretical P\&L \[RTPL]**                                                                                                                      | As-of T-1, the daily P\&L (from T-2 to T-1) of the desk (or firm-wide) based on model-generated prices for the T-2 portfolio.                                                                                                                                                 |
| **VaR measures**                                                                                                                                       | As-of T-1, the model-generated one-day value-at-risk measures for the T-1 portfolio. <br />Note: <br />The as-of T-1 VaR measures are interpreted as a prediction of P\&L for COB T. So, when comparing with the P\&L values, the VaR measures need to be shifted by one day. |
| **p-values** [^7]                                                                                                                                      | As-of T-1, the empirical probability of observing a profit that is less than (or loss greater than) the actual (or hypothetical) P\&L [^8].                                                                                                                                   |

[^1]: All IMA desks (i.e. excluding SA desks), as per the FAQ: BCBS 395 section 2.7 Q1.

[^2]: This use case relies heavily on custom inputs (for example, asset class) beyond what can be included in the Solution.

[^3]: Based on BCBS 352 paragraph 183 and Appendix B; BCBS 395/437 FAQs; and clarifications in BCBS 436.

[^4]: From BCBS 352 Appendix B: “the mark-to-market value of the trading desk’s instruments derived from the bank’s pricing models including all risk factors”.

[^5]: Excluding fees and commissions.

[^6]: Assuming no trading activity (from T-2 to T-1).

[^7]: Not required by regulations, but mentioned in BCBS 352 paragraph 182 (b) as something the supervisor may request.

[^8]: According to the model