A general approach to smooth and convex portfolio optimization using lower partial moments

We propose a new nonparametric kernel (NPK) mean-lower partial moments model for portfolio construction that includes transaction costs. In the theory section, we study the properties of the solution to this model. We use simulated financial returns to demonstrate that the NPK model outperforms the traditional moment (MOM) model in terms of estimation accuracy, portfolio performance and transaction costs. We then empirically test our model using actual hedge fund returns, because holding these assets can expose investors to substantial downside risk. Portfolios formed using our NPK model significantly outperform those formed using the MOM model and other conventional investment strategies, regardless of the performance metric examined. Our NPK model will therefore be useful in a wide variety of contexts requiring downside risk management