Best-day clusters versus trend filters

A slogan treated as a rule-design drill

The missed-best-days argument is the claim that a long fully invested path is condemned if a handful of the largest one-day advances are skipped.

Editorial reading: treat that slogan as a rule-design drill for a mechanical trading system. A trend-following moving-average crossover is not graded on whether it captures isolated rebound sessions. It is graded on whether those sessions sit inside rebound clusters whose adjoining declines exceed the rebound.

Twenty best days and their adjoining declines

The comparison used the twenty largest one-day S&P 500 advances from 1955 through 2005 rather than only the ten largest days in a ten- or twenty-year window.

The largest one-day advance in that fifty-year sample was 9.1 percent on 21 October 1987, after a 5.3 percent gain on 20 October 1987 and a one-day drop of more than 20 percent on 19 October 1987.

Several of the next-largest 2002 advances, including 5.7 percent on 24 July and 5.4 percent on 29 July, occurred while the index was recovering from a decline of about 45 percent from the August 2000 peak.

Ranked advances of 5.1 percent on 28 October 1997 and 8 September 1998 each followed nearby declines of 6.9 percent and 6.8 percent.

The 5 percent advance on 27 May 1970 sat inside an 8 May to 1 June stretch that included 13.9 percent of gains and 16.1 percent of losses.

Across the full list of twenty, each best day was accompanied by neighboring declines larger than that day's advance.

A fully invested deletion is not a timing test

Removing the ten, fifteen, or twenty best days from a 1955-to-sample-end fully invested path reduced the ending result, but that comparison does not test whether a timing rule can also avoid the adjoining losses.

Editorial reading: a mechanical trading system is a fully specified timing procedure whose signals can be checked as a single path through a sample, rather than as a list of isolated up days. Deleting only the rebound leaves the adjoining decline on the comparison path, so the slogan never asks the question the rule is built to answer.

Scoring a moving-average crossover as one path

A moving-average crossover is a mechanical exposure signal that changes participation when a shorter average of price crosses a longer average, turning a repeatable chart condition into a testable stay-in or stay-out hypothesis.

Trend following treats entry, exit, and abstention as one rule set keyed to market state, so a skipped rebound is judged together with the decline that preceded or followed it.

A simple moving-average crossover was described as missing nearly all of those best days together with the larger adjoining declines those days were tied to.

Editorial reading: that described path is the relevant score for the drill. The question is not whether isolated rebound sessions were captured. The question is whether the rebound cluster, including the larger adjoining decline, was handled as one procedure.