The risk-return trade-off is the core of equity investments. The literature has focused on the properties of risk measures but not the trade-off. We found that popular risk measures lacked empirical risk-return trade-off capacity and balanced market investability, and the empirical studies were mainly under Markowitz's Mean-variance models. Using the newly introduced mark to market value at risk (MMVaR), we build a new Mean-MMVaR model and present the outperformance of the model over popular models in terms of better risk-return trade-off and portfolio selection under diversified markets and risk levels being from regulators’ tight rules to investors’ comfort beliefs.

Joint work with Tongbo Liu (School of Economics, PKU), Zhicheng Wang (Guanghua Management School, PKU).

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