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Considering market-based inflation expectations, we show that investors' forecasts are non-linear. We capture this non-linear behavior with a Markov-switching model that allows us to identify a regime of high uncertainty, and a regime of low uncertainty and low concern about inflation. Using a complete cross-asset panel of equity sectors, bonds, and commodities, we perform regressions in both regimes including several control variables, and show that the exposure of European assets returns to implied inflation is regime-dependent. We show that inflation-indexed government bonds and oil are the best way to get exposure to slow upward revisions of future inflation that correspond to periods of rallying inflation. We thus identify alternatives to hedge oneself against revisions in inflation forecasts when inflation is considered as a variable of interest by market participants, which, in fact, corresponds to periods of breaks in the trend of realized inflation. In particular, we provide empirical evidence that some equity sectors exhibit good inflation-hedging properties. [ABSTRACT FROM AUTHOR]