# Alpha Decay Dynamics

> This twelve-page report, including the colophon, examines monthly US factor premia and a systematic equity/cash rule over January 1990 through December 2025, using an August 2026 historical vintage. It compares market-only and six-factor annualized residuals under a declared 25 bp cost scenario and discusses uncertainty and limits. Includes six selected primary sources.

Published: 2026-10-11
Publisher: BlackRidge (https://blckridge.com/)
Canonical: https://blckridge.com/research/alpha-decay-dynamics-20261007/
PDF: https://blckridge.com/research/alpha-decay-dynamics-20261007/alpha-decay-dynamics-20261007-en.pdf

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# Alpha Decay Dynamics

This report examines monthly US factor premia from January 1990 through December 2025 and how estimates of unexplained returns vary with the factor model used. It also evaluates a systematic trading rule under alternative return models and declared trading-cost scenarios.

## Six factors lower the rule’s gross residual from 2.37% to 0.36%

The equity/cash rule leaves a 2.37% annualized residual under a market-only regression. With six explanatory factors and a trading-cost scenario, the estimate falls to 0.22%.

- Model
- Annual residual (%)
- 95% interval (%)
- Market-only gross
- 2.37
- −0.70 … 5.44
- Six-factor gross
- 0.36
- −2.74 … 3.46
- Six-factor net, 25 bp
- 0.22
- −2.90 … 3.34

## All six means are positive, with four intervals crossing zero

Across the full US sample, the market-excess factor averaged 8.87% a year, with a 95% interval above zero.

Monthly returns in percent. Lines compound each factor spread on a hypothetical one-unit base from January 1990 through December 2025, shown on a logarithmic scale. Long-short factor returns are zero-investment conventions, so the paths do not represent funded investor wealth. Sources: [01] [02] .

- Factor
- Annual arithmetic mean (pp/year)
- 95% interval (pp/year)
- Market excess [Mkt-RF]
- 8.87
- 3.92 … 13.82
- Size [SMB]
- 0.82
- −2.50 … 4.15
- Value [HML]
- 1.72
- −2.70 … 6.14
- Profitability [RMW]
- 4.08
- 0.85 … 7.31
- Investment [CMA]
- 1.88
- −0.87 … 4.62
- Momentum [Mom]
- 5.28
- −0.19 … 10.74

## Including momentum mechanically reduces its factor intercept to zero

The published momentum factor has an annual intercept of 7.92% in a market-only regression and 7.53% in the five-factor model. Add momentum itself as a regressor, and the fitted intercept vanishes by construction.

- Model
- Annual intercept (% per year)
- R² (%)
- Market-only
- 7.92
- 7.9
- Five-factor
- 7.53
- 15.2
- Five-factor plus momentum
- 0.00
- 100.0

## At 25 bps, the rule cut endpoint loss but lagged passive CAGR

At 25 bps, the 12-month rule had smaller endpoint losses but lower CAGR than passive US equities.

Log-scale wealth index, starting at 1 in December 1989, through December 2025. Gross trend rule, net trend rule at 25 bps, and passive market end at 36.50, 34.46, and 41.39. Market and factor inputs: [01] [02] . The 25-bps charge is a scenario, not an empirical estimate [06] .

- Cost (bps, one-way full-sleeve)
- CAGR (%)
- Annual six-factor residual (%)
- Arithmetic cost drag (pp/year)
- 10.51
- 0.36
- 0.00
- 10.44
- 0.30
- 0.06
- 10.33
- 0.22
- 0.16
- 10.16
- 0.08
- 0.32
- 9.80
- −0.20
- 0.64

## Observed residual ranks at the 66.4th percentile

Across all nonzero circular shifts, the observed six-factor residual sits at the 66.4th percentile. Gross returns rank higher.

Empirical ordered curve of annual six-factor residuals, in percentage points per year, across all 431 nonzero circular shifts of the January 1990-December 2025 signal. The horizontal reference marks the observed residual. Factor data: [01] , [02] . Method context: [03] .

- Metric
- Observed
- Rotation median
- 5th-95th range
- Rank (%)
- Gross annual excess-return mean
- 8.11
- 6.98
- 5.43 … 9.28
- 76.1
- Six-factor residual
- 0.36
- −0.08
- −1.86 … 2.21
- 66.4

## Six-factor residual turns positive, but the difference includes zero

Across two equal windows, the estimated annual unexplained return changes sign. The later-minus-earlier estimate remains too imprecise to distinguish from zero.

Monthly decline from the prior peak, in percent, January 1990 to December 2025. Compares the 12-month rule net of 25 basis points per trade with buy-and-hold market returns. Factor inputs use the French Data Library’s 202608 vintage, including the data reconstruction from January 2025 [01] [02] .

- Period
- Months
- Annualized six-factor residual (%)
- Approximate normal 95% interval (%)
- CAGR (%)
- January 1990 to December 2007
- −1.40
- −4.39 … 1.58
- 11.29
- January 2008 to December 2025
- 1.83
- −3.21 … 6.87
- 9.38

## All four residual intervals cross zero

Across tested lookbacks, annual residual estimates remain modest after trading costs. Every reported interval spans zero, so this sample does not establish a positive residual.

Bars show annual residual estimates for fixed 6-, 9-, 12-, and 18-month lookbacks, in percentage points per year. Whiskers are 95% intervals, all crossing zero. Period: January 1990 to December 2025, 432 monthly observations. Returns use the 202608 US five-factor and momentum data vintages [01] [02] . The factor-model context is Fama and French [04] .

- Lookback (months)
- Exposed months (%)
- One-way changes
- CAGR (%)
- Annual residual (pp/year)
- 95% band (pp/year)
- 74.8
- 9.11
- 0.68
- −2.66 … 4.03
- 79.4
- 9.62
- 0.24
- −2.90 … 3.37
- 81.5
- 10.33
- 0.22
- −2.90 … 3.34
- 83.6
- 9.45
- −0.29
- −3.26 … 2.67

## At 25 bp, rolling residual estimates span -3.84 to 4.39 pp/year

At a 25-basis-point cost assumption, the six-factor model leaves an annualized residual estimate of 0.22 percentage points. The uncertainty range crosses zero.

Percentage points per year. Annualized six-factor residual estimates after the 25 bp cost assumption, with 95% Newey-West confidence bands, across rolling 120-month windows dated Jan 1999 to Dec 2025 [01] [02] [04] .

- Newey-West lag (months)
- Annual estimate (percentage points per year)
- 95% interval (percentage points per year)
- 0.22
- −2.29 … 2.73
- 0.22
- −2.71 … 3.15
- 0.22
- −2.90 … 3.34
- 0.22
- −2.77 … 3.21

## At 25 bp, the rule's annual residual is 0.22%

After six-factor adjustment, this illustrative US rule retains an estimated annual residual of 0.22% under a 25 bp cost scenario. Persistent alpha is not established.

- Check
- Observed measure
- What remains unknown
- 01 Model adjustment
- 2.37 → 0.36
- The intercept depends on included factors; unexplained return is model-specific.
- 02 Cost case
- 0.22
- The 25 bp assumption is a scenario, not observed fills, spreads, slippage or financing.
- 03 Rotation rank
- 66.4%
- The circular-shift percentile is a diagnostic, not a universal null distribution.
- 04 Half-sample gap
- −2.61 … 9.07
- The interval spans zero and wide differences, so stability across the two halves remains unresolved.

## Two primary files match across 432 months through December 2025

Both primary files match for 432 months from January 1990 through December 2025 in the August 2026 archive, a frozen historical endpoint rather than the latest observation [01] [02] . CIZ reconstructs history from January 2025, the risk-free provider changes in June 2024, and real-time vintages were not validated. Signals use pre-sample returns, and every result is computed from the primary series rather than copied from paper abstracts [01] [02] .

In this report, we matched the monthly momentum series to the five-factor series by month and used momentum as the sixth explanatory series. This is a modelling choice in this report, not a six-factor model prescribed by the source.

CIZ reconstruction from January 2025. Risk-free provider change, June 2024. Market-return warm-ups: Jan-Dec 1989 (12 months), Jul 1988-Dec 1989 (18 months). Both files match all months without drops. Codes -99.99/-999 fail validation, no imputation.

Our circular-shift diagnostic compares the observed strategy with 431 shifted paths, a construction of this analysis rather than a replication of the paper's random model.

U.S. equities, USD. Factor portfolios follow the sources' published gross-return conventions, while the market factor is measured above the risk-free rate [01] [02] . Strategy returns are gross until illustrative switch-month costs are applied. Premiums and fitted intercepts are annualized percentage points. The cost cases are assumptions, not execution-cost estimates. These historical calculations are not investable fund performance or personal investment advice.

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## Sources

- [01] [Kenneth R. French Data Library, U.S. 5 Factors](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_5_factors_2x3.html).
- [02] [Kenneth R. French Data Library, Momentum Factor](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_mom_factor.html).
- [03] [The Mathematics of Market Timing, PLOS ONE (2018)](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0200561).
- [04] [Fama and French, A five-factor asset pricing model, Journal of Financial Economics (2015)](https://www.sciencedirect.com/science/article/pii/S0304405X14002323).
- [05] [McLean and Pontiff, Does Academic Research Destroy Stock Return Predictability?, Journal of Finance (2016)](https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12365).
- [06] [Frazzini, Israel, and Moskowitz, Trading Costs of Asset Pricing Anomalies, working paper (December 2012)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2294498).

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## Citation context

The annualized residual is 2.37% gross under a market-only model, 0.36% gross under a six-factor model, and 0.22% net under the six-factor model with a declared 25 bp cost scenario. The net estimate is an annualized regression intercept, not CAGR. Its 95% interval, -2.90% to 3.34%, includes zero.

The retrospective rule is evaluated on 432 monthly US observations from January 1990 through December 2025, using the August 2026 historical vintage. Residuals are annualized regression intercepts, with the six-factor specification adding size, value, profitability, investment, and momentum controls.

This is a retrospective US equity/cash illustration, with no untouched future test or live provider or FX evidence. It establishes no universal decay rate, and zero is not proven. Costs are assumptions, not measured execution costs.

Primary input: [Kenneth R. French Data Library, U.S. 5 Factors](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_5_factors_2x3.html).

Stable permalink: [https://blckridge.com/research/alpha-decay-dynamics-20261007/#citation-context](https://blckridge.com/research/alpha-decay-dynamics-20261007/#citation-context).

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