FRTB P&L Attribution Tests and Backtesting

Accelerator Cube Specification and File Format

Overview

This page describes the implementation of P&L Attribution Tests and Backtesting in the ActiveViam FRTB Accelerator.

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. Customising ² trade level inputs and analytics to support analysing recent exceptions/outliers.

Definitions ³

• T-1: the most recent close of business. This is the AsOfDate in the cube.

  • 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.

  Note: 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.

Cube Overview

There are two cubes which are tied together via FRTBCombinedCube:

• The PLCube for recent data at the trade level (where investigations and sign-off can take place)
• The PLSummaryCube for historical data at the book and legal entity levels (to fill out one-year history)
• The FRTBCombinedCube seamlessly ties the two together.

The PL Cube:

• Collects recent data at the trade (or position) level, including the VaR P&L vectors.
• It is expected that this cube will be customised to support analysing exceptions/outliers.
• PL Cube data can be exported via PLCubeExport DEE Template Order found within the directory frtb-starter/src/main/resources/DEETemplateOrders/PLCubeExport.json read more.

The PL Summary Cube:

• Collects aggregated data with a long history (at least the 1 year required by the regulations) at the desk and firm-wide levels. Including:
  • Daily P&L values (actual, hypothetical, and risk-theoretical).
  • Daily VaR P&L vectors

Combined Cube:

• Includes the analytics required for P&L Attribution Tests and Backtesting. Including:
  • The Spearman correlation metric; i.e. the correlation between Risk-Theoretical P&L and Hypothetical P&L.
  • The Kolmogorov-Smirnov test metric, i.e. the similarity of the distributions of Risk-Theoretical P&L and Hypothetical P&L.
  • A count of the number of exceptions when comparing the Actual P&L and Hypothetical P&L against the VaR at the 97.5% and 99% confidence levels.

PL Cube

The PL cube is aimed at calculating desk and firm-wide VaR values from trade level VaR P&L vectors and, with customisation, supporting the analysis of recent exceptions/outliers.

Input Files

PL_VaR_Vector.csv

File pattern match: PL_VaR_Vector*.csv The VaR P&L vectors

PL_VaR_Scenario.csv

File pattern match: PL_VaR_Scenario*.csv A description of the VaR scenarios.

Shared files

The following files are shared with the IMA cube and used to map the trades into the organisation hierarchies.

• Trade_Attributes.csv
• BookParentChild.csv
• LegalEntityParentChild.csv

Hierarchies

Additionally, the following organisational hierarchies are shared with the IMA cube:

• Books
• Desks
• FRTBModel
• Trades
• Legal Entities
• BookHierarchy

PL Summary Cube

The PL Summary cube is aimed at desk and firm-wide monitoring of the P&L Attribution Tests and Backtesting.

It contains aggregated data with at least a year of history including:

• Daily P&L values (Actual, Hypothetical, and Risk-Theoretical)
• Daily VaR P&L vectors

This cube can be customised to add KPIs to monitor the above metrics, and workflows to manage exceptions.

Input Files

PL_Summary.csv

File pattern match: PL_Summary*.csv

This file contains all the data for the PL Summary cube.

The key fields for this file are AsOfDate, Book and Legal Entity .

Hierarchies

Measures

Both Cubes share the same measures which are seamlessly tied together within the FRTBCombinedCube.

• Common Measures:

  • VaR PL: A technical vector-valued measure from the PL field in the input files (after currency conversion).
  • VaR PL Expand: VaR PL Vector expanded along the Scenario analysis hierarchy.
  • Hypothetical PL: from input file (after currency conversion).
  • Actual PL: from input file (after currency conversion).
  • Theoretical PL: from input file (after currency conversion).
  • Unexplained PL: difference between Theoretical PL and Hypothetical PL.
  • VaR 99: The value-at-risk with 99% confidence level [^9].
  • VaR 97.5: The value-at-risk with 97.5% confidence level
  • VaR 99 (previous day): VaR 99 of previous day (T-2)
  • VaR 97.5 (previous day): VaR 97.5 of previous day (T-2)
  • ES 99: The Expected Shortfall with 99% confidence level
  • ES 97.5: The Expected Shortfall with 97.5% confidence level
  • p-value (Actual): p value for Actual PL given PL Vector input as distribution.
  • p-value (Hypothetical): p value for Hypothetical PL given PL Vector input as distribution.
  • Exception 99 (Actual): Exception at 99% confidence level for Actual P&L
    • 1 if Actual PL < VaR 99 (previous day);
    • 0 otherwise.
  • Exception 99 (Hypothetical): Exception at 99% confidence level for Hypothetical P&L
    • 1 if Hypothetical PL < VaR 99 (previous day);
    • 0 otherwise.
  • Exception 97.5 (Actual): Exception at 97.5% confidence level for Actual P&L
    • 1 if Actual PL < VaR 97.5 (previous day);
    • 0 otherwise.
  • Exception 97.5 (Hypothetical): Exception at 97.5% confidence level for Hypothetical P&L
    • 1 if Hypothetical PL < VaR 97.5 (previous day);
    • 0 otherwise.
  • Outlier 99: MAX(Exception 99 (Actual), Exception 99 (Hypothetical)).
  • Outlier 97.5: MAX(Exception 97.5 (Actual), Exception 97.5 (Hypothetical)).

• FRTBCombinedCube Measures

  • For PL Attribution Tests:
    • Spearman Correlation Metric: the correlation between RTPL and HPL
    • Kolmogorov-Smirnov Test Metric: the similarity of the distributions of RTPL and HPL.
    • Hypothetical PL Lookback: The Hypothetical PL values expanded along the Lookback analysis hierarchy.
    • Theoretical PL Lookback: The Theoretical PL values expanded along the Lookback analysis hierarchy.
    • Variance Hypothetical PL: The Variance of historical Hypothetical PL data.
  • For Backtesting
    • Exception 99 Count (Actual) The number of Exceptions at the 99% confidence level over the past year using Actual PL.
    • Exception 97.5 Count (Actual) The number of Exceptions at the 97.5% confidence level over the past year using Actual PL.
    • Exception 99 Dates (Actual) An array of dates of the Exceptions at the 99% confidence level over the past year using Actual PL.
    • Exception 97.5 Dates (Actual) An array of dates of the Exceptions at the 97.5% confidence level over the past year using Actual PL.
    • Exception 99 Count (Hypothetical) The number of Exceptions at the 99% confidence level over the past year using Hypothetical PL.
    • Exception 97.5 Count (Hypothetical) The number of Exceptions at the 97.5% confidence level over the past year using Hypothetical PL.
    • Exception 99 Dates (Hypothetical) An array of dates of the Exceptions at the 99% confidence level over the past year using Hypothetical PL.
    • Exception 97.5 Dates (Hypothetical) An array of dates of the Exceptions at the 97.5% confidence level over the past year using Hypothetical PL.
    • Exception 99 Count MAX(Exception 99 Count (Actual) , Exception 99 Count (Hypothetical)).
    • Exception 97.5 Count MAX(Exception 97.5 Count (Actual), Exception 97.5 Count (Hypothetical)).
  • Extras
    • Outlier 97.5 Count: The number of Exceptions at the 97.5% confidence level over the past year.
    • Outlier 99 Count: The number of Exceptions at the 99% confidence level over the past year.

FRTBCombinedCube Context Values

• PLALookback the number of business days to look back when calculating the Spearman correlation and KS test metrics for PLA Tests. This may also be expressed as a period, to look back a number of calendar days, for example, “1M”, “3M”, “1Y”.
• BackTestingLookback the number of business days to look back when counting the number of exceptions in the VaR backtesting. This may also be expressed as a period, to look back a number of calendar days, for example, “1M”, “3M”, “1Y”.