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2020issue C078-13

Stock power ratio as a growth trend filter

This editorial article reconstructs a historical workflow that turns a growth-rate input into a growth-forecast baseline, then measures persistence by comparing signal power with noise power over a fixed lookback. The power ratio is taught as a trend filter, not as a forecast of returns.

  • A growth-forecast baseline maps a growth-rate input and an interpolated earnings path into a multi-year price-change projection and is used only as a quantitative baseline, not as a valuation verdict.
  • Moving-window power averages squared, lookback-normalized price changes so the measure is scale-free. The same calculation on the moving-average signal component and the residual noise component yields signal power and noise power.
  • A power ratio compares those two energies and functions as a trend filter over a defined sampling interval and lookback, not as a return forecast.
  • Market-cap-weighted power can be charted for the whole universe or inside size buckets. In the archive charts the combined ratio is largest at the 100-day window, smallest at the 20-day window, and highest among mega caps, with group ratios diverging on rallies and converging on selloffs.
Entries in this reading3 entries
Current trackFourier analysis41 readingsTrend following168 readingsTrend filter184 readings

Start with a growth-forecast baseline

A growth-forecast baseline is a multi-year price-change projection built from an earnings path and a growth-rate input. The archive uses that projection only as a quantitative baseline rather than as a valuation verdict.

The construction is meant to be testable. Once growth has been written as an explicit price-change path, a later measure can ask how much of the associated price series looks persistent over a defined sampling interval and lookback.

Turn growth into a price-change path

A 1962 valuation identity maps a growth-rate input G and an earnings forecast E into a price forecast by scaling earnings with the factor 8.5 plus twice G. A zero-growth name is assigned a price of 8.5 times earnings.

A five-year price path can be assembled from a five-year consensus growth forecast and an earnings path obtained by linear interpolation of last-year, current-year, and next-year earnings expectations. That path is then converted into an annualized percent change labeled growth.

Applying the same construction across a universe of about 2,253 US names produces a cross-section of price forecasts and annualized growth values that can be used as a quantitative baseline.

Measure energy, then split signal from noise

Moving-window power at time j is the average of squared price observations in an N-length window. Each observation is divided by the window first price so the measure is scale-free and tracks changes rather than raw levels. The same quantity is a discrete-signal estimate of how much energy the series carries in that window.

Price is split into an N-day moving-average signal component and a noise component equal to price minus that moving average. The same lookback-normalized power calculation is then run separately on each component, giving signal power and noise power.

A power ratio is a scaled comparison of signal power with noise power. In this workflow it is used as a trend-strength filter rather than as a return forecast. A trend filter admits, ranks, or withholds names according to measured trend strength over a defined sampling interval and lookback.

Inspect the power ratio on controlled series

On synthetic linear ramps and sinusoids with added 0.1% noise, a threshold-scaled square-root power ratio rises with slope or amplitude, approaches a limit on linear series, and oscillates on sinusoidal series.

A scatter of Sharpe ratio against signal and noise power ratios, shown with 20-day and 50-day moving averages, is used to inspect whether the constructed power measures line up with a risk-adjusted return statistic. The archive presents that scatter as an inspection. This editorial article does not treat the scatter as evidence that the power ratio forecasts return.

Read capitalization-weighted power

Capitalization-weighted averages of signal and noise power at 20-day, 50-day, and 100-day windows can be charted as a market-wide trend filter. That aggregate is market-cap-weighted power. In the archive charts the combined power ratio is largest at the 100-day window and smallest at the 20-day window.

The same capitalization-weighted construction applied inside mega-cap, big-cap, mid-cap, and small-cap buckets, plus an S&P 500 reference, shows mega caps with the highest power. Group power ratios diverge on rallies and converge on selloffs.

Keep trend following a separate procedure

Trend following, as used here, is a procedure that turns the filter output, together with market state, into explicit entry, exit, or abstention decisions over a holding period. The archive describes that as one testable procedure.

This editorial article stops at the construction of the growth-forecast baseline and the power-ratio trend filter. It does not specify those decisions and it does not recommend trades.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
26 of 26 in the Fourier analysis track
1992Track finished · Next track: Fractal indicatorConstructing fractal templates from successive index changes14 readings
All readings on this track · 26 readings
  1. 1982Critiquing Fourier, Elliott, and seasonal commodity models
  2. 1982Evaluating half-hour crossovers with cycle priors and stops
  3. 1984Building moving-window spectral cycle forecasts
  4. 1988Fourier cycles versus calendar seasonal regimes
  5. 1989Constructing analog cycle signatures from price lows
  6. 1990Curve fits fail the forecast test
  7. 1991Auditing moving-average length with Fourier spectra
  8. 1991Closed-form phase for dominant-cycle spectra
  9. 1993Evaluating windowed spectral forecasts of index turning points
  10. 1994Window length for moving-window spectral forecasts
  11. 1994Constructing WAMI power and phase spectra
  12. 1994Fourier-tuned momentum filter design
  13. 1994Aliasing, leakage, and dominant-cycle reads from sampled prices
  14. 1995Constructing indicator lookbacks from Fourier spectra
  15. 1996Constructing phase from a dominant-cycle sine and cosine pair
  16. 1999Sinusoidal pseudo-securities for indicator evaluation
  17. 2000Constructing dominant cycle length from Hilbert phase
  18. 2000Constructing adaptive channel breakouts from a measured cycle period
  19. 2005Embedding forex prices into a singular-spectrum forecast basis
  20. 2005Constructing recurrent forecasts from grouped spectral components
  21. 2007Constructing a dominant cycle from transformed Fourier spectra
  22. 2010Why cycle indicators fail when parameters shift
  23. 2019Constructing futures momentum as open-interest-scaled rate of change
  24. 2019Judging a dominant cycle and a trend filter by sample, lag and the move they keep
  25. 2020Constructing futures turnover time and urgency
  26. 2020Stock power ratio as a growth trend filter
By fieldIndicators and filters874 readingsBy year2020165 readings
All 41 readings tagged Fourier analysis
Also on Fourier analysis5 readings
1999Sinusoidal pseudo-securities for indicator evaluation2019Judging a dominant cycle and a trend filter by sample, lag and the move they keep2020Constructing futures turnover time and urgency1982Building FFT spectra to size cycle filters1982Critiquing Fourier, Elliott, and seasonal commodity models