Profit and loss attribution: An empirical study

ArXiv ID: 2309.07667 “View on arXiv”

Authors: Unknown

Abstract

The profit and loss (p&l) attrition for each business year into different risk or risk factors (e.g., interest rates, credit spreads, foreign exchange rate etc.) is a regulatory requirement, e.g., under Solvency 2. Three different decomposition principles are prevalent: one-at-a-time (OAT), sequential updating (SU) and average sequential updating (ASU) decompositions. In this research, using financial market data from 2003 to 2022, we demonstrate that the OAT decomposition can generate significant unexplained p&l and that the SU decompositions depends significantly on the order or labeling of the risk factors. On the basis of an investment in a foreign stock, we further explain that the SU decomposition is not able to identify all relevant risk factors. This potentially effects the hedging strategy of the portfolio manager. In conclusion, we suggest to use the ASU decomposition in practice.

Keywords: Profit and Loss (P&L) Attribution, Risk Factors Decomposition, Sequential Updating (SU), Average Sequential Updating (ASU), One-at-a-Time (OAT), Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 6.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs sophisticated financial mathematics like Shapley value decomposition and recursive multi-period analysis, but grounds these in rigorous empirical testing over 20 years of market data, comparing methodologies with quantifiable metrics.

  flowchart TD
    A["Research Goal: Analyze P&L<br>Attribution Methods"] --> B["Methodology: Comparative Analysis<br>of OAT, SU, and ASU"]
    B --> C["Input: 20 Years Financial Market Data<br>(2003-2022) Multi-Asset Class"]
    C --> D{"Computational Process:<br>Decompose P&L via three principles"}
    D --> E["OAT Decomposition"]
    D --> F["SU Decomposition<br>Order Dependent"]
    D --> G["ASU Decomposition<br>Average Order"]
    E --> H["Key Findings & Outcomes"]
    F --> H
    G --> H
    H --> I["1. OAT generates significant<br>unexplained P&L"]
    H --> J["2. SU fails to identify all risks<br>e.g., Foreign Stock Investment"]
    H --> K["Recommendation:<br>Use ASU for accurate hedging"]