We investigate whether risk seeking or non-concave utility functions can help to explain the cross-sectional pattern0 of stock returns. For this purpose, we analyze the stochastic dominance efficiency classification of the value-weighted market portfolio relative to benchmark portfolios based on market capitalization, book-to-market equity ratio and momentum. We use various existing and novel stochastic dominance criteria that account for the possibility that investors exhibit local risk seeking behavior. Our results suggest that Markowitz type utility functions, with risk aversion for losses and risk seeking for gains, can capture the cross-sectional pattern of stock returns. The low average yield on big caps, growth stocks and past losers may reflect investors' twin desire for downside protection in bear markets and upside potential in bull markets.