Asset Allocation by Penalized Least Squares

This paper shows how the problem of mean-downside risk portfolio allocation can be cast in terms of penalized least squares (PLS). The penalty is given by a power function of the returns below a certain threshold. We derive the asymptotic properties of the PLS estimator, allowing for possible nonlinearities and misspecification of the model. We illustrate the usefulness of this new class of estimators with two empirical applications. First, we estimate an autoregressive model,in the spirit of the GARCH literature. Second, we suggest a simple strategy to derive the optimal portfolio weights associated to a mean-downside risk model