On the Use of Efficient Frontier Functional Coefficients in Asset Allocation

We propose three novel methods to improve asset allocation using the functional efficient frontier coefficients. Efficient frontiers can be decomposed to their functional form, a square-root second- order polynomial, and the coefficients of this function captures the information about the return vector and covariance matrix in the current time period. We define a set of three interpretable efficient frontier coefficients. The first model improves out-of-sample Sharpe ratios through forecasting the future efficient frontier using its functional coefficients, then investing in the portfolio on the current efficient frontier that is the minimum Euclidean distance from the tangency portfolio on the forecasted efficient frontier. The second model forecasts the market’s monthly binary return using CART trained on the feature-engineered efficient frontier coefficients, then integrates these forecasts to a mean-variance framework using the expected returns conditional on the binary market forecast. The third model uses the efficient frontier coefficients as a feature set to cluster market states on which to define a Markov process. The model maps each state to a tangency portfolio calculated using only data in that state, then simulates the Markov process, and invests in the associating tangency portfolio. Each of these proposed models provides an implication of the structure of the market, and demonstrates that the efficient frontier coefficients can provide insight into the market. To empirically validate these proposed models, we employ two sets of assets that span the market.