Ownership and Holdings Networks

A spreadsheet listing "Fund X owns 4% of Company Y" is a fact. A thousand such facts, stacked in rows, is a filing database. But the same thousand facts, drawn as a graph — funds and companies as nodes, ownership stakes as weighted, directed edges — reveals patterns a spreadsheet never will: which handful of funds sit at the center of ownership across an entire sector, which companies are jointly owned by the same small set of investors (common ownership), and which ownership chains run through holding companies several links deep before reaching a real controlling party. An ownership and holdings network is exactly this: the same disclosed data, restructured so that structure itself becomes the signal.

The analogy: a family tree versus a list of birth certificates

A pile of individual birth certificates tells you, one record at a time, who is whose child. It takes real effort to answer "who are this person's second cousins" from that pile alone. A family tree drawn as a diagram answers it at a glance — because the relationships between records are exactly what a tree encodes and a flat list does not. Ownership filings are the birth certificates; the ownership network is the family tree. Questions like "which two seemingly unrelated companies share three of the same top-five owners" are trivial to spot once drawn as a graph and genuinely hard to spot scanning rows of a filing table.

Building the graph

Nodes come in at least two types (making this graph heterogeneous by nature): owner nodes (funds, holding companies, individuals, sovereign wealth funds) and company nodes (the equities being held). A directed, weighted edge runs from owner to company, weighted by stake size — often the percentage of shares outstanding, $w_{ij} = \frac{\text{shares held by } i \text{ in } j}{\text{shares outstanding of } j}$. In words: the edge weight is simply the fraction of the company that owner controls, so a 12% stake and a 0.5% stake are visibly different in the graph, not just numerically different in a table. Holding companies introduce indirect ownership: if $A$ owns 60% of $B$ and $B$ owns 40% of $C$, $A$'s effective indirect stake in $C$ is often approximated by multiplying stakes along the chain, $0.60 \times 0.40 = 0.24$, i.e. roughly a 24% effective interest — though real corporate-control questions (who can actually outvote whom) need more care than a simple product once ownership chains branch or loop.

Worked example 1: finding common ownership by hand

Suppose funds $F_1$, $F_2$, $F_3$ each disclose top-ten holdings, and companies $A$ and $B$ (direct competitors in the same industry) each appear in exactly the same three funds' top-ten lists, with stakes: in $A$, $F_1$ holds 6%, $F_2$ holds 5%, $F_3$ holds 4%; in $B$, $F_1$ holds 7%, $F_2$ holds 6%, $F_3$ holds 3%. Combined stake of these three funds in $A$: $6+5+4=15\%$. In $B$: $7+6+3=16\%$. The same three institutions collectively hold roughly 15-16% of two direct competitors — a common-ownership signal that shows up immediately as "three owner nodes, each with edges into both $A$ and $B$" in the graph, but would require deliberately cross-referencing three separate 13F filings to notice in tabular form.

Worked example 2: multiplying through a holding-company chain

A sovereign wealth fund $SWF$ owns 80% of holding company $H$, which in turn owns 25% of operating company $O$. The naive indirect-stake estimate: $0.80 \times 0.25 = 0.20$, i.e. an effective 20% interest in $O$. Now suppose $O$ also has a direct stake held by $SWF$ of 3% (bypassing $H$ entirely, say through a separate fund vehicle). Total effective interest: the indirect $20\%$ (through $H$) plus the direct $3\%$, giving $23\%$ combined economic exposure to $O$ — a figure that could trigger a disclosure threshold (many jurisdictions require additional filings above 20-25% aggregate ownership) that neither the $H\!\to\!O$ filing nor the direct $SWF\!\to\!O$ filing would individually reveal.

An ownership network's adjacency structure can be represented as a matrix exactly like the one above; multiplying stake matrices along a chain (as in worked example 2) is literally matrix multiplication through successive ownership layers.

What this means in practice

Ownership networks feed antitrust and market-structure research (do the same large asset managers commonly owning direct competitors soften competitive pressure between them), concentration-risk monitoring (is a security's free float dominated by a handful of funds who might move in lockstep), and forensic work tracing beneficial ownership through layered holding structures. The data itself is the main limitation: 13F filings only cover a subset of U.S. equity holdings above a size threshold, disclosure lags run to 45 days after quarter-end, and non-U.S. or private-holding-company chains are often invisible entirely — so any ownership graph built from public filings is a real but structurally incomplete picture, understating true concentration.

Practice

1. Recompute worked example 2's total effective interest if $H$'s stake in $O$ were 40% instead of 25%.
2. Explain in one sentence why multiplying stakes along an ownership chain can overstate real control once ownership loops back or funds hold non-voting share classes.
3. Given three funds each owning 5-8% of two competing companies, describe in one sentence how you'd represent this as a graph query rather than a spreadsheet filter.