Exploratory Research
Historical Research
Retrospective, cross-sectional, and sector-level observations from the current RG dataset. Preliminary and approximate.
Research Caveat
This page presents exploratory observations based on an approximate, limited dataset. All results are preliminary. No predictive or causal claims are made. RG is a descriptive heuristic indicator — not a forecasting model and not investment advice. Sample sizes are small, data coverage is partial, and all values are approximations derived from public sources via yfinance. Do not draw strong conclusions from this analysis.
What the current evidence tentatively suggests
n = 127 companies · historical anchor: 2023 · current prices approx. early 2026 · exploratory only1. Cross-Index Snapshot
Median RG10 and interquartile range by index for the most recent quarterly observation per company. Only companies with a valid, non-near-boundary RG10 are included.
| Index | n | P25 | Median RG10 | P75 |
|---|---|---|---|---|
| S&P 500 | 29 | 1.92 | 2.55 | 3.21 |
| SMI | 10 | 1.66 | 2.07 | 2.48 |
| CAC 40 | 15 | 0.96 | 1.86 | 3.34 |
| Nikkei 225 | 19 | 0.83 | 1.38 | 2.17 |
| FTSE 100 | 15 | 0.71 | 1.28 | 2.33 |
| DAX 40 | 28 | 0.50 | 1.07 | 1.77 |
| Hang Seng | 42 | 0.41 | 0.91 | 1.42 |
Higher RG10 suggests the market is assigning a larger multiple to the fundamental base. Whether this reflects overvaluation, expected future earnings growth, or structural differences between markets cannot be determined from RG alone.
2. Current RG10 Distribution
Distribution of the most recent RG10 across 158 of 161 covered companies. 3 classified as "not fundamentally covered" (FB ≤ 0 for all N). 0 flagged as near-boundary and excluded from distribution.
P25
0.72
Median
1.43
P75
2.37
3. Sector Comparison
Median RG10 by sector. Bar length represents median; n = number of companies. Sectors with fewer than 3 companies should be interpreted with particular caution.
Sector differences may reflect structural characteristics (capital intensity, intangibles, leverage) rather than relative valuation stretch. Sectors are as classified in the dataset.
4. Cross-Sectional Snapshot Over Time
Median RG10 and interquartile range across all qualifying quarterly observations per period. Only periods with ≥ 15 qualifying companies are shown. This is not a panel dataset — the company composition varies across periods.
| Period | n | P25 | Median RG10 | P75 |
|---|---|---|---|---|
| Q1 2025 | 19 | 0.21 | 0.57 | 0.88 |
| Q2 2025 | 83 | 0.51 | 1.01 | 1.94 |
| Q3 2025 | 69 | 0.69 | 1.58 | 2.87 |
| Q4 2025 | 125 | 0.65 | 1.46 | 2.59 |
| Q1 2026 | 99 | 0.69 | 1.28 | 2.33 |
The dataset covers only 4 recent quarters of quarterly data plus a limited number of annual historical observations. No robust trend conclusions can be drawn from this sample.
5. Valuation Fragility: Core RG vs. Narrative RG
Aggregate market expensiveness tells only part of the story. Fragility analysis splits companies into a fundamentals-anchored core and a narrative-driven segment, then measures how far they have diverged. A large and growing spread is a structural signal — it captures market splitting, not just aggregate elevation.
Panel construction
Balanced panel of 0 companies with valid RG10 in all 6 target periods. Grouping: bottom third = Core RG group; top third = Narrative RG group.
FY 2023 and FY 2024 use historical closing prices (annual observations). Q1–Q4 2025 use current market cap (as of data fetch, approx. early 2026) — within-2025 variation reflects changes in smoothed earnings G only, not quarterly price movements.
Three Market Structures
Case A — Uniformly expensive
Core RG and Narrative RG are both elevated, with a small spread and ratio near 1. The whole market is stretched relative to earnings — the same signal as a high Macro RG. Not intrinsically more fragile than a split market; the risk is broad, not concentrated.
Case B — Split market
Core RG remains moderate while Narrative RG is very high — spread large, ratio high. The fundamentals-anchored segment and the narrative-driven segment are pricing entirely different futures. This structural split is the clearest fragility signal: the gap cannot persist indefinitely without either earnings catching up or prices correcting.
Case C — Selective bubble
A small number of names with extreme RG values drag Narrative RG upward while Core RG is low. Spread is large. Unlike Case A, most of the market is conservatively priced; but the concentrated pocket of overvaluation creates asymmetric risk — a correction in the high-RG segment can have outsized index impact if those names are heavily weighted.
Fragility Spread and Ratio are complements to Macro RG (CAPE/10), not substitutes. Macro RG measures aggregate elevation; Fragility measures structural splitting within the distribution.
Fragility Snapshot
Core RG (latest)
0.00
Q4 2025
Narrative RG (latest)
0.00
Q4 2025
Current Fragility Spread
0.00
Q4 2025
Current Fragility Ratio
0.0×
Q4 2025
Peak Fragility Spread
0.00
FY 2023
Peak Fragility Ratio
0.0×
FY 2023
Core RG vs. Narrative RG — Time Series
Open panel (all companies with valid RG10 per quarter, n varies). Q1 2024: 21 companies only (tercile method). Shaded area = Narrative RG − Core RG (spread).
Fragility Spread — Time Series
Narrative RG minus Core RG. Higher values indicate greater structural divergence in market valuations.
Gini Coefficient — Time Series
Distributional inequality of RG10 across all companies per quarter (0 = perfect equality, 1 = maximum concentration). Independent of quartile boundaries — captures the full distribution shape. Peak: Q1 2025 (0.539) · Latest: Q4 2025 (0.443).
What the Gini shows that Spread doesn't
2023 → 2024: top-quartile expansion, not broad inequality
Q4 2023 → Q4 2024: Spread jumped from 3.20 → 4.60 (+1.40), but Gini barely moved (0.486 → 0.496, +0.010). The quartile extremes widened dramatically while the overall distribution shape stayed nearly the same. Conclusion: the expensive tail grew away from the rest — the middle didn't shift.
2024 → 2025: broad-based compression across the whole distribution
Q4 2024 → Q1 2025: both Gini (0.496 → 0.376) and Spread (4.60 → 2.35) fell sharply together. When Gini and Spread move in parallel, the compression is structural — it affects the full distribution, not just the extremes. Consistent with either a genuine valuation reset or the 2025 market-cap caveat.
Neither of these dynamics is visible from Spread or Ratio alone. A stable Gini with a rising Spread is a specific structural signal: the market is not becoming more unequal overall — only the existing extremes are pulling further apart.
Core RG vs. Narrative RG Over Time
Fragility Spread Over Time (Narrative RG − Core RG)
Fragility Ratio Over Time (Narrative RG / Core RG)
Full Fragility Metrics by Period
| Period | Data | Core RG | Narrative RG | Spread | Spread Δ | Ratio | Ratio Δ | >3.0 share |
|---|---|---|---|---|---|---|---|---|
| FY 2023 ↑ peak | annual | 0.00 | 0.00 | 0.00 | — | 0.0× | — | % |
| FY 2024 ↑ peak | annual | 0.00 | 0.00 | 0.00 | +0.00 | 0.0× | +0.0× | % |
| Q1 2025 ↑ peak | quarterly | 0.00 | 0.00 | 0.00 | +0.00 | 0.0× | +0.0× | % |
| Q2 2025 ↑ peak | quarterly | 0.00 | 0.00 | 0.00 | +0.00 | 0.0× | +0.0× | % |
| Q3 2025 ↑ peak | quarterly | 0.00 | 0.00 | 0.00 | +0.00 | 0.0× | +0.0× | % |
| Q4 2025 ↑ peak | quarterly | 0.00 | 0.00 | 0.00 | +0.00 | 0.0× | +0.0× | % |
Transition Matrix: Q4 2023 → Q4 2025
Panel of 118 companies with valid RG10 in both periods. Rows = 2023 position, columns = 2025 position. Thresholds computed independently per period (quartile split). Diagonal = stable quartile position (71% of panel). Highlighted: extreme cross-boundary moves.
| 2023 ↓ / 2025 → | Core 2025 | Middle 2025 | Narrative 2025 |
|---|---|---|---|
| Core 2023 | 25 21% | 7 6% | — |
| Middle 2023 | 5 4% | 40 34% | 11 9% |
| Narrative 2023 | — | 11 9% | 19 16% |
RG positions are sticky
71% of the 118-company panel remained in the same quartile group between Q4 2023 and Q4 2025. Valuation structure, as captured by RG, tends to persist — a property that simple price-based multiples reset with every price move.
No direct Core ↔ Narrative crossings
Every company that changed extreme — from cheap to expensive or vice versa — passed through the middle quartiles first. Zero companies jumped directly between Core and Narrative. This suggests RG extreme positions are not easily or quickly reversed.
Core is more stable than Narrative
78% of Core companies stayed Core; only 63% of Narrative companies stayed Narrative. Narrative positions erode faster — consistent with the idea that high-RG valuations carry more reversion pressure than low-RG ones.
The middle acts as a one-way buffer
Movement between extremes runs through the middle, making the middle group a structural transition zone rather than a stable resting place. This is distinct from P/G, where re-ranking can occur with a single earnings revision.
How to read Core RG / Narrative RG Divergence
Rising spread or ratio
A widening gap between Narrative RG and Core RG means the most narrative-driven valuations are moving further from the fundamentals-anchored core. In this dataset, the fragility spread peaked in FY 2024, approximately 45% above the FY 2023 level.
Rapid divergence growth
Accelerating spread growth — as observed from FY 2023 to FY 2024 — may indicate increasing speculative concentration in the Narrative RG segment. This does not prove a crash or correction, but increases structural vulnerability if the divergence cannot be sustained by earnings growth.
Subsequent contraction
The fragility spread contracted sharply from its FY 2024 peak to the current level. Core RG rose slightly throughout. Narrative RG fell significantly from its 2024 peak — consistent with repricing of the most overvalued names, though the causal interpretation is unclear.
What this does not prove
This analysis does not establish that RG fragility predicted any market event. The dataset is small (31 balanced-panel companies), spans only three meaningful historical points, and uses approximate market cap data. No causal, predictive, or investment-relevant claim is made.
Panel limitation: Only 31 of 77 covered companies appear in all 6 target periods. The balanced panel overrepresents companies with consistently aligned fiscal-year reporting. The annual periods (FY 2023, FY 2024) and quarterly periods (2025) use structurally different market cap sources; this is a methodological break in the time series, not a continuous panel.
Sector Internal Fragility
How far apart are the cheap and expensive halves within each sector — current snapshot.
Sectors with ≥ 4 companies. n ≥ 8: quartile split; n < 8: median split. Sorted by spread descending.
Automotive — the most internally split sector
Traditional automakers (low RG, earnings-anchored) sit in the same sector as high-narrative EV companies. The within-sector spread of 4.07 is the widest in the panel, making Automotive more internally divergent than even Technology.
Semiconductors: growth premium concentrated in the top half
The sector spans from mature foundry-model companies (TSMC-type, lower RG) to pure-play AI infrastructure names trading at high multiples of smoothed earnings. Spread of 6.00.
Technology: smaller spread than expected
With the broadest company count, Technology shows a moderate spread of 2.51 — suggesting the label "Technology" covers a more homogeneous RG band than Automotive or Semiconductors.
RG Persistence
Which companies are structurally anchored in their RG group — and which rotate? Classified across all available periods (7 quarters max).
Persistently Narrative / Core = ≥ 70% of observed quarters in the top or bottom quartile respectively. Thresholds computed independently per period.
Persistently Narrative — 28 companies
Persistently Core — 28 companies
Middle-anchored / Rotators — 70 companies (n ≥ 3)
The Narrative cluster is structurally stable — and US-dominated
Every company in the persistently Narrative group has been in the top quartile in every single observed period. These are not momentum trades — they are structurally expensive by RG's smoothed-earnings logic. The group is almost entirely US-listed growth and quality names: semiconductors, payments, consumer staples, streaming. No European or Japanese company appears here.
The Core cluster is structurally stable — and geographically concentrated
Persistently Core companies are dominated by German automakers (BMW, Mercedes-Benz, Volkswagen, Porsche SE), Japanese industrials and banks (Toyota, Honda, Mitsubishi UFJ), and German financials (Deutsche Bank) and utilities (RWE). These names have been in the bottom quartile consistently — structural value by RG logic, or structural earnings weakness.
Alphabet and Meta sit in the middle — not with Nvidia
Despite being classified as Big Tech alongside Nvidia and AMD, Alphabet and Meta have never been in the top quartile across any observed period. Their smoothed earnings are high enough relative to their market cap to keep them out of the Narrative cluster. This is a structural distinction RG draws that a simple "tech sector" label does not.
Convergence to Fair Value (RG = 1)
RG = 1 is the instrument's theoretical anchor: market cap equals ten times smoothed earnings. Do companies actually move toward it over time — or drift further away?
Panel of 118 companies with valid RG10 in both Q4 2023 and Q4 2025. Converging = distance to RG 1.0 decreased by > 0.05; Diverging = increased by > 0.05.
Converging
68
58% of panel
Diverging
38
42% of panel
By starting group
Strongest convergence — approaching RG 1.0
Strongest divergence — moving away from RG 1.0
Convergence rate by sector (n ≥ 3)
Core companies converge faster than Narrative
70% of companies starting below RG 0.8 moved closer to fair value — likely via rising smoothed earnings, not falling prices. Only 57% of companies starting above RG 1.5 corrected toward 1.0. The expensive tail is stickier than the cheap tail, which is consistent with the fragility hypothesis: narrative valuations resist downward revision.
A soft internal validation
The majority of the panel (58%) moves in the direction RG theory predicts — toward the fair-value anchor. This does not prove predictive power, but it is consistent with the instrument's internal logic. The 42% diverging group — led by names like Tesla and Broadcom — represents the genuinely open question: will those correct, or has the smoothed-earnings baseline itself shifted?
Caveat: 2025 market cap bias
As with all 2025 observations: current market cap is used rather than end-of-quarter prices. Companies that report higher smoothed earnings in 2025 will mechanically show lower RG, appearing to converge even without a price correction.
Geographic Fragmentation
Is RG fragility a global phenomenon — or primarily an American one? Six regions are compared across S&P 500 (US), DAX 40 (DE), FTSE 100 sample (GB), CAC 40 sample (FR), SMI (CH), and Nikkei/TOPIX sample (JP).
Open panel — companies present per period. European annual reporters contribute to the period of their fiscal year-end; quarterly reporters appear in all six periods. Minimum n = 4 per region per period.
Median RG10 by Region
Latest Snapshot: Core vs Narrative per Region
Teal = Core quartile median · Orange = Narrative quartile median · Vertical mark = overall median.
US exceptionalism confirmed — but France and Switzerland challenge it
The US median RG (2.73) remains the highest among all six regions. Yet France (1.93) and Switzerland (2.08) both exceed Germany (0.94) and Japan (0.78), driven by luxury-goods and life-sciences heavyweights with structurally high narrative premiums. High RG is not an exclusively American phenomenon — it tracks sector composition as much as country.
Germany and the UK are the most conservatively valued large-cap markets
DE (0.94) and GB (1.84) show the lowest medians, consistent with value-heavy banking, energy, and industrials sectors dominating their indices. Both markets nonetheless show meaningful internal spread between Core and Narrative quartiles (DE spread: 2.00, GB spread: 2.83), confirming that polarisation exists across all markets.
RG fragility clusters by sector, not just by flag
Narrative-cluster companies (luxury, pharma, tech) elevate the FR and CH medians above those of the more diversified UK and German indices. This suggests that the geographic hierarchy is a secondary effect: the primary driver is whether a market is dominated by asset-light, story-driven sectors or by capital-intensive, cash-flow-anchored businesses.
Super-Narrative Cluster
The upper decile (top 10% by RG10 per period) is defined independently for each quarter. Are the same companies always there — or does the composition rotate?
7 periods analysed (Q4 2023, Q1 2024, Q4 2024, Q1 2025, Q2 2025, Q3 2025, Q4 2025). A company counts as a "fixture" if it appears in the upper decile in ≥5 of 7 periods.
Permanent Fixtures — upper decile in ≥5 / 7 periods
| Company | Sector | Country |
Periods in top 10% | Q4 2023 | Q1 2024 | Q4 2024 | Q1 2025 | Q2 2025 | Q3 2025 | Q4 2025 |
|---|---|---|---|---|---|---|---|---|---|---|
| AMD | Semiconductors | US | 5 / 7 | 7.84 | — | 5.24 | — | 5.02 | 6.80 | 5.77 |
| Eli Lilly | Healthcare | US | 5 / 7 | 7.03 | — | 7.09 | — | 3.40 | 3.70 | 4.06 |
Orange highlight = period in which this company was in the upper decile for that quarter.
Recurring Entries — upper decile in 3–4 periods
The super-narrative tier is structurally stable
AMD, Eli Lilly occupy the upper decile in 5 of 7 periods. This is not a market-phase rotation: the same companies persistently carry the highest narrative premium regardless of which quarter is measured. The overall Fragility Spread is therefore not a statistical artefact of random outliers — it reflects a stable structural tier.
All permanent fixtures are US companies
Every company in the permanent cluster (AMD, Eli Lilly) is incorporated in the US. No German or Japanese company appears in the upper decile across multiple periods. This reinforces the geographic fragmentation finding: extreme narrative pricing is not just more common in the US — it is concentrated in a small, persistent subset of US companies.
Implication for the Spread metric
Because the Narrative quartile is anchored by the same companies period after period, the Spread measures a persistent structural gap — not noise. Any compression of the Spread would require either a significant RG decline in the fixture companies (via price correction or earnings growth) or their replacement by companies from outside the current cluster.
RG Change Decomposition: Price vs. Earnings
For 115 companies in the balanced panel (Q4 2023 → Q4 2025): was the RG change driven by market cap movement or by earnings growth? RG = MC / (E × 10), so a falling RG can reflect either a price correction (MC down) or earnings improvement (E up) — or both.
"Earnings-led": RG fell and earnings grew faster than market cap. "Speculative expansion": RG rose because market cap outpaced earnings.
Speculative Expansion — MC outpaced earnings (64 companies)
| Company | RG Δ | MC | Earnings |
|---|---|---|---|
| TeslaUS | +10.26 | +130% | -74% |
| BroadcomUS | +6.62 | +346% | +53% |
| LonzaCH | +2.95 | +26% | -81% |
| ContinentalDE | +2.71 | +27% | -127% |
| KeringFR | +2.36 | -27% | -82% |
| BPGB | +1.69 | +8% | -99% |
| Nongfu SpringCN | +1.39 | +135% | +18% |
| Sino BiopharmaceuticalCN | +1.07 | +140% | +20% |
Earnings-Led Convergence — earnings outpaced MC (29 companies)
| Company | RG Δ | MC | Earnings |
|---|---|---|---|
| SafranFR | -7.08 | +77% | +561% |
| Rolls-RoyceGB | -3.97 | +302% | +632% |
| Eli LillyUS | -2.97 | +63% | +233% |
| AdidasDE | -2.86 | -14% | +399% |
| RELXGB | -2.78 | -21% | +17% |
| AstraZenecaGB | -2.67 | +40% | +121% |
| AMDUS | -2.07 | +41% | +268% |
| Merck & Co.US | -1.93 | -3% | +124% |
| Dassault SystemesFR | -1.80 | -51% | +21% |
| SikaCH | -1.43 | -37% | +3% |
| NetflixUS | -1.36 | +48% | +106% |
| CapgeminiFR | -0.98 | -34% | +2% |
| SymriseDE | -0.97 | -24% | +17% |
| SAPDE | -0.96 | +8% | +70% |
| AmazonUS | -0.82 | +54% | +432% |
| Li AutoCN | -0.82 | -46% | +-3% |
| Trip.comCN | -0.45 | +69% | +488% |
| NestleCH | -0.45 | -20% | +-3% |
| L'OrealFR | -0.41 | -10% | +5% |
| Partners GroupCH | -0.39 | -4% | +19% |
| MastercardUS | -0.35 | +21% | +32% |
| FreseniusDE | -0.31 | +85% | +212% |
| LVMHFR | -0.23 | -26% | +-20% |
| HermesFR | -0.22 | +6% | +19% |
| Air LiquideFR | -0.17 | +4% | +17% |
| HenkelDE | -0.15 | +10% | +57% |
| Budweiser APACCN | -0.14 | -31% | +-31% |
| Anta SportsCN | -0.10 | +19% | +32% |
| Sunny OpticalCN | -0.10 | +29% | +55% |
What drives convergence — and what doesn't
Where RG fell, it was driven by earnings growth, not price correction. No company in the earnings-led group saw a significant market-cap decline as the primary driver. This means the market has not repriced narrative-premium stocks downward — it simply got left behind by accelerating fundamentals in a minority of cases. The majority (56%) saw market caps outrun earnings further.
Dominant dynamic: speculative expansion (56%)
In 64 of 115 companies, market caps grew faster than smoothed earnings, pushing RG higher. Tesla is the extreme case: earnings fell 74% while market cap rose 130%, producing an RG of 13.27. Broadcom added 6.62 RG points despite genuine earnings growth of 53% — because market cap rose 346%.
Earnings-led convergence: real but limited (25%)
The 29 companies where RG fell show genuine fundamental improvement — Eli Lilly's smoothed earnings grew 233%, Amazon's 432%, AMD's 268%. This is positive from a fundamental standpoint, but it has not brought any of these companies close to RG = 1. The narrative premium persists; it is merely less extreme than in 2023.
No evidence of mean-reversion via price correction
Not a single high-RG company in the panel saw RG fall primarily because its market cap declined. The market has not priced out any narrative premium through a correction in the 2023–2025 window. If mean-reversion occurs, it will require either continued earnings growth (the earnings-led path) or a repricing event not yet visible in the data.
Macro vs. Micro: Index Level vs. Company Level
The CAPE-based macro RG (market-cap weighted, index level) and the bottom-up company median (equal-weighted) tell different stories about the same market. Both are useful — but the gap between them reveals where fragility is concentrated.
Macro RG source: Shiller CAPE data (S&P 500) and trailing P/E (DAX 40). Bottom-up: company-level medians from this dataset, Q4 2025 snapshot.
S&P 500
DAX 40
S&P 500 Historical Context
S&P 500 Macro RG10 — Annual (2000–present)
Macro–micro gap reveals where fragility concentrates
The S&P 500 macro RG (4.13) sits 1.40 points above the equal-weighted company median (2.73). The difference reflects market-cap weighting: Tesla, Broadcom, AMD — the permanent super-narrative fixtures — are also among the largest index constituents. A passive index investor's effective RG exposure is substantially higher than the median company in the index implies.
Approaching the 1999 peak — with a different composition
At 4.13, the S&P 500 macro RG stands at 93% of its December 1999 peak of 4.42, and 2.3× the 144-year long-run average of 1.78. In 1999 the concentration was in broad-market technology. Today the extreme valuations are even more concentrated: the same four companies recur in the top decile across all measured periods.
Geographic hierarchy holds at both levels
Macro: S&P 500 4.13 vs DAX 40 1.82 — ratio 2.3×. Bottom-up: US median 2.73 vs DE median 0.94 — ratio 2.9×. The different methodologies produce different absolute levels but the same structural ordering. US equities carry meaningfully higher valuation multiples at every level of analysis.
Sector vs. Country: What Drives the Reality Gap?
With 159 companies across 7 markets, we can decompose RG variation into a sector effect (same sector, different countries) and a country effect (same country, different sectors). Which signal is stronger?
Snapshot: most-recent available RG10 per company. One company per row in the decomposition.
R² measures how much of the cross-company RG variance is captured by knowing only the sector or only the country. Neither model uses both simultaneously.
Sector Median RG10 (all markets combined, n ≥ 3)
Cross-Tab: Median RG10 by Sector × Country
Cells with a single company show that company's value. Empty = no data. Heat: teal = low, orange = medium, red = high.
| Sector | US | DE | JP | GB | FR | CH | CN | All |
|---|---|---|---|---|---|---|---|---|
| Semiconductors | 8.47 | 4.47 | 2.65 | — | — | — | — | 4.47 |
| Industrials | — | 1.84 | 1.88 | 3.00 | 3.61 | 3.37 | — | 2.23 |
| Consumer Staples | 2.38 | 0.46 | — | 1.72 | 2.13 | 2.06 | 1.75 | 2.18 |
| Healthcare | 2.69 | 1.60 | 1.75 | 2.31 | 0.61 | 2.55 | 1.80 | 2.02 |
| Consumer Discretionary | 2.55 | 1.39 | 2.10 | 0.05 | 3.28 | 1.59 | 1.13 | 1.59 |
| Technology | 2.48 | 1.96 | 0.90 | 3.97 | 1.46 | — | 1.15 | 1.51 |
| Materials | — | 1.32 | 1.42 | 0.70 | 1.99 | 2.27 | — | 1.44 |
| Utilities | — | 1.21 | — | 1.15 | — | — | — | 1.15 |
| Energy | 1.24 | — | — | 1.44 | 0.76 | — | 0.12 | 0.75 |
| Financials | 0.93 | 0.72 | 0.75 | 0.60 | 0.53 | 1.27 | 0.21 | 0.69 |
| Automotive | 12.01 | 0.36 | 0.46 | — | — | — | 1.00 | 0.56 |
| Telecommunications | — | 0.85 | 0.83 | — | — | — | 0.39 | 0.53 |
| Country median | 2.55 | 1.19 | 1.38 | 1.28 | 1.86 | 2.07 | 0.91 | 1.94 |
Sector explains more variance than country (20% vs 8%)
Knowing only a company's sector accounts for 20% of the cross-company variation in RG10. Knowing only its country accounts for 8%. Both effects are real, but sector membership is the stronger signal. This explains why France and Switzerland rank above Germany in the geographic analysis — their indices are dominated by luxury goods and pharmaceuticals, two sectors with structurally elevated narrative premiums.
High-RG sectors are consistently high across borders
Semiconductors and Industrials sit at the top of the sector ranking regardless of the country of incorporation. Conversely, Automotive and Telecommunications cluster at the bottom in every market. The sector ceiling and floor are more stable than the country ceiling and floor.
Country adds a systematic level shift above the sector baseline
US companies in the same sector as their European or Japanese peers consistently command a higher RG. This residual country premium — visible in the cross-tab — represents the structural US narrative premium that cannot be explained by sector composition alone.
6. RG vs Simpler Metrics: Retrospective Grouping
Four valuation metrics measured at the 2023 historical anchor for 71 companies. Returns approximate price change from that date to current (approx. early 2026). Low group = companies in the bottom half by metric value; High group = top half. Quartile detail also shown.
Return = (current market cap − 2023 market cap) / 2023 market cap. Market cap approximated as historical closing price × current shares outstanding. 2023 anchor period: 2023-Q4 (n=45) with fallback to 2023-Q3/Q2/Q1.
Low vs High Group: Avg Approximate Return
| Metric | n | Low group avg | High group avg | Visual | Spread | ρ (return) |
|---|---|---|---|---|---|---|
| RG10 | 127 | +63% | 38% | | +25% | -0.28 |
| PG | 124 | +56% | 43% | | +12% | -0.19 |
| MTE | 102 | +67% | 40% | | +26% | -0.26 |
| EY | 127 | 43% | +57% | | -14% | +0.16 |
Quartile Breakdown
Assessment
RG10 and P/G produce nearly identical low/high splits on this sample (spread ~47–49%). Their rank correlation is 0.87 — they are measuring closely related quantities. M/TE shows a cleaner monotonic gradient. EY behaves as expected (high EY = cheap = better returns). Whether RG adds information beyond P/G cannot be determined from this window.
Illustrative cases
Selected observations from the retrospective analysis. Not representative — shown to ground the aggregate results in concrete examples.
| Company | RG10 | P/G | M/TE | ≈Return | Case type |
|---|---|---|---|---|---|
| Mitsubishi UFJ | 0.27 | 0.78 | 0.4 | +255% | Consistent with pattern |
| Deutsche Bank | 0.18 | 0.43 | 0.3 | +125% | Consistent with pattern |
| Toyota Motor | 0.34 | 0.84 | 0.6 | +91% | Consistent with pattern |
| Daiichi Sankyo | 3.70 | 9.20 | 6.2 | -35% | Consistent with pattern |
| Adidas | 4.53 | 11.51 | 7.5 | -23% | Consistent with pattern |
| Broadcom | 4.61 | 3.03 | — | +250% | Exception to pattern |
| Alphabet | 0.73 | 0.93 | — | +342% | Ambiguous |
| UnitedHealth | 2.27 | 2.42 | — | -43% | Ambiguous |
Coverage Composition: Substance vs. Earnings
RG's denominator is FB = TE + 10·Ḡ — tangible equity plus capitalized ten-year earnings. The headline RG hides the mix: two firms at the same RG are economically opposite if one is carried by substance and the other almost entirely by capitalized earnings.
Substance share s = TE / FB. Latest valid observation per company; n=159.
29 of 159 companies (18%) have negative tangible equity.
For these firms the conservative "substance floor" the metric rests on is not just absent — it is negative, so the fundamental base is carried entirely by the capitalized-earnings term. This is typically the footprint of sustained buybacks and capitalized intangibles, not weakness. For them RG is effectively a pure earnings multiple, and the most sensitive of all to the choice of N.
| Coca-Cola | RG 2.4 | s 4% |
| Safran | RG 3.6 | s 5% |
| Roche | RG 2.1 | s 6% |
| Qiagen | RG 1.6 | s 7% |
| E.ON | RG 1.7 | s 7% |
| Eli Lilly | RG 3.5 | s 7% |
| Apple | RG 3.1 | s 8% |
| ABB | RG 3.4 | s 10% |
| Continental | RG 3.6 | s 100% |
| Honda Motor | RG 0.5 | s 100% |
| Sony Group | RG 5.7 | s 100% |
| XPeng | RG 4.3 | s 100% |
| Baidu | RG 0.8 | s 76% |
| Lonza | RG 4.9 | s 76% |
| Longfor Group | RG 0.3 | s 73% |
| China Mengniu Dairy | RG 1.8 | s 73% |
Coverage % — the metric the core question actually asks
The paper's core question is literally "how far is market value still covered?" The direct answer is the reciprocal 1 / RG = FB / MC, bounded and intuitive: RG10 2.0 → 50% covered, RG10 4.0 → 25% covered, RG10 0.8 → 125% (over-covered). The median company here is 69% covered.
Parameter Fragility: N-Sensitivity per Firm
RG decreases monotonically in the capitalization factor N. The band between RG8 and RG12 measures how much a firm's reading depends on that assumption: elasticity e = (RG8 − RG12) / RG10.
Latest valid observation per company; n=159. Median e = 0.27.
| Vinci | RG 3.4 | e 1.38 |
| Sartorius | RG 5.0 | e 1.23 |
| RELX | RG 4.0 | e 0.80 |
| Compass Group | RG 0.1 | e 0.80 |
| Salesforce | RG 3.5 | e 0.77 |
| Siemens Healthineers | RG 2.7 | e 0.60 |
| Capgemini | RG 1.8 | e 0.59 |
| Unilever | RG 2.2 | e 0.58 |
| Continental | RG 3.6 | e 0.00 |
| Honda Motor | RG 0.5 | e 0.00 |
| Sony Group | RG 5.7 | e 0.00 |
| Volkswagen | RG 0.1 | e 0.00 |
| XPeng | RG 4.3 | e 0.00 |
| Lonza | RG 4.9 | e 0.10 |
| Longfor Group | RG 0.3 | e 0.10 |
| Baidu | RG 0.8 | e 0.11 |
Substance share predicts N-fragility almost perfectly
Across 159 companies, corr(s, e) = -0.99. The N-fragile names are exactly the earnings-backed and negative-TE firms from the section above. RG8/RG10/RG12 is therefore not three independent numbers but a single substance-share axis: the more a firm's coverage rests on capitalized earnings, the more its RG depends on the chosen N — a robust reading needs the substance share, not all three RG variants.
Earnings Quality: Dispersion within the Smoothing Window
The earnings component of FB is a smoothed mean Ḡ over the operational 8-quarter window. The dispersion of those quarters — coefficient of variation CV = stdev / |mean| — measures how reliable that mean is: a low CV is steady earning power; a high CV means Ḡ rests on volatile, cyclical, or one-off-laden quarters.
Latest valid observation per company; n=147. Median CV = 0.14. 8-quarter operational window (matches the site's approximation, not the paper's 10-year window).
| Meituan | RG 2.6 | CV 4.75 |
| BP | RG 2.1 | CV 3.87 |
| Baidu | RG 0.8 | CV 3.30 |
| Lonza | RG 4.9 | CV 2.52 |
| Porsche SE | RG 0.1 | CV 1.93 |
| SoftBank Group | RG 1.0 | CV 1.49 |
| BASF | RG 1.0 | CV 1.41 |
| Safran | RG 3.6 | CV 1.20 |
| China Telecom | RG 0.1 | CV 0.00 |
| Vinci | RG 3.4 | CV 0.00 |
| China Mobile | RG 0.5 | CV 0.00 |
| China Unicom | RG 0.4 | CV 0.00 |
| CITIC | RG 0.2 | CV 0.01 |
| Henkel | RG 0.5 | CV 0.01 |
| Hermes | RG 3.3 | CV 0.01 |
| Schneider Electric | RG 3.8 | CV 0.01 |
Double fragility: earnings-backed and volatile
The firms below sit below the median substance share and above the median earnings CV: their fundamental base is held up mainly by capitalized earnings, and those earnings are themselves the least stable. For them a high RG is the least reliable — the denominator rests on a shaky, volatile stream.
RG × Earnings-Trend Interaction
The trend code (++ … --) is reported alongside RG but never tested for whether it adds information. Here: forward market-cap return from a 2024 anchor, split by RG level (above/below median) and trend direction.
Anchor 2024; n=125. Average approximate return to the latest quarter.
| Trend ↑ (++/+) | Trend = | Trend ↓ (--/-) | |
|---|---|---|---|
| High RG (≥ median) | +12% n=41 | -7% n=5 | +20% n=17 |
| Low RG (< median) | +24% n=41 | +42% n=4 | +47% n=17 |
Within high-RG firms, an improving earnings trend is associated with a -8 pp difference in forward return versus a declining trend — a first, transparent test of whether the trend appendix carries independent information rather than decoration. (Illustrative; small per-cell n.)
7. What Historical RG Analysis Might Reveal
Market-wide valuation stretch
If median RG rises consistently over multiple years, it could suggest that market prices are moving further from fundamental bases — a pattern reminiscent of valuation-stretch indicators like the Shiller CAPE. With the current 4-quarter dataset this cannot be assessed.
Sector rotation signals
Differences in median RG across sectors may reflect varying market expectations for earnings growth, capital intensity, or risk. Persistent high-RG sectors could be candidates for closer scrutiny in a longer historical study.
Retrospective sorting analysis
In a sufficiently long dataset, one could group companies by their RG quartile at a historical date and observe subsequent price performance. This is the approach used in academic factor research. The current dataset is too small and too short for such an analysis to be meaningful.
Dispersion as a bubble indicator
Widening dispersion between high-RG and low-RG companies — or rapid upper-tail expansion — could serve as an exploratory signal of concentrated valuation stretch. This requires multi-year historical data not yet available in this dataset.
8. Historical Coverage Status
The current RG dataset covers only a short modern slice of market history. The two most important historical stress tests — the dot-com cycle and the global financial crisis — are outside the current observation window. This section documents the coverage gap, what partial data exists, and what each extension phase requires.
Current observation window: 2023–2026 only
Current observation window: 2023–2026 only. All fragility and retrospective analysis on this page is based on this narrow modern period. No conclusions about long-run RG behaviour or historical crisis dynamics can be drawn from this window.
Dataset Coverage Timeline (1995–2026)
Required Extension Phases
| Phase | Period | Status | Available | Missing | Next step |
|---|---|---|---|---|---|
| Dot-com | 1995–2003 | No data | Nothing | All fundamentals + prices | New source required (Compustat / WRDS) |
| GFC | 2004–2011 | Partial | fundamentals.db: 30 US tickers, earnings + equity from 2007 | Historical closing prices | Fetch prices via yfinance → compute RG from fundamentals.db |
| Extended modern | 2012–2022 | Partial | fundamentals.db: full 30-ticker coverage | Historical closing prices | Same as GFC — prices only |
| Current | 2023–2026 | Full | 77 companies, all indices, quarterly + annual | — | Active coverage |
An SEC XBRL fundamentals database (fundamentals.db) is already in place covering 30 US companies from 2007 to present with ~3,025 rows. This is the foundation for Phase 2 and Phase 3 extensions. The missing piece for all historical RG computation is historical market cap data, which requires fetching historical closing prices at each fiscal period-end.
What the historical stress tests would show
None of the above is a proven pattern. These are research hypotheses that require actual historical data to test. The dot-com and GFC periods represent the most important validation targets for the RG fragility framework.
9. Data Limitations
- – Coverage: 77 companies across three indices (S&P 500 top 30, Nikkei 225 top 19, DAX 40 top 28). This is not a complete index. Results do not generalise to index-level conclusions.
- – Earnings smoothing: G is approximated as the mean of the last 8 available quarterly net income figures, annualised. This is an operational simplification; the paper defines G more rigorously.
- – Tangible equity: TE may fall back to book equity when goodwill and intangibles are not separately available from the data source (yfinance). Affected observations are flagged teIsApprox = true.
- – CPI adjustment for US companies: Inflation adjustment uses FRED CPIAUCSL. Non-US companies use nominal earnings, which affects cross-index comparability.
- – Historical market cap: Annual historical observations use historical closing price × current shares outstanding. Share count changes are not reflected.
- – Historical tangible equity: Annual historical observations use the current TE snapshot (not historical TE). This introduces an approximation into all historical annual RG values.
- – No audited data: All values are derived from yfinance / Yahoo Finance public data. Figures may differ from audited financial statements.
- – No predictive validation: RG has not been validated as a predictive indicator. The relationship between RG values and future returns is unknown.
All values are illustrative approximations and are provided for research purposes only. Not investment advice.