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We study risk-averse equilibrium bidding in first-price and second-price sealed-bid auctions where bidders have signalling concerns, i.e., they care about how the auction outcome is interpreted by an outside observer. We find that when the winner’s identity and her payment are revealed to the outside observer, risk aversion yields less aggressive bidding behaviour in the second-price sealed-bid auction than in the risk-neutral case. Our analysis explains various revenue ranking reversals relative to the risk-neutral equilibrium observed in a recent experiment by Bos (2021).