We explore to what extent real returns on investment portfolios can be hedged against inflation risk by using existing financial market instruments. We find that inflation-linked bonds offer only limited protection against inflation risk and that nominal debt and stocks play at least comparable roles in this respect. These findings apply to both a static and a dynamic setting. The demonstrated limits of hedging inflation risk are of particular relevance for long-term investors, such as pension funds with participants concerned about the real value of their pension benefits.