USO 10-day forward gap vs Brent, conditioned on top-quartile Brent realized volatility
Contango logic says USO should bleed hardest against Brent spot right when crude volatility spikes and steepens the curve, making the ETF's daily roll more expensive. The data over the past three years don't cooperate. Across 712 shared trading days, Brent's 20-day realized volatility sat in the top quartile on 178 of them; on those days the average 10-day USO-minus-Brent gap was positive and larger (+1.27%) than on all other days (+0.41%). The high-vol window moved the gap in the opposite direction of the thesis.
Statistically, the spread is noise by conventional standards: the Newey-West corrected high-minus-low estimate lands at +0.86% with a t-stat of 0.75, nowhere close to significant. The continuous Spearman rank correlation between Brent RV20 and the 10-day forward gap is likewise weakly positive. Whatever contango and roll-cost pressure may exist, Brent volatility alone isn't carrying it.
The full study below lays out the panel construction, volatility cutoff, overlapping-window regression, and charts that make the verdict visible — the evidence cuts against the easy narrative.
For USO over the past ~3 years, does its 10-day return gap versus Brent crude become more negative when Brent's 20-day realized volatility is in the top quartile? Thesis: high crude volatility steepens contango and roll costs, causing the ETF to bleed relative to spot.
How this was measured
I built a daily panel of USO and Brent closes on shared calendar dates, computed Brent 20-day realized volatility as the annualized trailing standard deviation of daily Brent returns, and defined the outcome as the forward 10-trading-day gap: USO 10-day return minus Brent 10-day return. Days were split at the in-sample 75th percentile of Brent RV20. Because forward 10-day windows overlap, I estimated the high-minus-low gap with a Newey-West HAC regression using 10 lags rather than a plain two-sample t-test. Spearman rank correlation between continuous RV20 and the 10-day gap is also reported.
The key numbers
Reading the numbers
The average 10-day gap is positive in both regimes — +1.27% in the high-volatility quartile versus +0.41% otherwise. That +0.86% difference has a p-value of 0.451, so it is not statistically clear and does not support the thesis that high volatility makes the gap more negative.
The charts
The top-quartile box has a mean gap of +1.27%, while the other days average +0.41%, so high-volatility days are not showing the more negative USO-minus-Brent gap the thesis predicted. The top-quartile distribution is wider, reaching from -20.14% to +25.88%, versus -5.84% to +13.28% on other days, meaning extreme negative gaps do occur under high volatility but are offset by large positive gaps. Look at the positive means: the central tendency is higher, not lower, when Brent's realized volatility is in the top quartile.
This scatter plots each day's Brent 20-day realized volatility against the forward 10-day USO-minus-Brent gap, and there is no downward-sloping pattern. The rank correlation is +0.159, so in plain terms higher volatility is actually associated with a slightly more positive gap, not a more negative one. Although the p-value of 0.000 means that weak positive association is statistically detectable, it points in the opposite direction from the original thesis.
The bar chart makes the comparison simple: the top-quartile bar sits at +1.27% and the other-days bar at +0.41%, so the high-volatility regime has the taller bar. If high crude volatility steepened roll costs and made USO bleed relative to Brent, this bar should be lower or negative. The 0.86 percentage-point gap between the bars is not statistically meaningful at conventional levels, so this visual difference should not be read as evidence that volatility hurts the ETF's relative performance.
Forward 10-day gap summary by Brent RV20 regime
| Regime | N | Mean gap | Median gap | Std gap |
|---|---|---|---|---|
| Top quartile | 178 | 0.0127 | 0.0136 | 0.0583 |
| Other days | 534 | 0.0041 | 0.003 | 0.0212 |
The takeaway
The thesis doesn't hold up: days with top-quartile Brent volatility did not have a more negative USO-versus-Brent 10-day gap—they had a slightly more positive one. Across 712 trading days (178 high-vol, 534 other), the average 10-day gap was +1.27% on top-quartile days versus +0.41% on other days, a high-minus-low difference of +0.86%. That is the opposite sign of what roll-cost and contango pressure would predict, and it's not close to significant: with a HAC t-stat of 0.75 and p=0.45, the gap could easily be random. The continuous Spearman correlation (+0.16) also points weakly positive, not negative. So this is basically a coin flip—there is no reliable evidence that high Brent volatility makes USO bleed relative to spot over the past three years. Practically, Brent-vol alone isn't a useful conditioning signal for the USO gap; the WTI-versus-Brent basis and USO's own dynamics are likely doing more work.
The fine print
- USO tracks WTI, not Brent, and Brent RV is measured from Brent closes only, so the gap mixes WTI-Brent basis moves with roll costs and ignores USO's own vol.
- Forward 10-day windows overlap; Newey-West with 10 lags reduces but doesn't fully remove the dependence.
- Top-quartile cutoff is in-sample; the real-time high-vol boundary could differ going forward.
- High-vol regime gap std is 5.8% vs 2.1% on other days, so the mean gap is very noisy.