Variable annuities (VAs) are highly popular personal savings and investment products with long-term financial guarantees. The hedging of these guarantees is crucial for VA providers, but is complicated by basis risk, i.e. the discrepancy in returns between the underlying mutual fund and suitable hedging instruments. Enhancing fund mapping methods with data analytic techniques for large sets of VA-underlying mutual funds and mapping instruments, we document that --- even under favorable conditions --- over 25% of the volatility of fund returns cannot be eliminated, no matter how sophisticated the hedge. Our findings persist across model specifications, asset classes, and most Lipper Objective Codes.