Case study · US bond ETFs
MBB
/ SPMB
Two ETFs, one benchmark. This example starts with an identifiable economic relationship, then examines it using PairScanner’s statistical tests.
Historical snapshot as of
Analysis: PairScanner
- Correlation
- 0.98 Daily returns
- P-value
- 0.0082 Test threshold: 0.05
- Closing Z-score
- -0.15 Window: 60 sessions
- Coefficient β
- 0.9950 Log-price regression
Period studied : 2021-07-27 → 2026-09-08 · 1284 shared sessions
Why these two ETFs are related
MBB (iShares MBS ETF) and SPMB (State Street SPDR Portfolio Mortgage Backed Bond ETF) track the Bloomberg U.S. MBS Index, an index of U.S. agency mortgage-backed securities. This shared benchmark motivates the comparison; it does not, by itself, prove cointegration.
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 0.98. 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(MBB) − β × ln(SPMB). 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 = 0.0082. The threshold is met; this ensures neither persistence of the relationship nor a successful trade.
How to read the hedge coefficient
β is 0.9950: it weights SPMB’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 = -0.15, inside the ±2 reference levels. It describes the gap at that close; it does not validate the relationship on its own.
The relationship passes the checks, but the ±2 deviation threshold is not reached at this close: a validated relationship does not mean an immediate entry.
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: 2026-09-08.
- Estimation
- β and the cointegration test use all 1284 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% (2021-07-27 → 2025-02-21), then frozen. The ADF test uses the spread over the following period (2025-02-24 → 2026-09-08): p = 2.13e-08, against a threshold of 0.05. Half-life is 1.82 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
- This pair was selected after reviewing historical results to illustrate a positive case, without changing thresholds or the period. This retrospective choice is not evidence of a strategy’s out-of-sample performance.
- Execution
- Closely tracking ETFs can leave deviations too small to cover bid-ask spreads, commissions, financing and borrowing the shorted asset. Costs, liquidity and distributions are not simulated here. A statistical relationship alone therefore does not make a trade attractive.
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
Coca-Cola / PepsiCo shows the other case: two familiar names and correlated returns, without cointegration established over the period studied.
Read the Coca-Cola / PepsiCo study →Also explore: KMI / WMB, an entry-zone Z demonstration →
Explore the scanner’s pairs
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Historical results do not determine future outcomes. This study is not an investment recommendation.