Morning Brief: WTI at $101.13 Ahead of the Fed, GDP and PCE

MacKinlay describes a market model in which normal security return is an intercept plus beta times market return. Its coefficients come from an estimation window; the abnormal return is observed return minus this fitted normal return. For a Gann-style calendar inspection, that structure offers a disciplined alternative to simply subtracting a peer's return. ETH is not the overall market portfolio for BTC, however. Calling the pair a market model would overstate the analogy; here ETH is explicitly an editorial proxy. Use a synthetic training set with peer returns of -2%, 0%, and 2% and target returns of -3%, 1%, and 5%. The three points fit intercept 1 percentage point and slope 2 exactly. If the peer gains 1% during a later event bar, the predicted target return is 3%. An actual 4% target return leaves a +1 percentage-point residual. One-for-one subtraction would give +3 points instead, but it imposes a different slope and zero intercept without testing them. Freeze both assets' UTC close convention and estimate parameters before the inspected candle. Report the coefficients and residual alongside the actual returns so a fitted response cannot be mistaken for a forecast of direction.

Try it

Training pairs (peer,target) in percent are (-2,-3), (0,1), (2,5). For a later peer return of +1% and target return of +4%, find fitted intercept, slope, and target residual.

Limits

Three exactly aligned training points are a synthetic demonstration, not a valid beta estimate. BTC and ETH share drivers and neither is a broad equity market portfolio. A fitted residual is sensitive to sample dates, extreme moves, and changing correlation.

Source

A. Craig MacKinlay, Event Studies in Economics and Finance, Section 4.B, Market Model, printed p. 18, equation (3); Section 5.A, OLS coefficient estimates, printed p. 20, equations (4)-(5). Peer-reviewed Journal of Economic Literature 35(1), 1997, pp. 13-39; article reproduced as a searchable PDF in a public court exhibit. Model concerns securities and market portfolios; BTC/ETH proxy choice is explicitly editorial.

Today

Oct 25 completed UTC BTC close $80,053.16; its return -0.887% versus ETH -1.215% on aligned UTC closes. Fitting only the prior 20 paired returns yields alpha +0.155 percentage points and beta 0.687; expected BTC return -0.680%, observed residual -0.208 percentage points. The peer proxy and BTC price share the Oct 25 UTC close on the inspection chart. This is a historical measurement, not a turning-point forecast. Coinbase BTC-USD with ETH-USD peer proxy, completed UTC daily candles, Latest session 2026-10-26T00:00:00Z: r_t = 100*(close_t/close_(t-1)-1); beta=sum((ETH_t-mean_ETH)*(BTC_t-mean_BTC))/sum((ETH_t-mean_ETH)^2) over 20 pre-event paired returns; alpha=mean_BTC-beta*mean_ETH; residual = BTC_event - alpha - beta*ETH_event. = -0.20757392501449412 percentage points (inputs: alpha_percentage_points=0.15522584630881137, beta=0.6872240015138207, btc_event_return_pct=-0.8871027948981314, btc_latest_completed_close_usd=80053.16, eth_event_return_pct=-1.2146763127504956, eth_latest_completed_close_usd=2326.75, paired_training_returns=20, predicted_btc_return_pct=-0.6795288698836373). Data source 1 Data source 2

A market-astrology timing note may put a clock beside a seasonal date, but a sundial and a uniform civil clock do not measure identical solar motion. The U.S. Naval Observatory explains the equation of time using two physical ingredients: Earth's axial tilt, or obliquity, changes how much of the Sun's apparent path projects east-west; orbital eccentricity changes Earth's orbital speed around the Sun. The tilt contribution is zero at equinoxes and solstices and can reach about ten minutes at other times. The eccentricity contribution is largest near early April and early October, roughly minus and plus seven and a half minutes respectively under the source's convention. These are diagnostic components, not independent clocks that may always be added exactly. USNO notes that the tilt contribution modulates the eccentricity contribution, so the resulting curve differs slightly from a simple sum. If a source says a solar event happened at 'noon,' ask whether that means apparent local solar noon, mean solar noon, or a timezone clock. Record the site and the time convention before aligning an astronomy timestamp with a market bar. That classification protects the timing comparison; neither component establishes a price direction or a tradable cycle.

Try it

USNO gives the orbital-eccentricity contribution as about -7.5 minutes in early April and +7.5 minutes in early October. What is the peak-to-peak difference? At a solstice, does a zero tilt contribution imply the full equation of time is zero?

Limits

The cited figures describe clock geometry, not a market reaction. Solar-noon offsets depend on date and convention; the simplified component values do not substitute for a site-specific USNO calculation. No price direction follows from their coincidence with a session.

Source

USNO, The Equation of Time, What Causes the Equation of Time? — obliquity and eccentricity sections, component graph and non-additivity explanation. Primary U.S. Naval Observatory astronomy reference. Market timestamp comparison is an editorial application, not an astronomical market effect.

Today

USNO gives upper solar transit at 16:40 UTC on Oct 25 at 40.7128°N, 74.0060°W. Mean solar noon by longitude is 16:56:01 UTC; apparent minus mean is -16.024 minutes (USNO rounds transit to a minute). The Coinbase BTC-USD candle at that same 16:40 UTC observation closed at $80,457.55 one minute later. Plot the timestamp and BTC price together; the clock offset does not predict the price. USNO New York apparent solar noon with Coinbase BTC-USD completed UTC minute close, Latest session 2026-10-25T16:41:00Z: apparent minus mean solar noon (minutes) = USNO upper transit UTC minutes - (720 - 4*longitude_east_degrees). = -16.024 minutes (inputs: btc_price_usd_at_transit_minute=80457.55, candle_start_unix_seconds=1792946400, mean_solar_noon_utc_minutes=1016.024, new_york_latitude_north_degrees=40.7128, new_york_longitude_east_degrees=-74.006, usno_transit_utc_minutes=1000). Data source 1 Data source 2