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An event chart can put the label "day zero" beside a cumulative line and invite a false reading. In MacKinlay's earnings-announcement example, Table 1 separates the daily average abnormal return (AR) from cumulative average abnormal return (CAR). CAR starts at event day -20, not at the announcement. For the market-model good-news group, CAR is 1.001% at day -1 and 1.966% at day zero. Yet the day-zero AR is 0.965%. Subtracting the two cumulative readings, 1.966 - 1.001, isolates that day's increment. Calling 1.966% the announcement-day response would count the pre-announcement prefix as though it happened on day zero. MacKinlay's example covers 600 quarterly earnings announcements from 30 Dow industrial companies during January 1989 to December 1993. It does not test Gann dates. For an inspection date on a current chart, label the starting day on every cumulative-return curve. Show the cumulative value immediately before the mark and the marked day's incremental abnormal return separately. Keep the same set of securities and normal-return model when comparing adjacent endpoints. In the same group, CAR drops from 2.217% on day +1 to 2.203% on day +2, a -0.014-percentage-point increment, despite the positive endpoint. The sum's origin and increments both belong beside a timing mark.

Try it

In MacKinlay's market-model Good News column, CAR is 1.001% at day -1, 1.966% at day 0, and 2.203% at day +2; day +1 CAR is 2.217%. What is the day-zero AR? What is the day +2 AR? Does the positive day +2 CAR make its daily AR positive?

Limits

These are sample averages for historical earnings announcements, not Gann-date observations or a trading rule. Cumulative abnormal returns add estimated residual returns, not compounded buy-and-hold returns. Rounding table entries to three decimal places may make adjacent differences differ slightly from a printed AR. A different start day changes the CAR endpoint.

Source

A. Craig MacKinlay, Event Studies in Economics and Finance, Journal of Economic Literature 35(1), 1997, printed p. 16, Section 3 sample; p. 22, Table 1, Market Model, Good News, days -1, 0, +1, +2; p. 23, Table 1 caption defining CAR; p. 24, equation (15). Peer-reviewed article reproduced as a searchable public court exhibit and checked against Boston University's author-hosted facsimile. Table 1 gives historical sample averages for 600 earnings announcements, not a reconstructed price series. Applying its measurement distinction to a Gann inspection date is editorial.

Ptolemy first assigns Aries and Libra to equinoxes, Cancer and Capricorn to solstices. These four signs start the seasonal quarters. Taurus, Leo, Scorpio, and Aquarius follow them; he calls these solid. Gemini, Virgo, Sagittarius, and Pisces close the quarters and are bicorporeal. This is a positional cycle: opening, established middle, and a late interval that shares characteristics with the next season. His explanation for the solid signs is unusually careful. He does not say their weather is inherently more extreme; people have become accustomed to the season and feel its quality more clearly. To classify an example, convert 47 degrees of tropical ecliptic longitude to 17 degrees Taurus. Taurus belongs to the second group, regardless of the asset or whether that day was volatile. The same rule would classify 77 degrees Gemini as bicorporeal. Label the tropical coordinate and the northern-season reference before comparing event dates with prices. That preserves what Ptolemy argued instead of turning a historical naming convention into a volatility forecast.

Try it

Using zero Aries as 0 degrees, classify 47 degrees and 77 degrees ecliptic longitude into Ptolemy's seasonal sign classes. Show signs and in-sign degrees.

Limits

These are categories in an ancient northern-season doctrine. They do not test realized returns, southern-hemisphere seasons, or whether signs cause volatility. A price study would need an independently specified event rule and sample.

Source

Ptolemy, Tetrabiblos, Book I, chapter 11, pp. 65-69 (Robbins translation, sign groups). Primary ancient astrology text, F. E. Robbins translation at LacusCurtius. Seasonal interpretation is historical doctrine, not astronomy or finance evidence.