When can expected utility handle first-order risk aversion?

•First-order conditional dependent risk aversion is consistent with the EU model.•Our model is compared with rank-dependent EU model.•Applications to equity premium puzzle and the cost of business cycles.

Expected utility functions are limited to second-order (conditional) risk aversion, while non-expected utility functions can exhibit either first-order or second-order (conditional) risk aversion. We extend the concept of orders of conditional risk aversion to orders of conditional dependent risk aversion. We show that first-order conditional dependent risk aversion is consistent with the framework of the expected utility hypothesis. Our theoretical result proposes new insights into economic and financial applications such as the equity premium puzzle, the cost of business cycles, and stock market participation. Our model is compared to the rank-dependent expected utility model.