Modeling asset allocations and a new portfolio performance score

Area of Science:

• Quantitative Finance
• Computational Geometry
• Financial Econometrics

Background:

• Traditional portfolio analysis often overlooks complex interdependencies and geometric properties of asset allocations.
• Accurate crisis detection and portfolio performance evaluation are critical for financial stability and investment management.

Purpose of the Study:

• To extend a geometric framework for representing portfolios and apply advanced computational tools to digital finance problems.
• To develop and validate an automated crisis detection indicator using copula-based methods.
• To introduce a novel computational framework and scoring system for evaluating asset allocation strategies.

Main Methods:

• Utilizing a geometric framework that models asset allocations as points in a convex polytope.
• Employing copula functions to model the relationship between portfolio return and volatility for anomaly detection.
• Developing a new portfolio score based on statistical properties within the geometric framework.

Main Results:

• The crisis detection indicator successfully identified all historical cryptocurrency market crashes and four out of five major crises in the DJ600-Europe index (1990-2008) with one false positive.
• A new, computationally efficient portfolio score was developed for evaluating management strategies.

Conclusions:

• The geometric framework provides a powerful approach for analyzing portfolios and addressing key challenges in digital finance.
• The proposed methods offer robust solutions for automated crisis detection and sophisticated portfolio performance evaluation.