Modeling and evaluating conditional quantile dynamics in VaR forecasts

ArXiv ID: 2305.20067 “View on arXiv”

Authors: Unknown

Abstract

We focus on the time-varying modeling of VaR at a given coverage $τ$, assessing whether the quantiles of the distribution of the returns standardized by their conditional means and standard deviations exhibit predictable dynamics. Models are evaluated via simulation, determining the merits of the asymmetric Mean Absolute Deviation as a loss function to rank forecast performances. The empirical application on the Fama-French 25 value-weighted portfolios with a moving forecast window shows substantial improvements in forecasting conditional quantiles by keeping the predicted quantile unchanged unless the empirical frequency of violations falls outside a data-driven interval around $τ$.

Keywords: Value at Risk (VaR), Quantile Forecasting, Time-varying Models, Fama-French Portfolios, Asymmetric Loss Functions

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced time-series econometrics with detailed derivations of quantile definitions and model specifications (High Math), and applies a structured backtest on Fama-French portfolios using a moving window and simulation-based loss function evaluation (High Rigor).

  flowchart TD
    A["Research Goal: Assess time-varying VaR modeling<br>and quantile forecast accuracy"] --> B["Methodology: Simulation &<br>Asymmetric Mean Absolute Deviation Loss"]
    A --> C["Data: Fama-French 25 Portfolios<br>Moving forecast window"]
    B & C --> D["Process: Estimate conditional mean<br>and standard deviation"]
    D --> E["Standardize Returns & Model<br>Time-Varying Quantile Dynamics"]
    E --> F["Evaluation: Update predictions only<br>if violation frequency deviates from target τ"]
    F --> G["Outcomes: Substantial improvements<br>in conditional quantile forecasting"]