Evaluating quarterly return runs with historical analogs

Scoring signed quarterly runs

Signed quarterly total-return sequences can be partitioned into same-sign runs and scored both by percentage extent and by duration in quarters. Run-extent is the cumulative percentage total return accumulated across one uninterrupted signed run. Run-duration is the number of consecutive quarters that keep the same return sign.

A runs-test is a count of consecutive same-sign quarterly total-return observations used to measure how long an advance or decline persists before an opposite-sign quarter interrupts it. An up-move is a run of consecutive quarters with positive total return. A down-move is a run of consecutive quarters with negative total return.

What the completed runs showed

The evaluation sample is quarterly average total returns on a capitalization-weighted industrial equity index from 1940 through the second quarter of 1991.

In that record, many positive quarterly runs exceeded a 25 percent cumulative total return, while very few negative quarterly runs exceeded 25 percent without an interrupting quarter. Negative quarterly runs rarely lasted more than two or three consecutive quarters, whereas positive quarterly runs were less regular in length and more often continued longer.

The negative-run group placed above 25 percent contained two tabulated extents: 32.6 percent and 33.5 percent. Positive-run durations grouped as longer than four quarters included lengths of 5, 7, 7, 10, 6, 5, 11, 5, and 5 quarters. Negative-run durations grouped as longer than four quarters included two sequences of 6 quarters each.

Ranking a live up-move

Historical-analog-comparison is a side-by-side placement of a live signed-return run against completed historical runs of the same sign, ranked by cumulative extent and duration.

A then-current positive run of three consecutive quarters and a 25 percent gain was compared with 41 completed positive runs, of which 14 later posted larger cumulative gains and 15 later posted longer durations.