Covariance Calculator: daily commentary archive

12 trading days, October 7, 2026 to October 22, 2026, newest first. Each is the commentary published with the page that day. This analysis was created with the assistance of large language model technology. Each describes that day's results; none is a forecast or investment advice.

October 2026

October 22, 2026

October 22, 2026: SPY/QQQ stays the tightest pair at 0.93 as most correlations barely move from the prior day

On this page's October 22, 2026 table, built from daily changes between October 22, 2025 and October 21, 2026, SPY (SPDR S&P 500 ETF Trust) and QQQ (Invesco QQQ Trust Series 1) again show the highest correlation, at 0.93. SPY against VIXCLS (CBOE Volatility Index: VIX) remains the strongest inverse relationship, at -0.83. Compared with October 21, 2026, nearly every correlation and beta shifted only in the third decimal place. KO/PEP and TLT/GLD moved somewhat more, and both rose.

KO (The Coca-Cola Company) and PEP (PepsiCo Inc) rose to a correlation of 0.600, up from 0.587 the day before.
TLT (ISHARES 20+ YEAR TREASURY BOND ETF) and GLD (SPDR Gold Shares ETF) rose to 0.144 from 0.128, but the r-squared of 0.02 means one explains very little of the other's daily variance.
SPY/VIXCLS stands at -0.83, little changed from the prior day. VIXCLS's average daily move per unit move of SPY is -7.81.
AAPL (Apple Inc.) and MSFT (Microsoft Corporation) remain the weakest stock pair at 0.118, with an r-squared of about 1.4%.
GLD's beta on DTWEXBGS (Nominal Broad U.S. Dollar Index) eased to -3.02 from -3.10, and the correlation held near -0.45. The GLD/DTWEXBGS window ends on October 16, 2026, with 246 observations.
SPY's beta on HYG (ISHARES IBOXX $ HIGH YIELD CORPORATE BOND ETF) is 2.51, alongside a correlation of 0.76. HYG's daily standard deviation is 0.24%, compared with SPY's 0.80%.

These figures summarize co-movement over the past year of daily changes; they do not show causation, how the relationships behaved within that year, or how they will behave in the future.

October 21, 2026

October 21, 2026: correlations across the 17 pairs barely moved; SPY/QQQ stays highest at 0.93

On the Covariance Calculator for October 21, 2026, every pair's one-year correlation stayed close to its October 20 value, with most edging slightly lower. SPY (SPDR S&P 500 ETF Trust) and QQQ (Invesco QQQ Trust Series 1) remain the most closely linked pair at 0.93, while SPY against VIXCLS (CBOE Volatility Index: VIX) remains the most negative at -0.83. The weakest links are still AAPL (Apple Inc.) with MSFT (Microsoft Corporation) at 0.12 and TLT (ISHARES 20+ YEAR TREASURY BOND ETF) with GLD (SPDR Gold Shares ETF) at 0.13.

SPY/QQQ correlation eased from 0.926 to 0.925, with an r-squared of 0.86; QQQ's beta on SPY is 1.44.
SPY/TLT correlation is positive at 0.31, slightly below the previous day's 0.31 reading at more decimal places (0.3131 to 0.3115).
SPY/HYG shows a 0.76 correlation and SPY's beta on HYG (ISHARES IBOXX $ HIGH YIELD CORPORATE BOND ETF) is 2.51, reflecting HYG's small daily standard deviation of 0.24% against SPY's 0.80%.
NVDA (NVIDIA Corporation) with AMD (Advanced Micro Devices Inc) was one of the few pairs whose correlation rose, from 0.511 to 0.512; SPY against crude oil (DCOILWTICO) became slightly more negative, from -0.377 to -0.378.
Among single-stock pairs, XOM (ExxonMobil Holdings Corp) with CVX (Chevron Corp) is highest at 0.85, followed by JPM (JPMorgan Chase & Co) with BAC (Bank of America Corp) at 0.74.
The FRED series run on shorter windows: VIXCLS, DGS10 and DTWEXBGS end October 16, 2026, and DCOILWTICO ends October 14, 2026, with 246 to 249 observations versus 251 for the ETF and stock pairs.

These one-year correlations and betas describe how daily changes moved together in the past and do not show why they did or whether the relationships will hold.

October 20, 2026

SPY/QQQ stays the tightest pair at 0.93 on October 20, 2026; most correlations moved only slightly

On October 20, 2026, the Covariance Calculator's 17 pairs, measured over a one-year look-back of daily changes, showed small moves from the October 17, 2026 table. SPY (SPDR S&P 500 ETF Trust) and QQQ (Invesco QQQ Trust Series 1) kept the highest correlation at 0.926, and SPY against VIXCLS (CBOE Volatility Index: VIX) kept the most negative at -0.828. AAPL (Apple Inc.) and MSFT (Microsoft Corporation) remained the weakest pair, at 0.119.

SPY/VIXCLS correlation moved from -0.823 to -0.828, and the VIX's beta on SPY stood at -7.82, meaning the VIX moved on average about 7.8 units opposite to each unit of SPY's daily move.
JPM (JPMorgan Chase & Co) and BAC (Bank of America Corp) correlation rose from 0.739 to 0.744, while KO (The Coca-Cola Company) and PEP (PepsiCo Inc) eased from 0.593 to 0.587.
SPY's correlation with EFA (ISHARES MSCI EAFE ETF) slipped from 0.790 to 0.787, and with TLT (ISHARES 20+ YEAR TREASURY BOND ETF) from 0.316 to 0.313.
TLT/GLD (SPDR Gold Shares ETF) remained near zero at 0.134, with an r-squared of 0.018.
GLD against DTWEXBGS (Nominal Broad U.S. Dollar Index) correlation moved from -0.443 to -0.447, with a GLD beta on the dollar index of -3.11.
Pairs against FRED series use windows ending earlier, on October 16 or October 14, 2026, with 247 to 250 observations, versus 251 for the other pairs.

These figures describe how daily changes moved together over the past year; they do not show why, and they do not indicate how the pairs will move in the future.

October 17, 2026

On October 17, 2026, one-year correlations moved only slightly; SPY/QQQ stays highest at 0.93, TLT/GLD lowest at 0.13

The Covariance Calculator's 17 pairs, measured on daily changes over a one-year look-back, showed small day-to-day shifts on October 17, 2026. SPY (SPDR S&P 500 ETF Trust) and QQQ (Invesco QQQ Trust Series 1) remain the most closely linked pair, with a correlation of 0.93 and an r-squared of 0.86. SPY against VIXCLS (CBOE Volatility Index: VIX) is the strongest negative relationship at -0.82, slightly more negative than -0.818 on October 16, 2026. Most correlations moved by less than a hundredth.

SPY against TLT (ISHARES 20+ YEAR TREASURY BOND ETF) has a positive correlation of 0.32, up from 0.31 the previous day; the beta of SPY on TLT rose from 0.42 to 0.43.
JPM (JPMorgan Chase & Co) and BAC (Bank of America Corp) saw their correlation ease from 0.75 to 0.74, while XOM (ExxonMobil Holdings Corp) and CVX (Chevron Corp) edged up from 0.845 to 0.846.
AAPL (Apple Inc.) and MSFT (Microsoft Corporation) remain weakly linked, with a correlation that slipped from 0.121 to 0.120 and an r-squared of 0.01.
SPY's beta on HYG (ISHARES IBOXX $ HIGH YIELD CORPORATE BOND ETF) is 2.51, up from 2.50, reflecting HYG's low daily standard deviation of 0.24% against SPY's 0.80%.
SPY against DGS10 (10-year Treasury yield, measured as a change in level) has a correlation of -0.36, a little more negative than -0.35 the day before.
GLD (SPDR Gold Shares ETF) against DTWEXBGS (Nominal Broad U.S. Dollar Index) is at -0.44, almost unchanged from the previous day.

These figures describe how daily changes moved together over the past year, with some series' windows ending earlier, as on October 9, 2026 for the dollar index; they do not show why the series moved together or whether these relationships will hold.

October 16, 2026

On October 16, 2026, one-year correlations barely moved; the bank and chip pairs edged up while SPY/HYG eased

Today's Covariance Calculator table covers 17 pairs, using daily changes over a one-year look-back ending October 15, 2026 for most pairs. Day-over-day changes in correlation were small across the table. SPY (SPDR S&P 500 ETF Trust) and QQQ (Invesco QQQ Trust Series 1) remain the most closely linked pair at 0.92. SPY and VIXCLS (CBOE Volatility Index: VIX) remain the most negative pair at -0.82.

JPM (JPMorgan Chase & Co) and BAC (Bank of America Corp) correlation rose from 0.742 to 0.747, and JPM's beta on BAC rose from 0.732 to 0.750.
NVDA (NVIDIA Corporation) and AMD (Advanced Micro Devices Inc) correlation rose from 0.502 to 0.508, with an r-squared of 0.26.
TLT (ISHARES 20+ YEAR TREASURY BOND ETF) and GLD (SPDR Gold Shares ETF) correlation rose from 0.131 to 0.140; it remains among the weakest links in the table, with an r-squared of 0.02.
SPY's beta on HYG (ISHARES IBOXX $ HIGH YIELD CORPORATE BOND ETF) eased from 2.51 to 2.50, and their correlation slipped from 0.761 to 0.759.
SPY and TLT show a positive correlation of 0.31, little changed from 0.313 the previous day.
AAPL (Apple Inc.) and MSFT (Microsoft Corporation) have a correlation of 0.12, essentially unchanged and low for two large stocks.

These one-year figures describe how the pairs have moved together in the past; they do not show why, whether the relationships held steady within the year, or how the pairs will move from here, and the windows for the pairs measured against FRED series end earlier, on October 14 or October 9, 2026.

October 15, 2026

SPY/QQQ stays the tightest pair at 0.93 on October 15, 2026; JPM/BAC correlation eases to 0.74

On October 15, 2026, the Covariance Calculator's 17 pairs, measured over a one-year look-back of daily changes, moved only slightly from October 14, 2026. SPY (SPDR S&P 500 ETF Trust) and QQQ (Invesco QQQ Trust Series 1) remain the most closely linked pair at a correlation of 0.93, while SPY against VIXCLS (CBOE Volatility Index: VIX) is the strongest negative link at -0.82. The largest visible shift was in JPM/BAC, where correlation slipped from 0.754 to 0.742.

SPY/TLT correlation fell from 0.322 to 0.313, and SPY's beta on TLT (ISHARES 20+ YEAR TREASURY BOND ETF) eased from 0.440 to 0.428; the two still move together rather than in opposite directions over this window.
NVDA/AMD correlation rose from 0.494 to 0.502, and QQQ/IWM rose from 0.726 to 0.735.
AAPL/MSFT (Apple Inc. and Microsoft Corporation) remains the weakest link in the table at 0.12, with an r-squared of 0.015, alongside TLT/GLD at 0.13.
SPY's beta on HYG (ISHARES IBOXX $ HIGH YIELD CORPORATE BOND ETF) is 2.51, reflecting HYG's much smaller daily standard deviation of 0.24% against SPY's 0.80%.
SPY/DCOILWTICO is unchanged at -0.37 because its data window still ends on October 6, 2026; the other FRED-series pairs also end earlier than the ETF and stock pairs, which run to October 14, 2026.

These figures describe how daily changes moved together over the past year and do not show why, nor whether the relationships will hold.

October 14, 2026

October 14, 2026: day-over-day correlation changes were small across all 17 pairs; SPY/QQQ remains the tightest pair at 0.92

On October 14, 2026, the Covariance Calculator's one-year correlations moved only slightly from October 13. SPY/QQQ remains the most closely linked pair at 0.92, with an R-squared of 0.85. SPY/VIXCLS remains the strongest negative pair at -0.81. AAPL/MSFT, at 0.12, and TLT/GLD, at 0.14, remain the weakest links in the table.

SPY/QQQ correlation edged down to 0.925 from 0.925 at three decimals (0.9246 versus 0.9255). QQQ moves about 1.43 units per unit move in SPY.
SPY/VIXCLS correlation was -0.815, slightly weaker than the previous day's -0.817. The VIX's average daily move is -7.84 units per unit move in SPY.
GLD/DTWEXBGS moved further negative, to -0.448 from -0.444. GLD's beta on the dollar index is -3.16, compared with -3.15 the day before.
SPY/TLT correlation stayed positive and rose slightly, to 0.322 from 0.319. SPY/DGS10 was -0.36, compared with -0.362.
Among the stock pairs, JPM/BAC rose to 0.754 from 0.751. XOM/CVX held at 0.84. KO/PEP was little changed at 0.587.
NVDA/AMD has the most volatile stock in the table: AMD's daily standard deviation is 4.28%, compared with 2.36% for NVDA and 0.80% for SPY.

These correlations describe co-movement over the past year and do not show cause or how the pairs will move next; the SPY/DGS10, SPY/DCOILWTICO and GLD/DTWEXBGS windows also end earlier than the others, on October 8, October 6 and October 2, 2026.

October 13, 2026

SPY/TLT correlation rises to 0.32 on October 13, 2026; SPY/QQQ remains the table's tightest pair at 0.93

On October 13, 2026, the 1-year correlation between SPY and TLT rose to 0.32 from 0.27 on October 10, 2026. SPY's beta on TLT rose to 0.44 from 0.37. Most other pairs moved little. SPY/QQQ stayed the most closely linked pair at 0.93, and SPY/VIXCLS stayed strongly negative at -0.82, compared with -0.83 the previous day.

SPY/QQQ correlation is 0.93, little changed from the previous day; its R-squared of 0.86 means each explains most of the other's daily variance.
SPY's negative correlations with the 10-year Treasury yield and with WTI crude both deepened: to -0.36 from -0.32, and to -0.37 from -0.35.
AAPL/MSFT has the weakest link in the table at 0.12, compared with 0.13 the previous day, with an R-squared of 0.015.
Among single stocks, XOM/CVX is the closest pair at 0.84, followed by JPM/BAC at 0.75. Both were nearly unchanged.
GLD's correlation with the broad U.S. dollar index held at -0.44, and its beta on the dollar was steady at about -3.15.
SPY's daily standard deviation over the window is 0.80%, against 1.86% for GLD and 0.58% for TLT.

These one-year figures describe how the pairs moved together in the past, not why they did or how they will move from here; several FRED-based windows also end earlier: October 8 for the 10-year yield, October 6 for WTI crude, and October 2 for the dollar index.

October 10, 2026

October 10, 2026: SPY/QQQ stays the tightest pair at 0.93; day-to-day correlation shifts were small

On today's Covariance Calculator table for October 10, 2026, SPY and QQQ remain the most closely linked pair, with a correlation of 0.93 and an R-squared of 0.86 over daily changes from October 10, 2025 to October 9, 2026. SPY against the VIX shows the strongest inverse link at -0.83. Against the previous day's table, most correlations moved only in the third decimal place. KO/PEP and SPY/DGS10 showed the clearest moves.

SPY/QQQ correlation was 0.928, essentially unchanged from 0.928 the day before; QQQ's beta on SPY is 1.42.
SPY/VIXCLS correlation was -0.83, the same as the previous day at two decimals; the VIX's beta on SPY is -8.01.
KO/PEP correlation rose to 0.59 from 0.58, and KO's beta on PEP rose to 0.53 from 0.51.
SPY/DGS10 correlation moved to -0.32 from -0.33, a slightly weaker inverse link between SPY and changes in the 10-year Treasury yield.
AAPL/MSFT remains among the loosest pairs at 0.130, down from 0.135, with an R-squared of 0.02; TLT/GLD is similarly low at 0.14.
SPY/TLT correlation is positive at 0.27, little changed from the previous day's 0.27.

These are one-year historical relationships in daily changes; they do not show how the pairs will move together in the future, and the FRED-based pairs use windows ending as early as October 2, 2026.

October 9, 2026

Covariance table for October 9, 2026: one-year correlations barely moved, SPY/QQQ still tightest at 0.93

Today's Covariance Calculator table for October 9, 2026 shows little change from October 8 across its 17 pairs, measured on daily changes over a one-year look-back. SPY and QQQ remain the most closely linked pair at a correlation of 0.93, while SPY against the VIX is the most negative at -0.83. Most correlations moved only in the second or third decimal place.

SPY/QQQ correlation is 0.928, against 0.929 the previous day, with an r-squared of 0.86; QQQ moved 1.42 units per unit of SPY.
SPY/VIXCLS correlation is -0.826, little changed from -0.826, with VIX moving -8.01 units per unit of SPY.
SPY/TLT stays positive at 0.27, slightly lower than 0.28 the day before, and its beta of SPY on TLT eased to 0.37 from 0.38.
KO/PEP correlation rose to 0.58 from 0.57, and XOM/CVX rose to 0.844 from 0.843.
GLD against the broad dollar index became slightly more negative, at -0.446 against -0.441, with a beta of GLD on the dollar of -3.17 against -3.13.
The weakest links are TLT/GLD at 0.14 and AAPL/MSFT at 0.14, each with an r-squared near 0.02.

These one-year averages do not show how the relationships varied within the year or what caused them, and the series from FRED end on earlier dates (as early as October 2, 2026) than the ETF and stock pairs.

October 8, 2026

Covariance table for October 8, 2026: SPY/QQQ remains the tightest pair at 0.93, with little change across the table

On October 8, 2026, correlations across the 17 pairs were close to the previous day's levels, with most moves showing only in the third decimal place. SPY/QQQ remained the most closely linked pair at 0.93, and SPY/VIXCLS remained the most strongly negative at -0.83. The largest visible shifts were small: SPY/TLT rose from 0.27 to 0.28, and SPY/DGS10 moved from -0.32 to -0.33.

SPY/QQQ correlation was 0.93 (0.93 the previous day), with an R-squared of 0.86. QQQ's beta on SPY was 1.42.
SPY/VIXCLS correlation was -0.83, little changed from the prior day's -0.83. The VIX's beta on SPY was -8.02.
Stock-bond correlation stayed positive, with SPY/TLT at 0.28, up from 0.27. SPY against the 10-year yield change (DGS10) moved from -0.32 to -0.33.
Among the stock pairs, XOM/CVX was the most closely linked at 0.84. AAPL/MSFT was the least linked at 0.14, with an R-squared of about 2%.
NVDA/AMD correlation edged up from 0.496 to 0.497. GLD/DTWEXBGS moved from -0.440 to -0.441.
SPY's daily standard deviation was 0.82% over the one-year window from October 8, 2025 to October 7, 2026, against 0.25% for HYG and 1.86% for GLD.

These figures describe how daily changes moved together over the past year and do not show cause; the FRED-series pairs also use shorter windows that end October 6 or October 2, 2026, so they are not fully aligned with the ETF and stock pairs.

October 7, 2026

October 7, 2026: SPY/QQQ is the most closely linked pair at 0.93 correlation; SPY/VIX is the most negative at -0.83

Today's Covariance Calculator table for October 7, 2026 covers 17 fixed pairs, mostly measured from daily changes between October 7, 2025 and October 6, 2026 (251 observations). Broad equity ETFs move closely together, while Treasuries, gold and two large technology stocks show weak links. No previous-day figures are shown, so today's table cannot be compared with yesterday's.

SPY and QQQ have a correlation of 0.93 and an r-squared of 0.86; QQQ's beta on SPY is 1.42, against 0.61 the other way.
SPY against the VIX has a correlation of -0.83, with VIX moving -8.02 units per unit move in SPY; SPY is also negatively correlated with 10-year Treasury yield changes (-0.32) and WTI crude (-0.34).
SPY and TLT show a positive correlation of 0.27 with an r-squared of 0.07, and TLT/GLD is weaker still at 0.14.
Among stocks, XOM/CVX (0.84) and JPM/BAC (0.75) are closely linked, while AAPL/MSFT shows a correlation of only 0.14 and an r-squared of 0.02.
AMD has the highest daily standard deviation in the table at 4.35%, compared with 2.38% for NVDA and 0.82% for SPY; the NVDA/AMD correlation is 0.50.
GLD against the broad dollar index shows a correlation of -0.44, on a shorter window ending October 2, 2026 with 247 observations.

These one-year correlations and betas describe how daily changes moved together in the past and do not show causes, how the relationships have shifted from the previous day, or whether they will hold.