Search
Close this search box.
Search
Close this search box.

Hierarchical Sensitivity Parity: Can Neural Networks be Used to Include Casual Dynamics for Optimization?

Hierarchical Sensitivity Parity: Can Neural Networks be Used to Include Casual Dynamics for Optimization?

Trading & Investing
Simplified view of a feedforward artificial neural network

Let’s take a look at the excellent paper:

Portfolio Optimization Based on Neural Networks Sensitivities from Assets Dynamics Respect Common Drivers written by Alejandro Rodriguez Dominguez!

The paper has been accepted for publication in the Machine Learning with Applications (MLWA) Journal.

Alejandro presents a framework for modeling asset and portfolio dynamics, incorporating this information into portfolio optimization.

Furthermore, Alejandro defines drivers for asset and portfolio dynamics and their optimal selection. For this framework, he introduces the Commonality Principle, providing a solution for the optimal selection of portfolio drivers as the common drivers.

Portfolio constituent dynamics are modeled by Partial Differential Equations. And solutions approximated with neural networks.
A visualisation of a solution to the two-dimensional heat equation with temperature represented by the vertical direction and color. Nicoguaro. Based on File:Heat eqn.gif by en:User:Oleg Alexandrov

Sensitivities with respect to the common drivers are obtained via Automatic Adjoint Differentiation, information on asset dynamics is incorporated via sensitivities into portfolio optimization. The common drivers selected with the commonality principle allow approximating causality with correlation following Reichenbach’s Common Cause Principle (1956) to form a casual geometric space in which constituents can be projected. Thus, portfolio constituents become embedded into the space of sensitivities with respect to their common drivers. In addition, a distance matrix in this space called the Sensitivity matrix becomes used to solve the convex optimization for diversification.

The sensitivity matrix measures the similarity of the projections of portfolio constituents on a vector space formed by common drivers’ returns. And becomes used to optimize for diversification on both idiosyncratic and systematic risks. While adding directionality and future behavior information via returns dynamics.

For portfolio optimization, Alejandro perform hierarchical clustering on the sensitivity matrix. The clustering tree is used for recursive bisection to obtain the weights. To the best of the author’s knowledge, this is the first time that sensitivities’ dynamics approximated with neural networks have been used for portfolio optimization. Secondly, that hierarchical clustering on a matrix of sensitivities solves the convex optimization problem.

Moreover, incorporates the hierarchical information of these sensitivities. Thirdly, public and listed variables can become used to obtain maximum idiosyncratic and systematic diversification. By means of the sensitivity space with respect to optimal portfolio drivers.

In conclusion, Alejandro reaches over-performance in many experiments with respect to all other out-of-sample methods for different markets and real datasets. Alejandro also includes a recipe for the methodology to increase performance even further. And lastly, tackle the main issues in portfolio management such as regimes, non-stationarity, overfitting, and selection bias.

This work can be extended by modeling portfolio dynamics with SDEs and approximating sensitivities with neural networks or finding new functions to represent sensitivity dynamics (path-dependent) that could add more trajectory information to diversification.

Read Alejandro’s Full Paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4234186

Trading & Investing

Hierarchical Sensitivity Parity: Can Neural Networks be Used to Include Casual Dynamics for Optimization?