BP beta to Brent crude: bottom vs top quintile of Brent 20-day realized volatility
For BP over the past ~3 years, is the daily-return beta of BP to Brent crude higher when Brent's 20-day realized volatility is in the top quintile than when it is in the bottom quintile? I expect BP to trade as a higher-beta crude proxy during high-vol regimes because traders reprice the supermajor more aggressively to oil swings when the commodity signal is loudest.
How this was measured
BP and Brent daily returns were computed from daily closes over the available overlapping ~3-year window. For each trading day, Brent 20-day realized volatility was computed on trailing Brent returns and shifted one day so the regime label at day t uses only data through t-1; days were then split into bottom and top quintile regimes using full-sample 20th/80th percentiles. Within each regime, BP's beta to same-day Brent returns was estimated with ordinary least squares; an interaction model tested whether the slope difference between the top and bottom quintiles is statistically distinguishable from zero.
The key numbers
Reading the numbers
BP's beta to Brent was actually lower in the high-vol regime (0.235 vs 0.423), the opposite of the expectation. The gap is statistically clear (p=0.0276), so the pattern is unlikely to be random noise.
The charts
The bar on the left, for bottom-quintile Brent volatility, is nearly twice as tall as the bar on the right for top-quintile volatility — 0.423 vs 0.235. That is backwards from the hypothesis: BP acted less like a crude proxy when oil was most volatile, even though average realized vol jumped from 19.68% to 65.79%. The statistically clear difference (p=0.0276) means this isn't just noise; in the data, calmer oil markets are when BP's daily returns track Brent more closely.
Regime-level OLS estimates
| Vol regime | N days | BP beta | Beta std err | R squared | Avg Brent 20d RV | Avg BP daily ret | Avg Brent daily ret |
|---|---|---|---|---|---|---|---|
| Bottom quintile | 137 | 0.4227 | 0.075 | 0.1906 | 0.1968 | -0.0008 | -0.0002 |
| Top quintile | 137 | 0.2346 | 0.0303 | 0.3069 | 0.6579 | 0.0008 | 0.0009 |
The takeaway
The answer is no — and in fact the result runs the other way. BP's daily beta to Brent was lower, not higher, during Brent's high-volatility regime: 0.235 in the top quintile versus 0.423 in the bottom quintile, a difference of -0.188. That gap is not noise: the interaction p-value is 0.0276, meaning there is roughly a 3-in-100 chance this difference would appear by luck, so the contrast is statistically clear at conventional confidence levels. Both regimes have 137 trading days, and the quintiles are genuinely distinct — average annualized Brent 20-day realized vol is 19.7% in the low bucket versus 65.8% in the high bucket. So the practical takeaway is that during the calmest crude-oil stretches BP has tended to track same-day Brent moves more closely, while in chaotic oil markets that same-day relationship loosens. For anyone using BP as a crude proxy, the intuitive "louder oil signal, higher beta" story is not supported by this three-year window; the relationship is real but opposite to the hypothesis.
The fine print
- Only 137 trading days per regime — a roughly three-year window, so the split could shift with a different period.
- Quintile thresholds are full-sample, in-sample cutoffs, not a live tradable rule.
- Beta is contemporaneous same-day only; lead-lag relationships could tell a different story.
- No equity-market factor is controlled for, so some of the beta difference may reflect broad market moves rather than pure crude exposure.