Which asset classes provide a hedge against the risk of headline and core inflation?

We look at equities, residential real estate and commodities to see which asset classes provide a hedge against the risk of headline or core inflation (in the United States and the euro zone). There may be big differences, with some asset returns reacting to commodity prices and others not. Looking at the correlations between the returns on these different asset classes and headline and core inflation at various time horizons, we see that: Equities and real estate provide a weak to very weak hedge against headline and core inflation; Commodities provide a good hedge against headline and core inflation in the United States, and a good hedge against headline inflation although a weaker one against core inflation in the euro zone.