Forecasting Tangency Portfolios and Investing in the Minimum Euclidean Distance Portfolio to Maximize Out-of-Sample Sharpe Ratios

TL;DR

This paper introduces a new asset allocation model that forecasts the future tangency portfolio to improve out-of-sample Sharpe ratios, addressing limitations of traditional methods that rely on stationary return and covariance estimates.

Contribution

The paper's novelty lies in forecasting the efficient frontier's coefficients to predict the tangency portfolio, then selecting the portfolio closest to this forecast for better out-of-sample performance.

Findings

The proposed method outperforms traditional models in empirical tests.

Forecasting the tangency portfolio improves out-of-sample Sharpe ratios.

The approach is validated on two diverse asset sets.

Abstract

We propose a novel model to achieve superior out-of-sample Sharpe ratios. While most research in asset allocation focuses on estimating the return vector and covariance matrix, the first component of our novel model instead forecasts the future tangency portfolio, and the second component then determines the optimal investment portfolio. First, to forecast the tangency portfolio, we forecast the efficient frontier by decomposing its functional form, a square root second-order polynomial, into three interpretable coefficients, which can then be used to calculate a forecasted tangency portfolio. These coefficients can be forecasted using vector autoregressions. Second, the model invests in the portfolio on the efficient frontier that is the minimum Euclidean distance from this forecasted tangency portfolio. A motivation for our approach is to address the limitation that the tangency portfolio only maximizes the Sharpe ratio when future returns and covariances are stationary, and can be directly estimated with historical data, which often does not hold in out-of-sample data. Our approach addresses this shortcoming in a novel way by forecasting the tangency portfolio, rather than estimating return and covariance. For empirical testing, we employ two sets of assets that span the market to demonstrate and validate the performance of this novel method.