Morning Brief: WTI at $98.08 Ahead of JOLTS and Friday Payrolls

MacKinlay's event-study discussion distinguishes an average abnormal return from the way returns vary with characteristics of each event observation. A cross-sectional model places the abnormal return on one side and pre-event characteristics on the other. For a seasonal inspection date, that suggests a narrower question than 'Did the date work?': did a prespecified exposure category help explain which stocks moved? First define the universe, the same observation window, the baseline return model, and an exposure label measured before the date. Keep a common event clock and use abnormal returns rather than raw price changes. In an editorial worksheet, four low-exposure names have abnormal returns of 1, 2, 0, and 1 percentage points; four high-exposure names have 3, 2, 4, and 3 points. Their group averages are 1 and 3 points. With a zero-one exposure indicator, the simple two-group regression intercept is 1 point and its exposure coefficient is 2 points. That coefficient describes the observed between-group gap, not a seasonal effect. The exposure might track sector, size, rate sensitivity, or another pre-existing condition. Check whether a single stock dominates the gap and whether overlapping event dates create correlated observations. Freeze the grouping and model before inspecting the window; otherwise the strongest-looking split is a search result, not a test.

Try it

On one hypothetical Gann inspection date, four low-exposure stocks have abnormal returns of 1, 2, 0, and 1 percentage points. Four high-exposure stocks have 3, 2, 4, and 3. For a regression with a zero-one high-exposure indicator, find the intercept and exposure coefficient. What does the coefficient describe?

Limits

Eight synthetic observations do not support a significance claim. Confounding characteristics, correlated names, an unstable baseline model, and a group chosen after seeing prices can all distort the slope. MacKinlay discusses economic events, not tested Gann dates; this worksheet is an editorial transfer of the method.

Source

A. Craig MacKinlay, Event Studies in Economics and Finance, Journal of Economic Literature 35(1), 1997, printed p. 33, section 9, Cross-Sectional Models, equation (26); court exhibit PDF page 22. Original peer-reviewed finance-methods article reproduced in a federal court exhibit. The seasonal grouping and eight-stock arithmetic are editorial examples, not the author’s empirical results.

JPL Horizons observer quantity 37 describes a formal position-uncertainty region in the plane perpendicular to the observer's line of sight. It reports the three-sigma ellipse's semi-major axis SMAA_3sig and semi-minor axis SMIA_3sig in arcseconds, plus Theta, the orientation of the major axis in degrees. The ellipse can be narrow in one sky direction and wide in another. Those axes describe uncertainty in where a target is calculated to appear, not the planet's apparent diameter or its motion across the sky. Consider an editorial ephemeris row with semi-major axis 6 arcseconds, semi-minor axis 2, and Theta 30 degrees under the manual's orientation convention. The long axis is three times the short one. For a planar ellipse its area is pi times the two semi-axes, about 37.7 square arcseconds. A circular uncertainty label of 6 arcseconds would erase both the anisotropy and the orientation. Keep the target, observer, UTC time, and source solution with all three fields; changing the observing site can change the projected geometry. If a proposed tight aspect depends on a target whose formal position uncertainty is material to the claimed orb, report that limitation beside the timing claim. Match the observation time to any proxy-price timestamp on the same chart. The error ellipse does not predict a market reaction.

Try it

A synthetic Horizons quantity-37 row reports SMAA_3sig = 6 arcseconds, SMIA_3sig = 2 arcseconds, and Theta = 30 degrees. Compute the long-to-short axis ratio and approximate ellipse area. What does Theta identify?

Limits

These are formal projected position uncertainties from the chosen orbit solution and observer, not guaranteed bounds or a measure of market direction. The planar area calculation is a synthetic worksheet. A well-measured major planet may have far smaller uncertainty than a poorly observed small body.

Source

NASA/JPL, Horizons System Manual, Definition of Observer Table Quantities, quantity 37, Plane-of-sky error ellipse; fields SMAA_3sig, SMIA_3sig, Theta, and Area_3sig. Primary NASA/JPL Solar System Dynamics technical manual, version 4.98e (August 25, 2026). The axis lengths and area calculation are synthetic.