Performance-based regularization for downside-risk cryptocurrency portfolios: Evidence from mean-lower partial moment strategies

Cryptocurrencies have become an important yet highly volatile asset class, where non-normal returns, pronounced downside risk, and rapid regime shifts often undermine classical portfolio rules. This study develops a performance-based regularized mean-lower partial moment (PBR-LPM) framework that explicitly targets downside risk while mitigating estimation uncertainty through a data-driven regularization scheme calibrated by a Sortino-ratio-based k-fold cross-validation procedure. Using daily data on mega-cap cryptocurrencies from 2017 to 2023, we conduct extensive out-of-sample portfolio experiments and benchmark PBR-LPM against widely used alternatives such as PBR mean-variance and sample average approximation. The results show that PBR-LPM portfolios deliver stronger and more stable out-of-sample performance across standard evaluation metrics, with particularly large gains in downside protection during market stress episodes, while remaining competitive in bullish periods. Overall, the evidence indicates that combining downside-risk objectives with performance-based regularization provides a practical and robust approach to cryptocurrency allocation in highly uncertain and non-normal markets.