This study proposes AC dynamic skew-𝑡 copula with cDCC model to capture the dynamic asymmetric tail dependence structure among multi-asset classes (government bonds, corporate bonds, equities, and REITs). We provide new evidence that lower tail dependence coefficients increased compared to upper ones for all pairs in the COVID-19 crash and the recent high inflation period, indicating that the diversification effect through multi-asset investment decreased. Our empirical analysis also shows that in terms of AIC and BIC, dynamic AC skew-𝑡 copula fits data of multi-asset classes better than other dynamic elliptical copulas because it can consider the above dependence structure characteristics. Furthermore, out-of-sample analysis reveals that considering an asymmetry of tail dependence structure at each point with an AC dynamic skew-𝑡 copula enhances expected shortfall (ES) estimation accuracy and the performance of a minimum ES portfolio. These results indicate that capturing dynamic asymmetric tail dependence is crucial for multi-asset portfolio management.