This paper analyzes optimal hedging of a tradable risk (e.g. price risk or exchange rate risk) with forward contracts in the presence of untradable inflation risk. Utility is defined over real wealth. Optimal forward positions are derived relative to a given initial exposure in the tradable risk. A nominally unbiased forward market usually implies a non-zero real risk premium and hence some risk taking. If untradable inflation risk is a monotone function of the tradable risk plus noise, cross hedging and speculating on the real risk premium are conflicting objectives; the level of relative risk aversion determines which objective is dominant in a nominally unbiased forward market.