Extending the Markowitz model with dimensionality reduction: Forecasting efficient frontiers

The Markowitz model is an established approach to portfolio optimization that constructs efficient frontiers allowing users to make optimal tradeoffs between risk and return. However, a limitation of this approach is that it assumes future asset returns and covariances will be identical to the asset's historical data, or that these model parameters can be accurately estimated, a notion which often does not hold in practice. Markowitz efficient frontiers are square root second-order polynomials that can be represented by three parameters, thus providing a significant dimensionality reduction of the lookback covariances and growth of the assets. Using this dimensionality reduction, we propose an extension to the Markowitz model that accounts for the nonstationary behavior of the portfolio assets' return and covariance without the necessity to forecast the complex covariance matrix and assets growths, something that has proven to be extremely difficult. Our methodology allows users to forecast the three efficient frontier coefficients using a time-series regression. By observing similar efficient frontiers, this forecasted efficient frontier can be used to select optimal assets mean-variance tradeoffs (asset weights). For exploratory testing we employ a set of assets that span a large portion of the market to demonstrate and validate this new approach.