AVGO leverage-effect test: does a down day lead to wider next-day ranges than an equal up day?
Surprisingly, AVGO does not display the classic leverage effect over the roughly three-year window studied. Across 750 trading days, next-day intraday ranges averaged 27.16% after negative days versus 34.29% after positive days, a raw gap of −7.13 percentage points that is statistically insignificant (Welch p = 0.451). A regression that allows negative moves to amplify next-day range produces γ = −0.531 with R² ≈ 0.002, so sign and move size explain almost none of the variation.
I tested daily close-to-close returns against the next session’s (high−low)/close, controlling for move magnitude by terciles and using Welch t-tests plus an OLS interaction term with HC1 robust SE. The full methodology, per-tercile results, charts and robustness checks follow below; the bottom line here is simple: the data do not support the thesis that AVGO’s down days meaningfully inflate next-day ranges.
For AVGO over the past ~3 years, is volatility asymmetric — after a down day does the next session's high-low range widen more than it does after an up day of the same magnitude, the classic 'leverage effect'? Thesis: negative returns are followed by materially wider next-day ranges than equally-sized positive returns, so fear inflates AVGO's volatility far more violently than greed does.
How this was measured
Resampled AVGO minute bars to daily OHLCV. Computed daily close-to-close return r_t and next-day intraday range proxy as (high−low)/close at t+1. To control for move size, partitioned days into terciles by |r_t| (Low/Mid/High) and, within each tercile, compared next-day ranges after negative vs positive r_t via Welch's t-test. In parallel, fit an OLS regression next_range = α + β·|r_t| + γ·1[r_t<0]·|r_t| with HC1-robust SE; γ>0 indicates a leverage-style asymmetry where negative moves amplify next-day range more per unit of |r_t|.
The key numbers
Reading the numbers
Across 750 trading days, the average next-day high−low range was about 27.16% after negative days versus 34.29% after positive days; the raw gap (Neg − Pos = −7.13 percentage points) is not statistically clear (Welch p = 0.4513).
The charts
The scatter of same-day return r_t against next-day range is a diffuse cloud with no obvious slope: returns span roughly −16.4% to +20.8% while next-day ranges average 0.3086 but spike to an extreme 10.4015. Those extreme high-range points dominate the vertical scale and make any small trend hard to see. Given the tiny OLS R² of 0.0023, the return on a day explains almost none of the next-day range, so there is no clear visual leverage effect in the raw scatter.
The box plots by |r_t| tercile and sign show inconsistent asymmetry and very heavy right tails: all six groups have max values near 9–10, which inflates means. For low |r| the mean next-day range is much larger after positive days (0.4293 vs 0.2411), while mid and high |r| terciles show either tiny or reversed differences (mid: 0.2581 neg vs 0.2451 pos; high: 0.3217 neg vs 0.3497 pos). In short, the distribution is skewed and outliers shift the means, and there is no consistent pattern of larger ranges following negative days.
The bar chart of mean next-day range by tercile lays out the numbers cleanly: Neg means are [0.2411, 0.2581, 0.3217] for Low/Mid/High, while Pos means are [0.4293, 0.2451, 0.3497]. Positive days have equal-or-larger subsequent ranges in the Low and High bins, with only the mid bin showing a small Neg>Pos edge. The high-|r| bin difference (Neg−Pos ≈ −0.02796) is small and the within-bin Welch test p = 0.8716 confirms that this bin-level difference is not statistically meaningful.
Within-bin contrast: Neg vs Pos (next-day range)
| |r_t| bin | N_neg | Mean_neg | N_pos | Mean_pos | Diff (Neg−Pos) | Welch p |
|---|---|---|---|---|---|---|
| Low |r| | 123 | 0.2411 | 127 | 0.4293 | -0.1881 | 0.29 |
| Mid |r| | 128 | 0.2581 | 122 | 0.2451 | 0.013 | 0.9267 |
| High |r| | 109 | 0.3217 | 141 | 0.3497 | -0.028 | 0.8716 |
The takeaway
No — the data do not support the classic leverage effect for AVGO over this ~3‑year window. Next‑day intraday ranges averaged 27.16% after negative days versus 34.29% after positive days, so the raw gap is actually -7.13 percentage points (Neg − Pos). That difference is not statistically meaningful: the overall Welch p = 0.451 on 750 days, and the high‑|r| tercile gap is only −2.80% with p = 0.872. A regression that allows negative moves to amplify range gives γ = −0.531 (opposite sign to the thesis) with p = 0.900 and R² = 0.0023, meaning move size and sign explain almost none of next‑day range. Bottom line: there’s no convincing evidence here that fear (negative returns) inflates AVGO’s next‑day intraday range more than equally sized gains; the pattern is noisy and inconsistent, not a reliable trading signal.
The fine print
- Next‑day range uses (high−low)/close and ignores overnight gaps, so it understates total next‑session variability.
- Magnitude bins are in‑sample terciles; thresholds and results could shift in a different date window or volatility regime.
- High‑magnitude tails are relatively sparse (see bin Ns) so within‑bin p‑values are noisy.
- The OLS is a simple linear check (HC1 SE); a fuller realized‑volatility or GARCH/EGARCH model might detect subtler dynamics.