Case study · US equities
Kinder Morgan
/ Williams
Two gas-infrastructure stocks, a statistical relationship and a deviation to examine. A frozen demonstration explaining a Z-score in the entry zone.
Historical snapshot as of
Analysis: PairScanner
- Correlation
- 0.85 Daily returns
- P-value
- 0.0276 Test threshold: 0.05
- Closing Z-score
- -2.38 Window: 60 sessions
- Coefficient β
- 0.7986 Log-price regression
Period studied : 2021-09-09 → 2026-09-09 · 1255 shared sessions
Why compare these two stocks
Kinder Morgan (KMI) and Williams (WMB) operate natural gas transportation infrastructure in the United States. Their shared sector motivates a comparison, without making their businesses identical or guaranteeing that their share prices will move together.
Compare the paths from the same starting point
Both series start at 100 on the first shared date. A level of 120 represents a 20% increase from that starting point, calculated from closing prices adjusted for dividends and splits. The chart compares changes, not dollar prices.
Daily return correlation is 0.85. It describes how day-to-day changes have moved together. It does not establish whether the gap between the two assets returns to a lasting equilibrium.
Test the stability of the relationship
PairScanner estimates β by regression, then constructs the spread S = ln(KMI) − β × ln(WMB). The Engle-Granger test uses log prices. Its null hypothesis is no cointegration; a p-value below 0.05 rejects that hypothesis at the selected level.
Here, p = 0.0276. The threshold is met; this ensures neither persistence of the relationship nor a successful trade.
How to read the hedge coefficient
β is 0.7986: it weights WMB’s log price in the spread. It is not directly a number of shares; translating it into quantities also requires prices and the capital allocated.
Locate the gap at the last close
The Z-score measures the spread’s distance from its rolling mean in standard deviations over 60 sessions. Dashed lines at ±2 are reference levels. Z can still be calculated when the cointegration test is inconclusive.
At the study date, Z = -2.38, beyond one of the ±2 reference levels. A large deviation does not validate a mean-reversion hypothesis on its own.
Investigate possible reasons for the spread
In a stock pair’s detail view, PairScanner automatically retrieves recent SEC filings and measures the number of articles recorded for each stock. This context helps investigate company-specific events behind a deviation; it does not establish its cause.
SEC forms (including 8-K and 10-Q) appear with their date and a link to the official document. Some filings also have a summary when available. Article counts come from the provider’s monitored feed, not the entire press.
Context captured on 2026-09-10. It may include information published after the close used for Z. No announcement is identified here as the definite cause of the spread.
KMI · Kinder Morgan
Article flow
13 articles recorded from 2026-09-08 up to this capture.
Provider reference: 4.5 articles per day on average over 28 days, excluding the recent window.
Recent SEC filings
WMB · Williams
Article flow
18 articles recorded from 2026-09-08 up to this capture.
Provider reference: 3.7 articles per day on average over 28 days, excluding the recent window.
Recent SEC filings
The recent window targets roughly 48 hours; its start is a calendar date on the provider’s side. Capped counts are shown with ≥. No press article headline or text is reproduced.
Examine the timeline of filings, any change in news activity, then read the official documents. More articles predict neither price direction nor a return to the mean.
Scope and limits of this reading
- Data
- Adjusted closing prices used by PairScanner. Shared dates only; missing, non-finite and non-positive observations are excluded. Last observation: 2026-09-09.
- Estimation
- β and the cointegration test use all 1255 observations in this study. Charts are descriptive and retrospective: β was not known in advance for each session shown.
- Out of sample
- Software criteria met. A separate β is estimated only on the first 70% (2021-09-09 → 2025-03-10), then frozen. The ADF test uses the spread over the following period (2025-03-11 → 2026-09-09): p = 0.0439, against a threshold of 0.05. Half-life is 48.22 sessions, against a limit of 60. It is estimated over the entire history with this frozen β, not just the test period. This single chronological check is not a profitability backtest.
- Multiple testing
- The displayed p-value belongs to this individual test. It is not a q-value adjusted across all scanner pairs. A p-value is not the probability of a profitable trade.
- Case selection
- The pair was selected after reviewing the latest available scan to illustrate two stocks with a validated relationship and a Z-score in the entry zone. The scan matrix’s five-year history is retained. This retrospective choice, separate from the pair of the day, is not a test of a strategy’s performance.
- Execution
- This demonstration simulates no order, profit or costs. Any potential transaction would require checking both companies’ earnings and announcements, liquidity, availability and cost of borrowing the shorted stock, financing and dividends. The relationship can still break down.
What this example helps you understand
Correlation describes daily changes, cointegration tests a relationship between price levels, and the Z-score locates a deviation. These three readings complement each other. This is a dated study: the application’s figures can change after subsequent closes.
This educational study is independent of the pair of the day, which is selected for its trading relevance.
Another result, the same method
MBB / SPMB complements this reading with two ETFs tracking the same benchmark. Compare the tests, spread and out-of-sample validation at a fixed date.
Read the MBB / SPMB study →Explore the scanner’s pairs
Find updated analyses and results in PairScanner.
Historical results do not determine future outcomes. This study is not an investment recommendation.