MSFT leverage-effect test: do losses drive higher next-day intraday volatility than equal gains? (≈3y window)
MSFT shows a measurable leverage effect over the past ~3 years: a same-sized decline tends to be followed by a larger next-day intraday range than an equal-sized gain. In an OLS model on 729 trading days the signed-return coefficient is c = −0.48346 (p = 0.00597), which translates to about a 0.97% bigger next-day high–low range after a −1% close. That result is statistically robust but modest in scale.
The study resampled minute bars to daily OHLC, regressed next-day (high−low)/close on |r_t| and r_t with Newey–West errors, and also ran bucketed comparisons. The R-squared is low (0.014), so sign/magnitude explain only a small slice of range variability; the detailed charts, tests and caveats are below.
For MSFT over the past ~3 years, does a down day spike the next session's volatility more than an up day of the same size — the asymmetric 'leverage effect' where fear drives volatility harder than greed? Thesis: a given-magnitude decline is followed by a meaningfully larger next-day high-low range than an equal-magnitude gain, so volatility reacts to losses rather than to moves in general.
How this was measured
Resampled MSFT minute bars to daily OHLCV over the last ~3 years. Computed daily close-to-close return r_t and next-day intraday volatility proxy as (high−low)/close on day t+1, aligned to r_t. Tested asymmetry two ways: (1) OLS regression vol_{t+1} = a + b·|r_t| + c·r_t with HAC (Newey-West, 5 lags) standard errors; a negative, significant c indicates that, holding magnitude fixed, losses precede higher next-day volatility than gains. (2) Bucketed days by absolute return quintiles and compared mean next-day ranges for negative vs positive days within each bin via Welch's t-test.
The key numbers
Reading the numbers
Across 729 trading days the average next‑day high–low range was 11.42%. The regression finds a negative asymmetry coefficient c = -0.4834568808721459 (p = 0.005970546843358322), implying about a 0.009669137617442917 (0.9669%) larger next‑day range after a 1% drop than after a 1% rise, though R² is only 0.014016229125365376.
The charts
This bar chart splits mean next‑day (H−L)/C by today's absolute return bin and by sign. Look at the 1.04–1.72% bin where negative days lead to a mean next‑day range of 0.1272 versus 0.0974 after positive days — the biggest gap in the chart. The top magnitude bin (1.72–11.60%) also shows higher next‑day range after losses (0.1264 vs 0.1113; neg−pos = 0.0151 noted above). The pattern of losses producing slightly larger next‑day ranges holds in most bins, but the differences are numerically modest.
The scatter plots each day's signed return (x from -0.0631 to 0.116, mean 0.0005) against the next‑day range (y from 0.0095 to 0.6716, mean 0.1142) for n=729. The cloud is wide with no tight slope, which matches the low OLS R² = 0.014016229125365376: most of the variation in next‑day range is noise. So although the regression picks up a statistically significant negative asymmetry, the scatter shows the effect is small relative to day‑to‑day dispersion and driven partly by a few large outliers.
Per-bin next-day volatility summary (pos vs neg)
| abs_ret_bin | N_pos | N_neg | mean_vol_next_pos | mean_vol_next_neg | diff_neg_minus_pos | welch_p |
|---|---|---|---|---|---|---|
| -0.10%–0.29% | 66 | 79 | 0.1008 | 0.1094 | 0.0086 | 0.5007 |
| 0.29%–0.61% | 84 | 62 | 0.1011 | 0.112 | 0.0109 | 0.3506 |
| 0.61%–1.04% | 73 | 72 | 0.1299 | 0.1303 | 0.0004 | 0.9782 |
| 1.04%–1.72% | 78 | 68 | 0.0974 | 0.1272 | 0.0298 | 0.0085 |
| 1.72%–11.60% | 74 | 72 | 0.1113 | 0.1264 | 0.0151 | 0.1861 |
The takeaway
Yes — over the last ~3 years MSFT shows a measurable leverage effect: losses of a given size tend to be followed by larger next-day high–low ranges than equal-sized gains. The signed-return coefficient in the OLS model is c = -0.48346 with p = 0.00597 across 729 trading days, which translates to about a 0.97% bigger next-day range after a −1% day (0.00967) and about 1.93% after a ±2% move (0.01934). That result is statistically robust but small in explanatory power: the regression R-squared is only 0.014, so the sign/magnitude story explains about 1.4% of day-to-day range variability. The bucketed tests show the asymmetry is clearest in the mid-large bin (1.04%–1.72%) where neg–pos gap = 2.98% (p = 0.0085), while the largest-move bin (1.72%–11.60%) has a 1.51% gap that is not significant (p = 0.1861). Bottom line: there is a real, statistically significant lean that losses spike next-day intraday volatility more than gains, but it’s modest in size and not uniform across the biggest moves — treat it as a useful tilt, not a dominant driver of volatility.
The fine print
- Volatility proxy is next-day high–low range; other estimators (Garman–Klass, Parkinson) could change magnitudes.
- Per-bin tests have uneven and sometimes small pos/neg counts; interpret bin p-values cautiously.
- Earnings and macro-event days were not excluded and can dominate large-move bins.
- Next-day range mixes overnight and intraday moves; channel (open vs intraday) was not separated.