Quote algebra · dollar baskets · non-circular testing
USD Strength and 6M: Identity, Common Factor, and Test
One screen shows 6M falling while a broad U.S.-dollar index barely changes. Another day the index rises and 6M falls with it. Both are possible because “the dollar” can mean a reciprocal bilateral quote, a weighted currency basket, or a shared U.S. shock. Those are different objects and require different evidence.
- Identity
- MXN/USD = 1 ÷ USD/MXN
- Basket
- Weighted currencies
- Factor
- Shared dollar shock
- Test
- MXN excluded from control
quote identity≠basket≠causal factorReciprocal math is exact for aligned spot quotes. A basket is a constructed measure. A common-dollar factor is an empirical hypothesis that needs controls.
Normalize firstTest second
The non-negotiable first step
Separate the Reciprocal Spot Identity From the Dated Futures Price
Established fact: the Federal Reserve's H.10 Mexican peso series is stated in Mexican pesos per U.S. dollar. CME's 6M contract is quoted in U.S. dollars per Mexican peso. They face opposite directions.
Aligned spot algebra
MXN/USD = 1 ÷ (USD/MXN)
If USD/MXN rises, the reciprocal MXN/USD falls. That is an identity for simultaneous quotes of the same underlying spot rate, before bid/ask and data-source differences. It is not evidence that a separate dollar variable caused the move.
- USD/MXN up
- USD stronger
- MXN/USD down
- MXN weaker
- 6M up
- MXN stronger
- Requirement
- Aligned timestamp
Mathematical identity
Same spot pair, inverted
Using USD/MXN to “confirm” an aligned reciprocal MXN/USD series adds no independent information. It is the same bilateral price expressed in reverse.
Dated futures relationship
6M is not exactly reciprocal spot
6M has a delivery month and can differ from spot through expected financing, basis, liquidity, and contract lifecycle. The directional quote convention still matters, but equality to reciprocal spot should not be imposed.
If the quote convention, timezone, timestamp, contract month, or roll treatment is unknown, stop. Do not repair an apparently reversed correlation by multiplying returns by minus one after seeing results. Use the 6M data-quality guide and the canonical 6M contract guide.
“USD index” is not one universal asset
A Dollar Basket Can Move Differently From USD/MXN
Established methodology: the Federal Reserve explains that its broad dollar index is a geometrically weighted combination of bilateral dollar rates for important U.S. trading partners, with trade-based weights. The official H.10 index page distinguishes broad, advanced-foreign-economy, and emerging-market-economy measures and notes that weights can be revised.
| Object | What it measures | Use | Circularity risk |
|---|---|---|---|
| USD/MXN spot | One bilateral price, pesos per dollar | Quote-aligned comparison with MXN/USD and 6M basis | Exact reciprocal spot is not independent confirmation |
| 6M | Dated MXN/USD futures price | Tradable futures observation with roll and basis controls | Cannot be treated as undated spot |
| Fed broad dollar index | Trade-weighted basket of multiple bilateral rates | Broad U.S.-dollar context | Includes MXN, so some co-movement is mechanical |
| Fed AFE dollar index | Dollar basket against advanced foreign economies | One official control that excludes the peso | Still a basket with its own composition and shocks |
| Research factor excluding MXN | Predeclared combination of other dollar pairs | Test a common-dollar component without direct peso input | Analyst-constructed; weights and universe can overfit |
Mechanism: the broad index can strengthen because the dollar rises against several other currencies even if the peso is stable or stronger. It can also appear closely related to 6M partly because MXN contributes to the index. Therefore, basket disagreement is not an error, and basket agreement is not automatically independent proof.
From co-movement to causal hypothesis
Name the Shared Shock That Could Strengthen USD
“USD strength” is a description until it identifies an information event and transmission channel. Several shocks can make the dollar rise broadly, but they need not have the same effect on Mexico, relative rates, risk appetite, or 6M basis.
U.S. data or FOMC communication can raise expected U.S. rates relative to Mexican rates. Hypothesis: that relative repricing may weigh on MXN and 6M, all else equal.
Stronger U.S. demand can support USD through rates while also supporting Mexican exports. The financial and trade channels can offset.
Demand for dollar liquidity and deleveraging can lift the dollar across markets while increasing volatility and reducing carry exposure.
Portfolio reduction can favor USD, but the outcome depends on shock location, existing positions, funding, and policy response.
Fiscal, political, inflation, policy, or trade news can weaken MXN while a broad dollar basket stays quiet. Calling this “USD strength” hides the source.
A large move in another basket constituent can move a dollar index without new information about Mexico. 6M need not follow.
Established U.S. event record: the Federal Reserve publishes FOMC statements, minutes, and projections and defined U.S. interest-rate series in H.15. Those documents establish the policy and data observations. Attribution of a 6M move to a particular dollar channel remains a testable inference.
Independent confirmation
Build a Control Set That Does Not Repackage MXN
The control must add information beyond the dependent variable. A reciprocal spot pair, a basket containing MXN, and a futures series derived from the same price feed can create impressive but circular confirmation.
Define the dollar shock
Policy, growth, funding, or risk—with an official event or predeclared market measure and timestamp.
Exclude MXN from the control
Use an official basket that excludes MXN or a frozen research factor built only from other currencies.
Add relative rates
Compare Mexican and U.S. policy-sensitive rates at matched horizons to distinguish rate transmission from a generic label.
Check Mexico-specific rivals
Control for Banxico, inflation, fiscal, trade, political, and local-liquidity events in the same window.
Confirm in executable 6M
Use the correct contract, roll state, spread, depth, and transaction-cost assumptions.
Permissible inference
Evidence is consistent with a common-dollar shock
An MXN-excluded dollar factor, matched U.S.-relative-rate move, other dollar pairs, and 6M align after a declared U.S. event while Mexico-specific rivals remain quiet.
Prohibited shortcut
The dollar index confirms 6M
The named index contains MXN, its composition is not checked, timestamps differ, and no relative-rate or event evidence is supplied.
Empirical boundary
Design the Test Before Looking for Leads and Lags
Hypothesis example: after a predeclared U.S. policy surprise, an MXN-excluded common-dollar factor and the U.S.–Mexico relative-rate change explain part of the quote-normalized 6M return over a specified event window. This page does not report that test or a result.
| Design choice | Required declaration | Rejection rule |
|---|---|---|
| 6M outcome | Dated contract or documented continuous series, quote direction, return horizon, roll treatment | Reject if contract mapping or timestamp lineage fails |
| Dollar input | Official index or frozen factor, constituent universe, weights, rebalance dates, MXN exclusion | Reject as circular if MXN contributes directly and is not removed |
| Event/sampling clock | Timezone, release time, bar construction, holidays, missing data, no look-ahead | Reject windows contaminated by unhandled asynchronous closes |
| Controls | Matched relative rates, Banxico events, Mexico data/fiscal/trade news, global risk | Reject attribution if a declared rival explains the window |
| Lead/lag grid | Finite horizons chosen before results and corrected for multiple testing | Reject a “best lag” discovered across an unbounded search |
| Validation | Point-in-time vintages, stable transformations, robustness, holdout, costs | Reject if sign, magnitude, or utility fails out of sample |
Contemporaneous returns can co-move because both react to the same news. Levels can trend or contain unit roots. A basket can embed the peso. A valid test needs returns or another justified transformation, synchronized clocks, a causal event or identification strategy, robust errors, and falsification. Route the full research pipeline to the 6M backtesting guide.
When the relationship breaks
Treat Divergence as Information, Not a Broken Rule
The dollar is one side of 6M, but a broad index and a bilateral futures contract need not move in lockstep. A divergence should trigger a source and mechanism audit.
| Observed divergence | Plausible explanation | What to check |
|---|---|---|
| Broad USD up, 6M also up | MXN-specific strength outweighs other basket moves | Banxico-relative rates, trade/fiscal news, basket constituents, timestamps |
| Broad USD flat, 6M down | Mexico-specific weakness or offsetting moves elsewhere in the basket | Local event record, other MXN crosses, rates, liquidity |
| USD/MXN and 6M appear to rise together | Clock mismatch, stale quote, wrong contract, basis jump, or label error | Reciprocal conversion, bid/ask, timestamps, expiry and roll |
| AFE dollar index moves, 6M does not | Advanced-economy shock lacks a material Mexico channel | EM currencies, relative rates, U.S. event type, Mexico rivals |
| Relationship changes by regime | Different policy, risk, funding, trade, or volatility channel dominates | Predeclared regime definition and out-of-sample stability |
Non-circular close
Reject Circular Signals Before Asking Whether USD Confirms 6M
Every “yes” is required for a common-dollar confirmation claim. A “no” does not imply the opposite direction; it means the proposed evidence is insufficient.
USD/MXN, MXN/USD, and 6M direction are explicit; timestamp and bid/ask conventions are aligned.
The active dated 6M contract, roll state, basis, and missing/stale observations are verified.
The index or factor name, methodology, constituents, weights, and vintage are recorded.
The independent confirmation measure does not directly contain peso returns, or the peso component is removed by a frozen method.
An official event or predeclared policy, growth, funding, or risk variable supplies the mechanism.
Mexican and U.S. observations use comparable horizons and timestamps, with risk-premium alternatives considered.
Banxico, fiscal, trade, political, global-risk, liquidity, and roll explanations are audited.
Lead/lag choice, multiple testing, holdout, transaction costs, and failure cases are predeclared and survive.
Research status: this page establishes quote algebra, measurement differences, and a testing framework. It reports no correlation, factor loading, lead/lag, directional hit rate, or trading performance. Until a non-circular, point-in-time study passes the checklist, “USD strength predicts 6M” remains unvalidated.
Sources, methods and editorial disclosure — reviewed August 13, 2026
- CME Group FX Product Guide and CME FX Link product conventions for the 6M USD-per-MXN quotation and the distinction from OTC USD/MXN convention.
- Federal Reserve H.10 historical Mexican peso rates for the official pesos-per-dollar series definition.
- Federal Reserve H.10 dollar indexes for official broad, advanced-economy, and emerging-market measures and weight-revision notice.
- Federal Reserve: methodology for the revised dollar indexes for geometric aggregation, trade-based weighting, and basket construction.
- Federal Reserve FOMC meeting materials and H.15 Selected Interest Rates for official U.S. event and rate evidence.
- Federal Reserve research: The Dollar Channel of Monetary Policy Transmission for an institutionally published research treatment of dollar transmission; its findings are not presented here as a 6M result.
Sources and methods were reviewed August 13, 2026. Dollar-index weights and series can be revised, so preserve the vintage used in any study. This article separates established quote and index facts from mechanisms, hypotheses, inferences, and possible applications.