  Investment returns naturally reside on irregular domains, however, standard
multivariate portfolio optimization methods are agnostic to data structure. To
this end, we investigate ways for domain knowledge to be conveniently
incorporated into the analysis, by means of graphs. Next, to relax the
assumption of the completeness of graph topology and to equip the graph model
with practically relevant physical intuition, we introduce the portfolio cut
paradigm. Such a graph-theoretic portfolio partitioning technique is shown to
allow the investor to devise robust and tractable asset allocation schemes, by
virtue of a rigorous graph framework for considering smaller, computationally
feasible, and economically meaningful clusters of assets, based on graph cuts.
In turn, this makes it possible to fully utilize the asset returns covariance
matrix for constructing the portfolio, even without the requirement for its
inversion. The advantages of the proposed framework over traditional methods
are demonstrated through numerical simulations based on real-world price data.
