Optimal Portfolio for Basic DAGs

Starting from the Markowitz’s formula for a portfolio we compute the solutions for three structures of dependencies and use acyclic directed graphs (DAGs) to represent the structures. Same levels of returns and volatilities are adopted for all assets in order to focus just on the role of correlations. We start with two structures of dependencies among three assets. We then compute the optimal solution for a four assets portfolio whose DAG is the superposition of the previous patterns.