Performance attribution with respect to interest rates, FX, carry, and residual market risks

Paper: arXiv 2302.01010

Authors: Jan-Frederik Mai

Abstract

We develop a method to decompose the PnL of a portfolio of assets into four parts: (a) PnL due to FX rate changes, (b) PnL due to interest rate changes, (c) carry gain due to time passing, (d) PnL due to residual market risk changes (credit risk, liquidity risk, volatility risk etc.). We demonstrate the usefulness of our approach by decomposing the performance of an FX- and interest rate-hedged negative basis position in our fund XAIA Credit Basis II, and we apply the methodology to decompose the performance of our fund XAIA Credit Debt Capital in the first quarter of 2022 into PnL contributions of the single positions.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 6.0/10 (capped from 6.5: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a practical mathematical framework for multi-factor performance attribution, explicitly separating interest rates, FX, carry, and residual risks. It demonstrates solid empirical utility by applying the decomposition to actual fund portfolios (XAIA funds) across distinct market regimes.

Research Flowchart

  flowchart TD
    A[Goal: Decompose Portfolio PnL into FX, Interest Rates, Carry & Residual Risk] --> B[Data Inputs: FX Rates, Yield Curves, Time Elapsed & Market Prices]
    B --> C[Methodology: Calculate Incremental PnL Attribution Components]
    C --> D[Compute FX, IR, Time Carry Gains & Residual Market Risks]
    D --> E[Outcome 1: Evaluated Hedged Negative Basis Position in XAIA Credit Basis II]
    D --> F[Outcome 2: Decomposed Position-Level Q1 2022 Performance for XAIA Credit Debt Capital]