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Local energy communities are proposed as a regulatory framework to enable the market participation of endconsumers. However, volatile local market-clearing prices, and consequently, volatile cost give rise to local market participants with generally heterogeneous risk attitudes. To prevent the increased operational cost of communities due to conservative trading decisions in the forward stage, e.g., a day-ahead market, we propose risk trading in energy communities via financial hedging products, the so-called Arrow-Debreu securities. The conditional value-at-risk serves as our risk measure for players to study different degrees of market completeness for risk. We define a risk-averse Nash game with risk trading and solve the Nash equilibrium problem for an incomplete market for risk as a mixed complementarity problem. We show that such a Nash equilibrium problem reduces to a single optimization problem if the market is complete for risk. Numerical findings indicate that a significant community cost saving can be realized when players engage in risk trading and sufficient financial hedging products are available. Moreover, risk trading efficiently protects less risk-averse players from highly risk-averse decision-making of rival players.