The literature has shown that supply chain performance is affected by the allocation of inventory risk. Traditionally, a pull supply chain generates a higher optimal order quantity and hence higher supply chain profit than a push supply chain when firms are risk neutral. Extended from the classic push and pull newsvendor models, this study investigates the impact of firms’ risk-averse attitudes on supply chain performance. Based on firms’ conditional value-at-risk (CVaR), our analysis indicates that push can lead to a higher optimal order quantity than pull when the supplier is sufficiently more risk averse than the retailer. Meanwhile, pull contracts cannot always survive push challenge like in risk-neutral supply chains. We demonstrate that three-part tariff revenue sharing and buy-back contracts can coordinate both the push and the pull supply chains to achieve the Pareto optimality maximizing combined supply chain CVaR.