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In this paper, we construct zero cost portfolios based on second and third degree stochastic dominance and show that they produce systematic, statistically significant, abnormal returns. These returns are robust with respect to the single index CAPM, the Fama-French three-factor model, the Carhart four-factor model, and the liquidity five-factor model. They are also robust with respect to momentum portfolios, transactions costs, varying time periods, and when broken down by a range of risk factors, such as firm size, leverage, age, return volatility, cash flow volatility, and trading volume. [ABSTRACT FROM AUTHOR]

Post and Levy (2005) find that investors are risk averse for losses and risk seekers for gains and that stocks which exhibit low risk in bear markets and high potential for gains in bull markets may demand a premium. The present study examines if this type of risk preference creates a premium in UK stock prices using a third-degree stochastic dominance test. We find that an arbitrage portfolio long on stocks with low past downside risk in bear markets and high past upside potential in bull markets and short on stocks with high past downside risk in bear markets and low past upside potential in bull markets generates a premium of 2.89% per month. This premium cannot be explained by the CAPM or the Fama and French 4-factor model, but it exhibits significant similarities to the momentum premium. [ABSTRACT FROM AUTHOR]

We use securities listed on 13 European equity markets to form size and momentum portfolios. We find limited evidence of a size premium but significant momentum returns in eight sample markets. We find that these premia may not constitute an anomaly because they are consistent with a varying-beta Capital Asset Pricing Model. We also show that systematic risk is related to the business cycle. Furthermore, the results suggest that although size and especially momentum returns are significant, it would be difficult to exploit them in the short to medium run, because they are positive and sizeable in very few years in our sample. [ABSTRACT FROM AUTHOR]