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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
Two screens disagreeDefine the object
quote identitybasketcausal factor

Reciprocal 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

IdentitySame pair, reciprocal quoteBasketWeighted bilateral ratesFactorEmpirical shared shock

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.

Data acceptance rule

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.

ObjectWhat it measuresUseCircularity risk
USD/MXN spotOne bilateral price, pesos per dollarQuote-aligned comparison with MXN/USD and 6M basisExact reciprocal spot is not independent confirmation
6MDated MXN/USD futures priceTradable futures observation with roll and basis controlsCannot be treated as undated spot
Fed broad dollar indexTrade-weighted basket of multiple bilateral ratesBroad U.S.-dollar contextIncludes MXN, so some co-movement is mechanical
Fed AFE dollar indexDollar basket against advanced foreign economiesOne official control that excludes the pesoStill a basket with its own composition and shocks
Research factor excluding MXNPredeclared combination of other dollar pairsTest a common-dollar component without direct peso inputAnalyst-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.

Federal Reserve path shock

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.

U.S. growth shock

Stronger U.S. demand can support USD through rates while also supporting Mexican exports. The financial and trade channels can offset.

Global funding/liquidity shock

Demand for dollar liquidity and deleveraging can lift the dollar across markets while increasing volatility and reducing carry exposure.

Risk-aversion shock

Portfolio reduction can favor USD, but the outcome depends on shock location, existing positions, funding, and policy response.

Mexico-specific shock

Fiscal, political, inflation, policy, or trade news can weaken MXN while a broad dollar basket stays quiet. Calling this “USD strength” hides the source.

Other-country shock

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.

1

Define the dollar shock

Policy, growth, funding, or risk—with an official event or predeclared market measure and timestamp.

2

Exclude MXN from the control

Use an official basket that excludes MXN or a frozen research factor built only from other currencies.

3

Add relative rates

Compare Mexican and U.S. policy-sensitive rates at matched horizons to distinguish rate transmission from a generic label.

4

Check Mexico-specific rivals

Control for Banxico, inflation, fiscal, trade, political, and local-liquidity events in the same window.

5

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 choiceRequired declarationRejection rule
6M outcomeDated contract or documented continuous series, quote direction, return horizon, roll treatmentReject if contract mapping or timestamp lineage fails
Dollar inputOfficial index or frozen factor, constituent universe, weights, rebalance dates, MXN exclusionReject as circular if MXN contributes directly and is not removed
Event/sampling clockTimezone, release time, bar construction, holidays, missing data, no look-aheadReject windows contaminated by unhandled asynchronous closes
ControlsMatched relative rates, Banxico events, Mexico data/fiscal/trade news, global riskReject attribution if a declared rival explains the window
Lead/lag gridFinite horizons chosen before results and corrected for multiple testingReject a “best lag” discovered across an unbounded search
ValidationPoint-in-time vintages, stable transformations, robustness, holdout, costsReject if sign, magnitude, or utility fails out of sample
Correlation is not a transmission estimate

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 divergencePlausible explanationWhat to check
Broad USD up, 6M also upMXN-specific strength outweighs other basket movesBanxico-relative rates, trade/fiscal news, basket constituents, timestamps
Broad USD flat, 6M downMexico-specific weakness or offsetting moves elsewhere in the basketLocal event record, other MXN crosses, rates, liquidity
USD/MXN and 6M appear to rise togetherClock mismatch, stale quote, wrong contract, basis jump, or label errorReciprocal conversion, bid/ask, timestamps, expiry and roll
AFE dollar index moves, 6M does notAdvanced-economy shock lacks a material Mexico channelEM currencies, relative rates, U.S. event type, Mexico rivals
Relationship changes by regimeDifferent policy, risk, funding, trade, or volatility channel dominatesPredeclared 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.

Quote normalized?

USD/MXN, MXN/USD, and 6M direction are explicit; timestamp and bid/ask conventions are aligned.

Contract controlled?

The active dated 6M contract, roll state, basis, and missing/stale observations are verified.

Dollar object defined?

The index or factor name, methodology, constituents, weights, and vintage are recorded.

MXN excluded?

The independent confirmation measure does not directly contain peso returns, or the peso component is removed by a frozen method.

Shock identified?

An official event or predeclared policy, growth, funding, or risk variable supplies the mechanism.

Relative rates checked?

Mexican and U.S. observations use comparable horizons and timestamps, with risk-premium alternatives considered.

Rivals tested?

Banxico, fiscal, trade, political, global-risk, liquidity, and roll explanations are audited.

Application validated?

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

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.