Paper: arXiv 2305.04801

Authors: Ali Shirazi, Fereshteh Sadeghi Naieni Fard

Abstract

Finding the hedge ratios for a portfolio and risk compression is the same mathematical problem. Traditionally, regression is used for this purpose. However, regression has its own limitations. For example, in a regression model, we can’t use highly correlated independent variables due to multicollinearity issue and instability in the results. A regression model cannot also consider the cost of hedging in the hedge ratios estimation. We have introduced several methods that address the linear regression limitation while achieving better performance. These models, in general, fall into two categories: Regularization Techniques and Common Factor Analyses. In regularization techniques, we minimize the variance of hedged portfolio profit and loss (PnL) and the hedge ratio sizes, which helps reduce the cost of hedging. The regularization techniques methods could also consider the cost of hedging as a function of the cost of funding, market condition, and liquidity. In common factor analyses, we first map variables into common factors and then find the hedge ratios so that the hedged portfolio doesn’t have any exposure to the factors. We can use linear or nonlinear factors construction. We are introducing a modified beta variational autoencoder that constructs common factors nonlinearly to compute hedges. Finally, we introduce a comparison method and generate numerical results for an example.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a logical progression from traditional linear regression to a modified beta Variational Autoencoder (beta-VAE) for risk compression and financial hedging. While it introduces solid regularization techniques incorporating transaction costs and nonlinear factor models, the empirical validation relies on basic numerical examples rather than exhaustive backtesting on historical market datasets.

Research Flowchart

  flowchart TD
    A["Research Goal: Overcome Linear Regression Limitations in Multi-Asset Hedging"] --> B["Inputs: Portfolio PnL, Assets & Cost Drivers"]
    B --> C{"Methodology Framework"}
    
    C -->|"Category 1"| D["Regularization Techniques: Penalize Hedge Sizes & Costs"]
    C -->|"Category 2"| E["Factor Analysis: Linear & Beta-VAE Factor Mapping"]
    
    D --> F["Compute Optimal Hedge Ratios & Risk Compression"]
    E --> F
    
    F --> G["Outcome: Stable Hedges Mitigating Multicollinearity & Transaction Costs"]