Recent academic studies have shown that since the mid-nineties, the passthrough of exogenous oil shocks into headline inflation has been increasing while the passthrough into core inflation seems to have ceased. This paper explores the implications in term of commodity allocation for inflation hedging portfolios these recent works have paved the way for. We proceed by first evidencing a linkage between the headline to core inflation spread and tradable commodities. We subsequently envisage exploiting it threefold: Firstly by devising an efficient strategic allocation using core inflation forecasts to determine the commodities natural weight in the portfolio as dictated by our macro approach. Secondly by testing a tactical allocation strategy which would time the passthrough cycle to determine dynamically the optimal share of commodities in the allocation. And eventually by proposing a strategy to arbitrage core inflation linked derivatives by cross-replicating them with commodity portfolios.