Expected returns with leverage constraints and target returns

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.