2003issue C101-7
How a one-rank rotation is constructed for an offset autocorrelation check
A one-rank mutual-fund rotation is constructed so a low annual switching rate can be treated as evidence of longer-than-random streaks, then inspected with Osc1, an offset autocorrelation statistic stated through switching rate and directional bias.
- A one-rank rotation is constructed so a low annual switching rate can be treated as evidence of longer-than-random up and down streaks.
- Osc1 is built from Pearson's correlation so persistence is stated through switching rate and directional bias, without a magnitude scale that obscures comparison.
- The unrotated sample showed a negative tilt that overstated buy-and-hold results; after the orls filter the same funds showed a positive tilt.
- A low switching rate is treated as necessary to the one-rank construction, and the rotation remains difficult to implement.
What the one-rank rule holds
A one-rank rotation is a mechanical mutual-fund rule that stays in the single highest-ranked fund under a defined switching rule. The long-short form of that rule is orls.
The construction treats a low annual switching rate as evidence of longer-than-random up and down streaks. Those streaks are then inspected with an offset autocorrelation statistic.
Switching rate and net-up days
Switching rate is defined as yearly fund days divided by streak period. With 252 yearly days and a switching rate of 42, the implied streak period is 6 days and the long-short net-up-day count is 84.
Net-up days are the simplified day-count remainder used to convert a yearly sample into an approximate compounded gain.
Negative tilt in the unrotated sample
Across 40 equity funds observed over 13 years from 1989 through 2001, average daily up-move and down-move magnitudes both rose linearly with daily standard deviation. The reported slope was near 0.65 for the unrotated sample.
That unrotated sample showed a negative tilt. Down-day magnitude often exceeded up-day magnitude by more than 0.1 percentage point, so a net-up-day gain formula overstated actual buy-and-hold results.
Positive tilt after the orls filter
After the long-short one-rank filter, the same fund sample showed a positive tilt of about 0.1 percentage point. Plotted actual rotation gains sat above the calculated-gain line rather than below it.
How Osc1 states persistence
Osc1 is constructed from Pearson's correlation so persistence can be stated through switching rate and directional bias. That step removes a magnitude scale that otherwise obscures comparison.
Directional bias is the share of sample days that close higher. It is treated as a persistence input rather than a forecast.
Comparison with the buy-and-hold baseline
Plots of annual return against Osc1 and against daily standard deviation are used to compare the rotation construction with an explicit buy-and-hold baseline on the same 40-fund sample from 1989 through 2001.
The archive workflow treats a low switching rate as necessary to the one-rank construction and presents offset correlation as a way to relate that rate to directional bias. It also states that the rotation remains difficult to implement.
All readings on this track · 15 readings
- 1987Evaluating weekly price cycles with autocorrelation cutoffs
- 1988Serial correlation is not an independence test
- 1988Event-triggered chi-square tests for jittered serial links
- 1988Reverse the rule before you trust the system
- 1990Chi-square evaluation of lagged breadth correlations
- 1990Two-gate out-of-sample tests for trading rules
- 1990Sign-cell correlation, chi-square checks, and lag shifts
- 1998Test serial dependence before you optimize a mechanical system
- 2003How a one-rank rotation is constructed for an offset autocorrelation check
- 2004Constructing first-order residual autocorrelation tests
- 2004A two-stage Durbin-Watson residual screen
- 2011Constructing trend labels from increment correlation atoms
- 2012Overnight versus daytime return evaluation
- 2012Constructing a multi-horizon folded-correlation reversal filter
- 2016Tuning indicators to measured market cycles