Markets and Macro Quarterly, October 2026

IntroductionWhat this analysis is, and what it is not

What it is

• A study of how 183 economic and market series move together: 45 daily market series (the S&P 500 and its sectors, interest rates, currencies, commodities, volatility and stock indexes abroad), 3 weekly series (jobless claims, the 30-year mortgage rate and financial conditions) and 135 monthly and quarterly economic series from the US and other large economies, from 1999 to 31 October 2026.
• It asks four questions: which series move together most and least; which relationships have changed, recently or since 2020; which series move first and give notice of another; and which readings are unusual today.
• The method was written down before any result was computed, and every finding is tested against what chance alone would produce, with tests that allow for the way financial data clusters in calm and stormy spells.
• Every relationship in it can be checked, and any pair of your own explored, in Gyre's free Covariance Calculator at gyreresearch.com/covariance.

What it is not

• Not investment advice, and not a recommendation to buy or sell anything.
• Not a test of a trading strategy: it measures relationships, not profits after costs. Testing whether an unusual gap between two stocks is worth betting on is the job of Pairs-Trade Analysis, in preparation.
• Not an explanation of causes: two series moving together does not mean one drives the other.
• Not a forecast: relationships change, and this issue shows several that did. A relationship that held for twenty years can stop.
• Not a model of the whole economy: it covers these series only. Section 5 sets out what the data cannot tell you.

Section 1Why covariance matters in finance

• Risk is a matrix, not a list. A portfolio's variance is the sum of every holding's variance and every pair's covariance. With 20 holdings there are 20 variances and 190 covariances: most of the risk is in the pairs.
• Diversification only works between assets that do not move together. Two assets with correlation 0.9 add little protection; a correlation near zero or below adds a lot.
• Hedges are covariances. A hedge ratio is a beta: the covariance of the position with the hedge divided by the hedge's variance.
• Relations change, and they change fastest when it matters. Correlations between risky assets tend to rise in sell-offs, just when diversification is needed. Some of that rise is mechanical (higher volatility alone raises a measured correlation); some is real.
• Macro data arrives late and is revised. A relation between a market and an economic release is only usable from the day the figure is published, and at the value first published.

1.1 How a lead works

• A lead is measured against the release, not the month described. Oil's change in January is set against the producer price index released in March, which describes February: a lag of 2 release months is a lead of 1 month of the period described.
• The usable time is to publication. From the end of the oil month to the release is 44 days at the median (331 releases since 1999): about 6 weeks.

Section 2How to use the calculator

Open the free calculator at gyreresearch.com/covariance: no sign-in, any two series, any frequency.

• Pick two series: a stock or ETF by ticker or name, or one of more than 850,000 FRED economic series.
• Pick a frequency (daily to annual) and a look-back. The menu offers only the look-backs both series can fill; security prices start 2023-12-01, FRED series reach back decades.
• The calculator measures each series the standard way by default: percent change for prices and quantities, change in level for rates and other series in percent.
• Read the result: the covariance (in the two series' units), the correlation (-1 to 1), R squared, and both betas, with their standard error when there are fewer than 30 observations, and notes on anything that limits the reading (a shortened window, series measured at different times of day, levels that trend).

2.1 The analyst: is the story in the data?

• Test a macro thesis before writing it. "Rising real yields hurt technology stocks": pick DFII10 and a technology stock or sector fund, weekly or monthly, 5 to 10 years. The correlation says whether the relation exists; the beta says how large it is; the window says whether it is recent or long-standing.
• Find what a company really moves with. A stock against oil, the dollar, the 10-year yield and credit spreads in turn: the strongest is its true macro driver, which is not always its sector label.
• Check that a relation is not two trends. Run it on changes (the default), never on levels: two rising series always look related as levels.
• Cite it. Every result names its data source; a pair, frequency and window can be shared as a link and reproduced by anyone.

2.2 The portfolio manager: what does the book really hold?

• Diversification check before adding a position. The correlation of the candidate with the portfolio's largest exposure (or with SPY): near 1 adds concentration, near 0 or below adds diversification.
• Hidden factor exposure. Each holding against the 10-year yield, the dollar, oil or credit spreads: several holdings with large betas to the same series are one bet, whatever their sectors.
• Stress view. The same pair over a calm and a volatile window (for example 2024 against 2020): correlations usually rise in sell-offs, so the diversification that shows in calm data is the most a book can count on, not the least.
• Benchmark fit. A fund or ETF held in the book against its benchmark (for example a sector fund against SPY): the beta is the market exposure it actually carries, the R squared how much of its movement the market explains.

2.3 The trader: what has changed, and how much to hedge

• Hedge ratio. The beta of the position on its hedge instrument, over a look-back that matches the holding period (1 to 3 months for a short-term trade); size the hedge as position value times beta.
• Relative-value pairs. Two related names (KO and PEP, XOM and CVX): the correlation says whether the pair is still a pair; the beta gives the ratio to trade them in.
• Regime check. The same pair over 1 month, 3 months and 1 year: a short-window reading far from the long one is the kind of aberration this paper tests for, and the first sign that a hedge or a pair has stopped working.
• Macro event read. A sector against the series behind the next release (payrolls, CPI, claims), monthly, to see how strongly the sector has moved with that figure.

Section 3The study: data and method

3.1 Data

• Markets, daily (45 series): the S&P 500 and its 11 sectors, each rebuilt cap-weighted from each day's index members and weights (1999 to now); US Treasury yields from 3 months to 30 years, the 10y-2y and 10y-3m curves, the 10-year real yield, breakeven inflation, the 5y5y forward inflation rate, the 10-year term premium, the Baa credit spread; VIX, oil and gold volatility, economic policy uncertainty; the broad dollar and 11 currencies; WTI, Brent, natural gas; the Nikkei 225, Bitcoin and Ether.
• Macro, monthly (108 series): for the US, euro area, Germany, France, Italy, the UK, Japan, Canada, China, India and Brazil, every indicator of growth, inflation, employment, confidence, rates, credit, trade and markets that FRED publishes monthly and current; global food, energy and metal prices.
• Quarterly, long history only (30 series): real GDP, fixed investment, house prices, US government debt to GDP.
• All economic data from FRED, only series it marks free to publish (Source: FRED, Federal Reserve Bank of St. Louis; each series' own source in Appendix A); sector returns calculated by Gyre Research.

3.2 Method (fixed before any result)

• Measurement: daily changes for markets; monthly changes for macro; release-dated, first-published values for every lead and lag test, each change taken within the release that first published it.
• Windows: two baselines (the pair's whole history; the last 12 months, 252 trading days) and three recent windows (6 months, 3 months, 1 month).
• Two correlations: Pearson and Spearman (rank); a finding counts only when both agree.
• Aberration: today's reading beyond the pair's own 1st or 99th percentile of the same measurement in its history; tested again within periods of similar volatility.
• Leads and lags: each series' own momentum removed first; a lead counts only if it passes a false-discovery test in 1999–2020 (or the pair's first common month to 2020) and is confirmed again in 2021–2026, years not used to find it.
• Discovery periods differ by pair: the monthly test starts at each pair's first common month, as pre-registered.
• Significance, honestly measured: market changes cluster in calm and stormy spells, and macro changes stay autocorrelated, so the ordinary correlation test finds too much. Every p-value here allows for both (a Newey-West test); a finding is also checked against a stricter multiple-testing rule valid under any dependence (Benjamini-Yekutieli), a bootstrap interval of its correlation, and, for three families, a family-wide check (Romano-Wolf). Section 4.9 shows what this changed.
• Chance: every result states how many findings chance alone would produce.
• Checked: 24 pairs equal the public calculator's figures and 6 pairs equal a hand calculation from FRED's own download (section 4.6).

Section 4Results

4.1 Strongest and weakest

A ranking, not a test: the 20 largest and the 20 closest to zero of 990 market pairs, on the last 252 trading days, Pearson and Spearman of the same sign.

4.2 Recent aberrations

Chance: 139 single flags against 118.8 from chance alone (5,940 tests × 2%). Strict (both baselines, at least two windows): 0.

Descriptive: the Consumer Staples sector against rates. 8 of the flags are Consumer Staples against rate series, every one below the pair's own 1st percentile: staples moved against rates more strongly than in 99% of their own history in these windows. Not strict, so not a finding.

For your consideration. No relation broke strictly from its own history, so hedges and diversification sized on the past year still hold on this evidence. The one coherent exception is Consumer Staples, which has recently moved against rising yields more strongly than in 99% of its history since 1999. Against the 30-year yield, a volatility-adjusted check (Forbes and Rigobon) reads the one-month reading as partly a change in the relation and partly the market's higher volatility, and the three-month reading as the market's higher volatility, not a change in the relation. The signal is weaker than the raw correlation suggests, but a defensive sleeve held for stability may still be carrying rate risk.

Are they tradeable? We don't know yet, and this issue doesn't claim it.

• A pair being unusual today says nothing about whether it will return to normal, or how fast.
• 139 flags against 119 expected by chance means most of them are probably noise; we cannot yet tell which flags are the real ones.
• Testing exactly this, “unusually wide, bet on a return to normal”, is the subject of a new Gyre analytic in preparation, Pairs-Trade Analysis (gyreresearch.com/pairs-trade): how often a gap closes, how long it takes, and whether that pays after costs against SPY.

4.3 Leads and lags

Daily: 148 leads

Chance: under no effect at all, the chance that this test finds even one lead is at most 0.25% (39,600 pair-lags); it found 148.

• Mostly measurement timing: 140 of 148 are a one-day lag between series measured at different times of day (a 4 pm US close moves the next day's noon exchange rate or the next Tokyo session).
• Same measurement time: 8 leads, all small: largest |r| 0.12 to 2020 (median 0.11), at most 0.21 in 2021–2026.

For your consideration. None of the daily leads is large enough to trade after costs. The one-day pattern across markets matters for hedging across time zones: a move at the US close is matched in Tokyo and in the New York noon exchange rates a session later, so a hedge checked the same day can look mismatched when it is not.

Monthly: macro releases and markets

Chance: under no effect at all, the chance that this test finds even one lead is at most 0.25%; it found 13.

(i) Construction: 9 leads into monthly averages

GS10 and FEDFUNDS are monthly averages of daily series. A daily move shows in the average partly in its own month and partly in the next, so any market series that moves with rates leads the average by one month. A reading of the results, not a test.

(ii) Energy: 2 leads

For your consideration. Oil gives some notice of the next consumer price print: its monthly change leads US CPI by two release months, and that lead held again after 2020. It is the only energy lead left once the test allows for clustered volatility and autocorrelation; energy stocks and producer prices no longer pass, and even oil-to-CPI does not survive the strictest family-wide check. A book exposed to inflation surprises can treat oil as a tendency worth watching ahead of the CPI release, not as a signal. This was tested against the published figures only, not against inflation-linked bonds or breakevens, where it may already be priced.

(iii) Others: 2 leads

Coincident (lag 0): 0 pairs. No macro release passes the test against the same month's market move.

For your consideration. No confirmed monthly lead points into US stocks: in this test, macro releases gave no advance notice of stock or sector returns. They belong in risk budgeting and scenario analysis, not in market timing.

Quarterly

Chance: at most 0.25% under no effect; found 0, not confirmed 66.

Detection limit: 2021–2026 holds 11–23 quarters per pair, so only large leads can be confirmed. A lead found to 2020 but not confirmed is reported as "not confirmed", never as found.

No quarterly lead passes both the test to 2020 and the confirmation in 2021–2026; the 66 found to 2020 but not confirmed are in Appendix D.

4.4 Changes over the last 12 months

Chance: 38 notable changes of 181 tracked relations (the 20 strongest and every daily lead, monthly and quarterly lead); chance alone gives 18.1. Notable: the 12-month change is beyond the relation's own 5th or 95th percentile of 12-month changes.

• The strongest relations held: 0 of the 20 strongest changed notably.
• The overnight link weakened: 16 of the notable changes are one-day leads from US markets into the next Tokyo session (9) or the Australian dollar (7); every one is weaker than 12 months ago (median +0.42 to +0.10).

For your consideration. Positions that rely on US moves carrying into the next Tokyo session or the Australian dollar (overnight hedges, relative-value pairs) have had a much weaker link over the past 12 months. Sizing them on longer history overstates the protection or the signal.

4.5 A post-run observation

4.6 Validation

24 of 24 pairs pass: the study's correlation equals the public calculator's to within 2e−12 (the bar is 1e−9); 6 pairs also equal a hand calculation from FRED's own download (largest difference 4e−14). Monthly changes, 2010-01 to 2025-12, lag 0.

4.7 What changed after 2020

When the turn came: this section compares 1999–2020 with 2021–2026, a split fixed before the data were seen. A break test that lets the data choose the dates (Bai and Perron) puts the stock-yield turn at 1 April 2022 and the yield-dollar turn at 30 March 2022: both came when the Fed began raising rates in 2022, not at the turn of 2021.

Chance: under no change at all, the chance that this test finds even one change is at most 0.25% (102,773 tests); it found 400. A change counts when the 1999–2020 and 2021–2026 correlations differ beyond the false-discovery bar and the rank correlations agree.

Significance is not size: with about 68 months since 2021, no change in a monthly relation passes the test once its errors allow for clustered volatility and autocorrelation (section 3.2); every change below is between daily market series.

Stocks and bond yields: the old relation is gone

• The headline change: the S&P 500's correlation with the 10-year Treasury yield went from +0.36 (1999–2020) to −0.10 (2021–2026); Real Estate from +0.19 to −0.34. The change passes every test, but the S&P 500's value since 2021 is close to zero (95% interval −0.21 to +0.01): before 2021 stocks and yields moved together, so Treasuries offset stock moves; since 2021 they are roughly unrelated. Real Estate now moves clearly against yields.
• It is broad: 19 of the 20 largest market changes are a stock sector or the index against a rate.

For your consideration. The core assumption of a balanced book, that Treasuries rise when stocks fall, has not held since the Fed began raising rates in 2022 (the data date the turn to 1 April 2022): the S&P 500's correlation with the 10-year yield fell from clearly positive to about zero, so Treasuries have stopped offsetting stock moves. Diversification sized on correlations from before 2022 is overstated; duration and equity risk should be measured together, and other diversifiers weighed against the current relation, not the long history.

The 10-year yield and the dollar

The 10-year yield and the broad dollar index went from −0.08 to +0.31: before 2021 unrelated, since then rising together. 9 rate-dollar pairs changed.

For your consideration. Rising US yields have come with a stronger dollar since 2021, so long US duration and unhedged foreign assets now tend to lose at the same time. For a US-based investor they are no longer independent bets; currency hedging decisions and duration decisions should be taken together.

Leads that changed

No lead changed between 1999–2020 and 2021–2026: of 39,600 daily and 179,820 monthly lead tests, none passes once the test allows for clustered volatility and autocorrelation.

4.8 New since 2021

Chance: under no effect at all, the chance that this test finds even one relation is at most 0.25% (89,488 tests); it found 95: 94 relations and 1 lead. Found in 2021–2023, confirmed in 2024–2026, and absent (or of the other sign) in 1999–2020.

New relations: 94

88 among daily market pairs, 6 monthly. Most are rates against stocks, the dollar or currencies: the same shift as section 4.7, seen from the other side.

Mortgage rates and Real Estate stocks: −0.11 before 2021, −0.62 in 2021–23, −0.51 since 2024 (monthly). It is not counted among the new relations: with three years of monthly data, the 2021–23 reading (p = 0.014) does not clear the family-wide bar once the test allows for autocorrelation; the reading since 2024 is clearly negative (p = 0.006).

For your consideration. Real-estate stocks now trade largely as a rate position (mortgage rate against Real Estate −0.51 since 2024, −0.11 before 2021). REIT holdings belong in a book's interest-rate exposure, and their hedge ratio should come from the post-2021 relation, not the longer history.

New leads: 1

1 monthly, on short samples (n 17–18); the largest |r| is 0.71. 36 leads already found to 2020 were found again.

Confirmation going forward

600 candidates were named on data to 2026-10-31 (158 daily market pairs; 282 monthly pairs; 125 daily leads; 35 monthly leads). Each month they are tested again on the data after that date only: a candidate is confirmed when the new data give the same sign, dropped when they give the opposite sign. Nothing is chosen again after the first naming.

4.9 What the stricter test changed

The same data and the same correlations, judged twice: first with the ordinary test, which assumes every day or month is independent and equally calm, then with tests that allow for clustered volatility and autocorrelation. Of 1,956 findings the ordinary test reported, 1,280 no longer pass. The other way, 29 results pass only under the stricter test (1 lead, 8 changes after 2020, 19 new relations, 1 new lead); none of them was reported in the earlier draft.

What still holds: the stock-yield and rate-dollar sign flips since 2021, the overnight links into Tokyo and the Australian dollar, the absence of any macro lead into US stocks, oil's lead over consumer prices. What does not: most monthly leads, every quarterly lead, every change in a monthly relation or a lead after 2020, and most energy leads.

Section 5What the data cannot tell you

• Not investment advice: the notes headed "For your consideration" describe measured relations and what they imply for risk; no trade was tested, and nothing in this paper is a recommendation to buy or sell.
• Gaps: no PMI (proprietary for every country); no current monthly CPI for the UK, Japan, Canada, China, India or Brazil; no monthly unemployment for China, India, Brazil or the euro area; no German total production; no services trade, capital flows, current account, deficit or productivity series that are monthly and current. Italy and UK wages are published only as year-on-year growth, which the method excludes.
• Sector history is rebuilt: each company carries its current sector label back in time; Real Estate was part of Financials until 2016 and Communication Services was formed in 2018. In 1999 8.0% of the index weight had no sector label (3.3% in 2005, 2.0% in 2010, 0.1% in 2020).
• Two price histories are joined to reach back to 1999.
• Measurement times differ: stocks close at 4 pm New York, Treasury yields are afternoon quotes, the Federal Reserve's exchange rates are noon New York, Brent is London, the Nikkei is Tokyo, crypto trades around the clock; pairs across these are measured on two-day changes.
• Exchange rates are published weekly, so their latest week lags the other series.
• Model estimates, not prices: the term premium and the policy uncertainty index.
• Revisions: correlations use today's revised values; leads and lags use the values first published.
• First-published values start at different dates: from 1927 to 2023 by series (Appendix B). A lead test can only start there.
• Missing changes: WTI closed below zero on 2020-04-20, so its 2 daily changes touching that day are missing; Brazil's share price index rounds to zero in 1980–1988, so 105 monthly changes there are missing.
• Indexes centred on zero: CFNAI (53.45% of its values since 1999 at or below zero) and NFCI (90.84% of its values since 1999 at or below zero) are measured as change in level, not percent change.
• Duplicate series kept once: the French and Italian 3-month interbank rates equal the German one since 1999; it is kept once, as the euro area 3-month interbank rate.
• Readings: the labels construction and timing are readings of the results, not tests.
• Corrected: a first run's monthly and quarterly lead tests mixed index bases across rebasings; it was corrected before publication.
• First prints left out: 3 first-published values that FRED corrected in its next release (BRABCCICP02STSAM 2018-10; CSCICP02BRM460S 2019-06; XTEXVA01CNM667S 2014-10) are left out of the lead tests.
• Correlation is not causation, and a past relation is not a forecast.

AppendixA. The series

Sources

Source: FRED, Federal Reserve Bank of St. Louis. Each FRED series' original source, as FRED lists it; † = FRED's terms ask for this source to be cited.

AppendixB. First-published values: coverage

The first release FRED holds for each monthly and quarterly series (its vintage history): a lead test on first-published values starts here.

AppendixC. Method reference

• Pre-registration: analytics/backtest_methodology.md section 15 in Gyre Research's repository, written and committed before any result.
• Commits: each code below identifies one dated entry in Gyre's version history (a “commit”) that cannot be changed afterwards. Together they show that each part of the method was written down before the results it governs were computed; we can show any entry on request.
  • 9208deda0: the study plan itself (section 15): which series, which tests, and what counts as a finding.
  • 4d031480d: corrections to the plan before the first run (15.9): how the data reaches the study, identical series counted once, leads tested in both directions.
  • 2c385d774: leads of up to six quarters, and the test on quarterly data (15.9.8).
  • a9fa03425: how values at or below zero are handled, where a percent change has no meaning (15.9.9).
  • 95d31f206: the count of chance findings measured from 1999, the study's start (15.9.10).
  • 0a4c45838: the comparison of before and after 2020, and what is new since 2021 (15.10).
  • ecadeb316: changes within a release, values revised after their first publication (15.11, method version 2).
  • ad39bca4a and e7ec5e5ea: the named first-published values left out (15.11).
  • 86d0ee586 and 26ea63e69: the stricter significance test this issue uses throughout, and how it is computed (15.13, 15.14, method version 3).
  • 66d9baaf5: the check that separates a real change in a relation from a more volatile market, used for Consumer Staples (15.16).
  • 7889563c8: the break test that dates the 2022 turns (15.18).
• Implementation readings: analytics/macro_correlation/macro_correlation.md section 3, written before any result.
• This paper's data: study run 781173, the record of this computation in Gyre's run log (store run 12, method version 3, data to 2026-10-31); validation run 770045, the run that checked the study's values against the data providers' own downloads (section 4.6).

AppendixD. Full result lists

Every aberration flag

Quarterly leads not confirmed

Every new relation since 2021

Every notable 12-month change

This document is published by Gyre Holdings LLC d/b/a Gyre Research for informational purposes only and does not constitute investment advice or a solicitation to buy or sell any security. Readers should consult a qualified financial professional before making any investment decision. It is licensed under CC BY 4.0: you may share and adapt it with attribution to Gyre Research.

Contact: team@gyreresearch.com