Classic mean–variance optimization is very sensitive to expected returns. An alternative and more robust approach is to calculate the implied returns given the current portfolio allocation and risk profile. Portfolio managers can then do a reality check on the implied returns and find opportunities for better allocations. The most common implied return calculation assumes normal distribution and unlimited leverage, and use volatility as risk measure and covariance matrix as model input. However, practitioners usually have leverage constraints, often use non-parametric risk models, and care about portfolio tail risk. This paper presents a new approach to calculate expected returns with leverage constraints. This approach is flexible enough to alleviate normal distribution assumption, connect with non-parametric risk models, and use tail risk measures, such as conditional VaR.

经典的均值-方差优化对预期收益非常敏感。另一种更强大的方法是在给定当前投资组合分配和风险状况的情况下计算隐含回报。然后，投资组合经理可以对隐含回报进行现实检查，并找到机会进行更好的分配。最常见的隐含收益计算假定正态分布和无限杠杆，并使用波动率作为风险度量，并使用协方差矩阵作为模型输入。但是，从业人员通常具有杠杆约束，经常使用非参数风险模型，并且关注投资组合尾部风险。本文提出了一种在杠杆约束条件下计算预期收益的新方法。这种方法足够灵活，可以缓解正态分布假设，与非参数风险模型相关联，