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This paper investigates the estimation of the value at risk (VaR) across various probability levels for the log-returns of a comprehensive dataset comprising four thousand crypto-assets. Employing four recently introduced adaptive conformal inference (ACI) algorithms, we aim to provide robust uncertainty estimates crucial for effective risk management in financial markets. We contrast the performance of these ACI algorithms with that of traditional benchmark models, including GARCH models and daily range models. Despite the substantial volatility observed in the majority of crypto-assets, our findings indicate that ACI algorithms exhibit notable efficacy. In contrast, daily range models, and to a lesser extent, GARCH models, encounter challenges related to numerical convergence issues and structural breaks. Among the ACI algorithms, Fully Adaptive Conformal Inference (FACI) and Scale-Free Online Gradient Descent (SF-OGD) stand out for their ability to provide precise VaR estimates across all quantiles examined. Conversely, Aggregated Adaptive Conformal Inference (AgACI) and Strongly Adaptive Online Conformal Prediction (SAOCP) demonstrate proficiency in estimating VaR for extreme quantiles but tend to be overly conservative for higher probability levels. These conclusions withstand robustness checks encompassing the market capitalization of crypto-assets, time-series size, and different forecasting methods for asset log-returns. This study underscores the promise of ACI algorithms in enhancing risk assessment practices in the context of volatile and dynamic crypto-asset markets. Full article