Hedging direct real estate portfolios is complicated by illiquidity, appraisal smoothing, and the reliance on index-based proxies, which generate substantial basis risk and unstable hedge ratios when estimated from limited data. We develop a robust static hedging framework within an asset–liability management setting that explicitly accounts for model uncertainty in the joint distribution of property and index returns. Allowing the reference probability model to vary within a Wasserstein ambiguity set, we derive a tractable distributionally robust formulation of the classical minimum tracking-error problem. The resulting objective augments variance-based basis risk with a penalty on hedge exposure, leading to optimal hedge ratios that exhibit an explicit shrinkage structure. The ambiguity parameter
governs the trade-off between hedge effectiveness and robustness, providing a transparent interpretation in terms of controlling estimation risk and proxy mismatch. The proposed framework offers an economically interpretable and practically implementable approach to robust index-based hedging in real estate portfolios.