Overcoming issues with time-scaling value-at-risk

Anastasia Maga and Arthur Lance Dryver

Abstract

This paper investigates the impact of time-scaling methods on the accuracy of value-at- risk (VaR) models. We compare the performance of traditional square-root-of-time scaling with a proposed distributional scaling method using both simulated and real-world market data. Our findings reveal that the choice of scaling method significantly affects VaR accuracy, particularly for models such as bootstrapped historically simulated VaR and conditional VaR at higher investment horizons. While traditional VaR models often exhibit high backtesting failure rates, our results suggest that appropriate scaling can mitigate these shortcomings. Our study underscores the importance of carefully selecting scaling methods and considering alternative risk modeling approaches to enhance risk management practices in the face of nonnormal market behavior and tail risks.