機関投資家保有データでグラフ検索とベクトル検索を比較

# Vector RAG vs Graph RAG: Real Holdings Benchmark


# Vector RAG vs Graph RAG: Real Holdings Benchmark

**Chapter 23: Knowledge Graphs for Financial AI**

**Docker image**: `ml4t-gpu`

This notebook benchmarks graph retrieval against embedding-based retrieval on
the real 13F holdings corpus used throughout Chapter 23.

**Learning Objectives**:
- Build a benchmark from real institutional holdings rather than synthetic prompts
- Compare graph retrieval and vector retrieval on direct lookup and multi-entity questions
- Measure support recall and retrieval-token budgets on the same corpus

**Book Reference**: Chapter 23, Section 23.3 (Deterministic relational reasoning with graph RAG)

**Prerequisites**: The 13F artifacts written by
`data/equities/positioning/13f_download.py` (run that first if missing).
This notebook requires `sentence-transformers` for the vector baseline
and does not simulate outcomes.

```python
"""Compare structured and embedding retrieval on real 13F holdings."""

from __future__ import annotations

import hashlib
import json
import logging
import warnings
from dataclasses import dataclass
from enum import Enum
from math import ceil

warnings.filterwarnings(
    "ignore",
    category=SyntaxWarning,
    message=r"'return' in a 'finally' block",
)

import matplotlib.pyplot as plt
import numpy as np
import polars as pl
import torch
from sentence_transformers import SentenceTransformer

from data import load_institutional_holdings_13f
from utils.style import COLORS, FIGSIZE, add_message_title, show_with_alt

logging.getLogger("matplotlib.font_manager").setLevel(logging.ERROR)
```

```python
MAX_STOCKS = 250
TOP_K_VECTOR = 10
EMBEDDING_MODEL = "sentence-transformers/all-MiniLM-L6-v2"
BENCHMARK_CUTOFF = "2026-02-17"
```

## 1. Load Real Holdings Data

```python
holdings_df = load_institutional_holdings_13f()
required_columns = {
    "cik",
    "company_name",
    "issuer",
    "cusip",
    "filing_date",
    "value_thousands",
    "shares",
}
assert required_columns <= set(holdings_df.columns)
assert holdings_df.filter(pl.any_horizontal(pl.col(list(required_columns)).is_null())).is_empty()
print(f"Loaded {len(holdings_df)} raw holdings rows from the 13F loader")
holdings_df = holdings_df.with_columns(
    pl.col(["company_name", "issuer"]).str.replace_all(r"\s+", " ").str.strip_chars()
)
```

### Point-in-Time Position Snapshot

Collapse all eligible filings to the latest disclosed row for each
institution-security pair at the fixed benchmark cutoff.

The source retains the legacy field name `value_thousands`, but post-2022 SEC
filings report these position values in dollars. Document text therefore
preserves the value at scale factor 1 and labels it in dollars.

```python
documents_df = (
    holdings_df.filter(pl.col("filing_date") <= pl.lit(BENCHMARK_CUTOFF).str.to_date())
    .group_by("cik", "company_name", "issuer", "cusip", "filing_date")
    .agg(
        pl.sum("value_thousands").alias("value_thousands"),
        pl.sum("shares").alias("shares"),
    )
    .sort("filing_date", descending=True)
    .unique(subset=["cik", "cusip"], keep="first", maintain_order=True)
    .with_columns(
        pl.concat_str(["cik", "cusip", "filing_date"], separator="|").alias("doc_id"),
        pl.format(
            "Institution {} reported holding {} shares of {} (CUSIP {}) "
            "with a reported value of ${} on {}.",
            pl.col("company_name"),
            pl.col("shares"),
            pl.col("issuer"),
            pl.col("cusip"),
            pl.col("value_thousands"),
            pl.col("filing_date"),
        ).alias("document_text"),
    )
)
assert documents_df.select(pl.struct(["cik", "cusip"]).is_duplicated().sum()).item() == 0
assert documents_df["filing_date"].max().isoformat() <= BENCHMARK_CUTOFF
snapshot_row_count = len(documents_df)
```

### Benchmark Universe

Rank stocks only after collapsing the corpus to one position per institution-stock pair.

```python
top_stocks = (
    documents_df.group_by("issuer")
    .agg(pl.sum("value_thousands").alias("total_value"))
    .sort("total_value", descending=True)
    .head(MAX_STOCKS)
)
documents_df = documents_df.filter(pl.col("issuer").is_in(top_stocks["issuer"].implode()))

top_institutions = (
    documents_df.group_by("company_name")
    .agg(pl.sum("value_thousands").alias("total_value"))
    .sort("total_value", descending=True)
)

print(f"Benchmark cutoff: {BENCHMARK_CUTOFF}")
print(f"Benchmark corpus rows: {len(documents_df)} latest institution-stock positions")
print(f"Institutions: {documents_df['company_name'].n_unique()}")
print(f"Stocks: {documents_df['issuer'].n_unique()}")
```

## 2. Benchmark Question Set

```python
class QueryKind(Enum):
    """Types of benchmark questions for RAG comparison."""

    HOLDERS = "holders"
    CO_OWNERS = "co_owners"
    HOLDINGS = "holdings"
```

### Benchmark Question Contract

```python
@dataclass
class BenchmarkQuestion:
    """A single benchmark question with expected support documents."""

    text: str
    kind: QueryKind
    issuer: str | None = None
    issuer_2: str | None = None
    institution: str | None = None
    support_doc_ids: tuple[str, ...] = ()
```

### Question Generators

Build benchmark questions from the real holdings data, recording the expected
support document IDs for recall measurement.

```python
def make_holders_question(issuer: str) -> BenchmarkQuestion:
    """Build a 'who holds this stock?' question with expected support rows."""
    support = (
        documents_df.filter(pl.col("issuer") == issuer)
        .sort("value_thousands", descending=True)
        .head(5)["doc_id"]
        .to_list()
    )
    return BenchmarkQuestion(
        text=f"Which institutions held {issuer}?",
        kind=QueryKind.HOLDERS,
        issuer=issuer,
        support_doc_ids=tuple(support),
    )
```

#### Institution-Holdings Questions

```python
def make_holdings_question(institution: str) -> BenchmarkQuestion:
    """Build a 'what does this institution hold?' question with expected support rows."""
    support = (
        documents_df.filter(pl.col("company_name") == institution)
        .sort("value_thousands", descending=True)
        .head(5)["doc_id"]
        .to_list()
    )
    return BenchmarkQuestion(
        text=f"What were {institution}'s largest holdings?",
        kind=QueryKind.HOLDINGS,
        institution=institution,
        support_doc_ids=tuple(support),
    )
```

#### Co-Ownership Questions

```python
def make_coowners_question(issuer_1: str, issuer_2: str) -> BenchmarkQuestion:
    """Build a 'who holds both stocks?' question with expected support rows."""
    holders_1 = set(
        documents_df.filter(pl.col("issuer") == issuer_1)["company_name"].unique().to_list()
    )
    holders_2 = set(
        documents_df.filter(pl.col("issuer") == issuer_2)["company_name"].unique().to_list()
    )
    shared_institutions = sorted(holders_1 & holders_2)

    support_rows = documents_df.filter(
        pl.col("company_name").is_in(shared_institutions)
        & pl.col("issuer").is_in([issuer_1, issuer_2])
    ).sort(["company_name", "value_thousands"], descending=[False, True])
    support = support_rows["doc_id"].head(6).to_list()

    return BenchmarkQuestion(
        text=f"Which institutions held both {issuer_1} and {issuer_2}?",
        kind=QueryKind.CO_OWNERS,
        issuer=issuer_1,
        issuer_2=issuer_2,
        support_doc_ids=tuple(support),
    )
```

```python
top_issuers = top_stocks["issuer"].head(4).to_list()
benchmark_questions = [
    make_holders_question(top_issuers[0]),
    make_holders_question(top_issuers[1]),
    make_coowners_question(top_issuers[0], top_issuers[1]),
    make_coowners_question(top_issuers[0], top_issuers[2]),
]
benchmark_questions.extend(
    make_holdings_question(institution)
    for institution in top_institutions["company_name"].head(3).to_list()
)

print(f"Benchmark questions: {len(benchmark_questions)}")
for question in benchmark_questions:
    print("-", question.text)
```

## 3. Graph Retrieval

Graph retrieval here is a deterministic, oracle-style structured lookup: it
resolves each question with the same relational predicates that define the gold
support set, so it returns exact rows by construction. It is the structured-
database baseline, not a model competing with vector search under semantic
ambiguity. The comparison isolates what an explicit relational representation
buys over embedding similarity, not which model is "smarter".

```python
def graph_retrieve(question: BenchmarkQuestion) -> list[str]:
    """Return exact support rows using structured holdings filters."""
    if question.kind == QueryKind.HOLDERS:
        rows = (
            documents_df.filter(pl.col("issuer") == question.issuer)
            .sort("value_thousands", descending=True)
            .head(5)
        )
        return rows["doc_id"].to_list()

    if question.kind == QueryKind.HOLDINGS:
        rows = (
            documents_df.filter(pl.col("company_name") == question.institution)
            .sort("value_thousands", descending=True)
            .head(5)
        )
        return rows["doc_id"].to_list()

    holders_1 = set(
        documents_df.filter(pl.col("issuer") == question.issuer)["company_name"].unique().to_list()
    )
    holders_2 = set(
        documents_df.filter(pl.col("issuer") == question.issuer_2)["company_name"]
        .unique()
        .to_list()
    )
    shared = sorted(holders_1 & holders_2)
    rows = documents_df.filter(
        pl.col("company_name").is_in(shared)
        & pl.col("issuer").is_in([question.issuer, question.issuer_2])
    ).sort(["company_name", "value_thousands"], descending=[False, True])
    return rows["doc_id"].head(6).to_list()
```

### Graph Token Budget

Estimate the token cost of a structured-row response by concatenating the
four selected fields with separators and applying the same rough
words-per-token multiplier the vector side uses. Counting both budgets the
same way is all that buys: the two payloads still differ in how many rows
they carry and which fields each row spells out, and section 6 separates
those from the formatting. Neither figure is a tokenizer count.

```python
def graph_token_budget(doc_ids: list[str]) -> int:
    """Estimate the token budget for structured graph rows."""
    if not doc_ids:
        return 0
    rows = documents_df.filter(pl.col("doc_id").is_in(doc_ids)).select(
        pl.concat_str(
            ["company_name", "issuer", "value_thousands", "filing_date"],
            separator=" | ",
        ).alias("row_text")
    )
    return sum(ceil(len(text.split()) * 1.3) for text in rows["row_text"].to_list())
```

## 4. Vector Retrieval

```python
assert torch.cuda.is_available(), "Production embedding inference requires CUDA"
encoder = SentenceTransformer(EMBEDDING_MODEL, device="cuda")
assert encoder.device.type == "cuda"
print(f"Embedding device: {encoder.device} ({torch.cuda.get_device_name(0)})")
document_texts = documents_df["document_text"].to_list()
document_ids = documents_df["doc_id"].to_list()
document_embeddings = encoder.encode(
    document_texts,
    normalize_embeddings=True,
    show_progress_bar=False,
)
```

### Embedding-Similarity Retrieval

```python
def vector_retrieve(question: BenchmarkQuestion, top_k: int = TOP_K_VECTOR) -> list[str]:
    """Retrieve the closest holdings rows by embedding similarity."""
    query_embedding = encoder.encode([question.text], normalize_embeddings=True)[0]
    scores = document_embeddings @ query_embedding
    top_indices = np.argsort(scores)[-top_k:][::-1]
    return [document_ids[idx] for idx in top_indices]
```

### Vector Token Budget

The vector payload uses the retrieved prose statements, whereas the graph
payload uses compact structured fields. Both estimates use the same rough
words-to-token multiplier. The difference therefore includes representation
format and is not a tokenizer-measured inference-cost comparison.

```python
def vector_token_budget(doc_ids: list[str]) -> int:
    """Estimate token budget from retrieved free-text holdings rows."""
    if not doc_ids:
        return 0
    texts = documents_df.filter(pl.col("doc_id").is_in(doc_ids))["document_text"].to_list()
    return sum(ceil(len(text.split()) * 1.3) for text in texts)
```

## 5. Run Benchmark

```python
rows: list[dict[str, object]] = []
for question in benchmark_questions:
    gold = set(question.support_doc_ids)
    assert gold, f"Question has no support rows: {question.text}"

    graph_doc_ids = graph_retrieve(question)
    vector_doc_ids = vector_retrieve(question)

    graph_recall = len(gold & set(graph_doc_ids)) / len(gold) if gold else 0.0
    vector_recall = len(gold & set(vector_doc_ids)) / len(gold) if gold else 0.0

    rows.append(
        {
            "question": question.text,
            "kind": question.kind.value,
            "system": "graph",
            "support_recall": graph_recall,
            "retrieved_docs": len(graph_doc_ids),
            "retrieval_tokens": graph_token_budget(graph_doc_ids),
        }
    )
    rows.append(
        {
            "question": question.text,
            "kind": question.kind.value,
            "system": "vector",
            "support_recall": vector_recall,
            "retrieved_docs": len(vector_doc_ids),
            "retrieval_tokens": vector_token_budget(vector_doc_ids),
        }
    )

results = pl.DataFrame(rows)
assert results.filter(pl.col("system") == "graph")["support_recall"].min() == 1.0
```

```python
summary = (
    results.group_by("system")
    .agg(
        pl.mean("support_recall").alias("avg_support_recall"),
        pl.mean("retrieval_tokens").alias("avg_retrieval_tokens"),
        pl.mean("retrieved_docs").alias("avg_retrieved_docs"),
    )
    .sort("system")
)

by_kind = (
    results.group_by(["system", "kind"])
    .agg(
        pl.mean("support_recall").alias("avg_support_recall"),
        pl.mean("retrieval_tokens").alias("avg_retrieval_tokens"),
    )
    .sort(["kind", "system"])
)

print("Per-question retrieval audit:")
results.select(
    "question",
    "kind",
    "system",
    "support_recall",
    "retrieved_docs",
    "retrieval_tokens",
)
```

Support recall measures whether each method retrieves the rows used to define
an answer as of the benchmark cutoff. The structured lookup is an oracle built
from those same predicates, so its perfect recall is a construction property,
not an estimated model advantage.

## 6. Headline metrics, and how to read them

One of these two numbers is a measurement and the other is an assertion. The
oracle's recall is 1 because its predicates are the ones that built the gold
set, so the "delta" between the systems is just one minus the vector arm's
recall wearing a comparative label. The vector figure is the only estimated
quantity here.

The token figures are each retriever's actual context budget, and three
things separate them. The relational side returns the 5 or 6 rows the
predicate matched while the vector side always returns `TOP_K_VECTOR` = 10,
so the count alone roughly halves it. Each relational row spells out four fields
and each prose row six, adding `shares` and `cusip`. Only what is left after
those two is formatting. The per-row figure below removes the count; the
field difference stays in it.

```python
graph_summary = summary.filter(pl.col("system") == "graph").row(0, named=True)
vector_summary = summary.filter(pl.col("system") == "vector").row(0, named=True)

recall_delta = graph_summary["avg_support_recall"] - vector_summary["avg_support_recall"]
token_reduction = 1.0 - (
    graph_summary["avg_retrieval_tokens"] / vector_summary["avg_retrieval_tokens"]
)
graph_per_row = graph_summary["avg_retrieval_tokens"] / graph_summary["avg_retrieved_docs"]
vector_per_row = vector_summary["avg_retrieval_tokens"] / vector_summary["avg_retrieved_docs"]
per_row_reduction = 1.0 - (graph_per_row / vector_per_row)

print("\nReal-data comparison")
print(
    f"Relational oracle support recall: {graph_summary['avg_support_recall']:.2%} (by construction)"
)
print(f"Vector support recall:            {vector_summary['avg_support_recall']:.2%}")
print(f"  the difference, {recall_delta:.2%}, is one minus the vector figure and nothing more")
print(
    f"Context budget: {graph_summary['avg_retrieval_tokens']:.0f} tokens over "
    f"{graph_summary['avg_retrieved_docs']:.1f} structured rows against "
    f"{vector_summary['avg_retrieval_tokens']:.0f} over "
    f"{vector_summary['avg_retrieved_docs']:.1f} prose rows ({token_reduction:.0%} fewer)"
)
print(
    f"  per retrieved row: {graph_per_row:.0f} against {vector_per_row:.0f} tokens "
    f"({per_row_reduction:.0%} fewer), which is the four structured fields against the "
    "six-field sentence"
)
```

### Retrieval Comparison by Query Type

Compare both support recall and estimated context by question type. The
structured arm is an oracle baseline because its predicates define the gold
support rows.

```python
query_kinds = ["holders", "co_owners", "holdings"]
kind_labels = ["Holder", "Co-owner", "Holdings"]
x = np.arange(len(query_kinds))
width = 0.36
graph_recalls = [
    by_kind.filter((pl.col("system") == "graph") & (pl.col("kind") == kind))[
        "avg_support_recall"
    ].item()
    for kind in query_kinds
]
vector_recalls = [
    by_kind.filter((pl.col("system") == "vector") & (pl.col("kind") == kind))[
        "avg_support_recall"
    ].item()
    for kind in query_kinds
]
graph_tokens = [
    by_kind.filter((pl.col("system") == "graph") & (pl.col("kind") == kind))[
        "avg_retrieval_tokens"
    ].item()
    for kind in query_kinds
]
vector_tokens = [
    by_kind.filter((pl.col("system") == "vector") & (pl.col("kind") == kind))[
        "avg_retrieval_tokens"
    ].item()
    for kind in query_kinds
]
```

#### Render Support and Context Panels

The oracle's recall is drawn as a reference line rather than as a series. It
is flat at 1 for every question kind and cannot be otherwise, so a bar for it
would put an assertion beside a measurement and invite the reader to compare
their heights.

```python
fig, axes = plt.subplots(2, 1, figsize=FIGSIZE["dual_v"], constrained_layout=True)
axes[0].bar(x, vector_recalls, width * 1.4, label="Vector retrieval", color=COLORS["amber"])
axes[0].axhline(
    graph_summary["avg_support_recall"],
    color=COLORS["blue"],
    linestyle="--",
    linewidth=2,
    label="Relational oracle (1 by construction)",
)
axes[0].set_xticks(x, kind_labels)
axes[0].set_ylabel("Average support recall")
axes[0].set_ylim(0, 1.15)
axes[0].legend(frameon=False, ncol=2, loc="upper center")

axes[1].bar(
    x - width / 2,
    graph_tokens,
    width,
    color=COLORS["blue"],
    label="Structured rows (5-6 matched)",
)
axes[1].bar(
    x + width / 2,
    vector_tokens,
    width,
    color=COLORS["amber"],
    label=f"Prose rows (top {TOP_K_VECTOR})",
)
axes[1].set_xticks(x, kind_labels)
axes[1].set_ylabel("Average retrieval tokens")
axes[1].set_title("Context budget per question, over each retriever's own payload", loc="left")
axes[1].set_ylim(0, max(vector_tokens) * 1.35)
axes[1].legend(frameon=False, ncol=2, loc="upper center")

add_message_title(
    axes[0],
    "Support recall by question kind, against the oracle ceiling",
    subtitle="Benchmark questions over the latest disclosed positions at the cutoff",
)
show_with_alt(
    fig,
    "Two stacked panels sharing three question-kind categories on the horizontal axis. Top: "
    "bars for vector retrieval's average support recall, well below a dashed horizontal "
    "reference line at one marking the relational oracle; the bars differ across the three "
    "kinds and none reaches the line. Bottom: paired bars of average retrieval tokens per "
    "question, the structured-row bar roughly a quarter the height of the prose-row bar in "
    "every category. The two bars cover different payloads: 5 or 6 matched rows of four "
    "fields against the top ten rows of a six-field sentence.",
)
```

### Machine-Readable Completion Record

```python
completion_record = {
    "embedding_device": str(encoder.device),
    "embedding_model": EMBEDDING_MODEL,
    "embedding_shape": list(document_embeddings.shape),
    "embedding_sha256": hashlib.sha256(document_embeddings.tobytes()).hexdigest(),
    "raw_rows": len(holdings_df),
    "snapshot_rows": snapshot_row_count,
    "corpus_rows": len(documents_df),
    "institutions": documents_df["company_name"].n_unique(),
    "stocks": documents_df["issuer"].n_unique(),
    "questions": len(benchmark_questions),
    "graph_support_recall": round(graph_summary["avg_support_recall"], 6),
    "vector_support_recall": round(vector_summary["avg_support_recall"], 6),
    "support_recall_delta": round(recall_delta, 6),
    "token_reduction": round(token_reduction, 6),
}
print("COMPLETION_RECORD=" + json.dumps(completion_record, sort_keys=True))
```

The structured lookup reaches perfect recall because the benchmark support is
defined by its own predicates - the assertion above enforces it, so a change
that broke the identity would stop the notebook rather than quietly produce a
comparison. The embedding baseline is the contrast worth having, and seven
generated questions over ten institutions do not establish production
accuracy or cost.

## Key takeaways

1. **Only one arm of this benchmark is measured.** The relational side runs
   the predicates that defined the gold support set, so its recall is 1 for
   every question and would be whatever those predicates returned. What the
   run estimates is how much of that support an embedding retriever recovers
   from prose descriptions of the same rows. Read the vector column; the
   difference between the columns adds nothing to it.

2. **The oracle is still the right baseline to draw.** It is what an explicit
   relational representation gives you for free, and its value here is that it
   fixes the ceiling rather than that it ranks above anything. A benchmark with two
   estimated arms would be a different and more expensive notebook.

3. **The token difference is three differences.** The relational side returns
   the rows its predicate matched, 5 or 6 of them; the vector side always
   returns ten, because a similarity ranking has no notion of when to stop.
   Each relational row is `institution | issuer | value | date` and each prose
   row spells out `shares` and `cusip` as well. The count roughly halves the
   budget on its own; the per-row figure printed above carries the extra
   fields together with the sentence scaffolding around them, which this
   notebook does not separate. None of the three is a measurement of
   retriever efficiency, and neither figure is a tokenizer count.

4. **Where the vector arm loses is worth reading per question kind**, and the
   per-question audit above is where to read it: one holder question is
   recovered completely and another is missed completely, which says more
   about how the issuer is named in the corpus than about question difficulty.

5. **Seven questions over ten institutions.** Enough to show the shape of the
   failure, not enough to size it.

**Next**: [`03_graph_rag_qa`](03_graph_rag_qa.ipynb) puts a read-only
text-to-Cypher layer over these lookups.
![notebook output](figures/p1_1.png)