We examine the risk-return trade-off in market anomalies within the A-share market, showing that even decaying anomalies may proxy for latent risk factors. To balance forecast bias and variance, we integrate the 1/N and mean-variance frameworks, minimizing out-of-sample forecast error. Treating anomalies as tradable assets, we construct optimized long-short portfolios with strong performance: an average annualized Sharpe ratio of 1.56 and a certainty-equivalent return of 29.4% for a mean-variance investor. These premiums persist post-publication and are largely driven by liquidity risk exposures. Our results remain robust to market frictions, including short-sale constraints and transaction costs. We conclude that even decaying market anomalies may reflect priced risk premia rather than mere mispricing. This research provides practical guidance for academics and investors in return predictability and asset allocation, especially in the unique context of the Chinese A-share market.

The objective of this study is to create optimal two-asset portfolios consisting of stocks from Western Europe, the United States, and the BRICS (Brazil, China, India, Russia, and South Africa), as well as sixteen commodity types during the BREXIT period. We utilized dynamic variances and covariances from the GARCH model to derive weights for the two-asset portfolios, with each portfolio consisting of one equity factor and one commodity factor. Subsequently, hedge ratios were calculated for these various assets. Our findings indicate that portfolios consisting of European stocks do not require the inclusion of commodities, whereas the other equities do.

Abstract: It is negative risk if there is a good chance of coming out better than our reference level. This paper proposes a general risk measure: bilateral partial moment, where downside risk is supplemented with the "upside potential". Variance, mean absolute deviation, semi-variance and other downside risk definition are all incorporated in this framework. The portfolio selection problems in this general class of risk model are discussed. The portfolio optimization provides the flexibility for the selection of an appropriate target return and the weightiness of upside potentials.