"Our results indicate that most of the significant abnormal returns from zero-cost strategies still exist after controlling for the risk factors. In other words, neither the Fama-French nor the alternative three-factor model can fully explain anomalies in international equity markets. We do not find the alternative model outperforms the Fama-French model in driving away anomalies in international markets. Our results are consistent with the study by Walkshausl and Lobe (2011), who compare the performance of the alternative model with the Fama- French model in countries beyond US.

Many studies have provided various explanations of the existence of anomalies. The existence of anomalies is usually due to either market inefficiency (mispricing) or inadequacies in underlying asset-pricing models. In this study, we do not attempt to address the inadequacy of existing asset-pricing models or seek additional risk factors. We focus on the test of mispricing explanation by examining the impact of idiosyncratic risk on stock abnormal return. In the traditional mean variance analysis, only the market risk should be priced in equilibrium as predicted in the CAPM model. Any idiosyncratic risk is completely eliminated through diversification. However, CAPM holds only when
investors are willing and able to hold a combination of the market portfolio and risk free asset. In practice, many investors are not able to hold such a portfolio due to various constraints, such as transaction costs, incomplete information, taxes, liquidity requirements, etc. It is also common that institutional investors often deliberately structure their portfolios to generate considerable idiosyncratic risk to obtain excess returns.

As Malkiel and Xu (2006) point out, the relative supply of the stocks that constrained investors are unable to hold is high, so the price of those stocks must be relatively low. Therefore, an idiosyncratic risk premium can be rationalized for such “unbalanced supply”. In addition, if the constrained investors are unable to hold all securities, the “available market portfolio” for unconstrained investors will automatically become less diversified because it is the total holdings from the two groups of investors that make up the whole market (Malkiel and Xu (2006)). The risk premium of the “available market portfolio” tends to be higher than the actual market portfolio in the traditional CAPM model. Portions of the systematic risk would be considered as idiosyncratic risk relative to the actual market portfolio. Therefore, it would be priced in the market.

Our results show that idiosyncratic risk exhibits a significant difference across countries. It varies from 0.074 (Luxembourg) to 0.312 (Portugal). The average idiosyncratic risk in developed countries is smaller than emerging countries (0.130 vs. 0.142). To examine the relationship between idiosyncratic risk and abnormal returns, we form 5×5 portfolios based on interactions of quintiles of conditional idiosyncratic risk and quintiles of individual anomaly in each country. We calculate abnormal returns at each idiosyncratic risk quintile by shorting stocks in the first anomaly quintile and longing stocks in the fifth anomaly quintile. We find that abnormal returns for high-idiosyncratic-risk stocks are always higher than lowidiosyncratic- risk stocks in every anomaly. It suggests that idiosyncratic risk is positively correlated with abnormal return. We also find that abnormal returns become insignificant in low-idiosyncratic-risk stocks for most of the anomalies. These findings are present in both developed and emerging countries. We also observe that for the same level of idiosyncratic risk, developed countries usually have a lower abnormal return than emerging countries for all anomalies studied in this paper. The results demonstrate that idiosyncratic risk is an important factor that limits arbitrage opportunities in international equity markets.

This paper contributes to the growing literature that examines anomalies in several ways. First, we document a list of anomaly variables across countries in a systematic way for a long time period. Although these anomalies are well known for the US market, they are less explored in other countries. Second, we provide strong evidence that idiosyncratic risk contributes to the existence of these anomalies. Most current studies on this topic focus on the US market. We provide results that support the limits of arbitrage theory in countries outside the US and for more anomalies as well. Finally, we provide new evidence to support the mispricing explanation by showing that the impact of
idiosyncratic risk on abnormal returns in developed countries is less than the impact in emerging countries."

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