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This article provides an analytical solution to the problem of an institution optimally managing the market risk of a given exposure by minimizing its Value‐at‐Risk using options. The optimal hedge consists of a position in a single option whose strike price is independent of the level of expense the institution is willing to incur for its hedging program. This optimal strike price depends on the distribution of the asset exposure, the horizon of the hedge, and the level of protection desired by the institution. Moreover, the costs associated with a suboptimal choice of exercise price are economically significant.