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.
October 2026
BlackRidge Research
BlackRidge Research: Alpha Decay Dynamics01
BlackRidge
FACTOR MODELS | 1990–2025
02 / 11
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%.
Market-only residual
2.37%
2.37% annualized
Six-factor net residual
0.22%
0.22% after 25 bp costs
Monthly observations
432
432 months
Market-only gross
2.37%
Six-factor gross
0.36%
Six-factor net, 25 bp
0.22%
Annualized residuals in percent per year for the 12-month equity/cash rule, January 1990 through December 2025, 432 months, August 2026 archive. Factor data and momentum series [01][02]. Factor-model limitations [04].
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
Observation
All fits use the same 432 monthly observations, January 1990 through December 2025, from the August 2026 archive. The net 0.22% estimate is alpha: 12 times the monthly excess-return regression intercept, not CAGR. Its 95% Newey-West interval is -2.90% to 3.34%. The interval crosses zero.
Interpretation
Model choice moves the estimate. A market-only fit leaves 2.37% a year; adding size, value, profitability, investment and momentum reduces the gross residual to 0.36%. The 25 bp scenario takes it to 0.22%. The 0.14-point gross-to-net change differs from the 0.16-point arithmetic cost drag because each regression is refitted.
Practical implication
The results show model dependence. They cannot establish zero skill or universal decay. A separate momentum-identity experiment excludes this trading rule from its own regressors.
Limitations
Fixed factor loadings cannot fully identify the timing rule’s changing exposures. Factor models have documented failures [04]. Rule selection remains unknown. This retrospective illustration has no untouched future test or live returns. Factor data come from the Kenneth French library [01], with its momentum series [02].
BlackRidge Research: Alpha Decay Dynamics02
BlackRidge
US FACTOR RETURNS | 1990 TO 2025
03 / 11
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.
Hypothetical accumulated value, log scale
Market excess [Mkt-RF]Value [HML]Momentum [Mom]
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
Observation
Profitability (4.08%) and momentum (5.28%) averaged positive returns. Profitability clears zero. Momentum's interval dips just below it. Size, value, and investment intervals cross zero. A positive factor mean alone says little about whether a particular trading rule will retain unexplained returns. No premium is guaranteed.
Interpretation
The 12-month rule returned a 10.3% compound annual rate in the 25 bp cost scenario. Yet its six-factor unexplained return was 0.22% a year, with a 95% interval from -2.90% to 3.34%. Zero remains plausible.
Practical implication
Adding factors raises the share of rule returns accounted for by the model from 64.3% to 71.5%, while reducing the estimated intercept from the market-only fit. A high compounded return and weak evidence of unexplained performance can coexist. Here, model choice changes the answer.
Limitations
The chart compounds each monthly factor spread on a hypothetical one-unit base and uses a logarithmic scale. Long-short factor returns follow zero-investment conventions, so these paths are not funded investor wealth. The sample covers US data from January 1990 through December 2025 [01][02]. Factor models have documented failures [04]. These results establish neither persistent alpha for an individual rule nor transferability from US equities to FX.
BlackRidge Research: Alpha Decay Dynamics03
BlackRidge
Factor-model identification check
04 / 11
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.
Market-only intercept
7.92%
7.92% per year.
Five-factor intercept
7.53%
7.53% per year.
Inclusion identity
0.00%
0.00% per year by construction.
Market-only
7.92%
Five-factor
7.53%
Five-factor plus momentum
0.00%
Units are percent per year for the annual intercept. The chart compares the published momentum factor regressed on the market alone, the five-factor model, and the five-factor model plus momentum, from January 1990 to December 2025 (432 months, 202608 source vintage) [01][02]. The final zero follows because momentum is the dependent series and one of its own regressors [02]. This identity makes no statement about unexplained returns elsewhere [04].
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
Observation
Each regression uses 432 monthly observations from January 1990 to December 2025. The downloaded 202608 factor files define the momentum series through size and prior 2-to-12-month returns [01][02].
Interpretation
The first two fits leave positive intercepts, while R² rises from 7.95% to 15.17%. With momentum on both sides of the equation, the zero intercept and 100% R² follow from identity. The result is mechanical. It does not estimate an independent premium.
Practical implication
This comparison isolates model dependence: a factor omitted from the controls can appear in the intercept, then disappear when included. That is a useful diagnostic for regression setup. The same logic cannot settle whether a separate portfolio or trading rule has unexplained return after controls.
Limitations
The five-factor model has documented empirical limitations [04]. Here, zero carries no meaningful confidence interval or significance test because the dependent series is included among the regressors. No rule is tested. The zero is a construction check. It offers no evidence that momentum premiums vanish across assets or strategies.
BlackRidge Research: Alpha Decay Dynamics04
BlackRidge
BACKTEST | US EQUITIES | JANUARY 1990 TO DECEMBER 2025
05 / 11
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.
Wealth index (initial value = 1)
Trend rule, grossTrend rule, net at 25 bpsPassive US market
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)
0
10.51
0.36
0.00
10
10.44
0.30
0.06
25
10.33
0.22
0.16
50
10.16
0.08
0.32
100
9.80
−0.20
0.64
Observation
At each month’s start, the rule multiplies the prior 12 completed monthly total-market returns. A product above 1 sends the portfolio into the US market for that month. Otherwise, it holds Treasury bills. The current month never enters the signal. Monthly return equals the risk-free rate plus q times market excess return, less one-way cost times the absolute change in q. Initial q is zero. The rule made 23 full-sleeve changes, including entry, and held equities in 81.48% of 432 months, from January 1990 through December 2025 [01][02].
Interpretation
At 25 bps, CAGR was 10.33% versus 10.90% for passive market exposure. Monthly-endpoint maximum drawdown was -21.09% versus -50.31%. Six-factor annual residual was 0.22 percentage points, with a 95% interval from -2.90 to 3.34. It spans zero.
Practical implication
Charges of 0, 10, 25, 50, and 100 bps are scenarios, not empirical cost estimates. At 25 bps, arithmetic drag is 0.16 percentage points per year. Frazzini et al. report that cost-aware implementation can retain anomaly premiums [06].
Limitations
Financing, taxes, fees, and terminal liquidation are excluded.
BlackRidge Research: Alpha Decay Dynamics05
BlackRidge
CIRCULAR-SHIFT DIAGNOSTIC
06 / 11
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.
Annual six-factor residual (pp/year)
Circular-shift residualObserved residual
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
Observation
The test rotates a 432-month binary signal through the full calendar, retaining 352 invested months, or 81.48% exposure, and the cyclical holding-run pattern. Annual arithmetic excess return averages 8.11%, against a rotation median of 6.98%. The observed mean ranks at 76.1%. The six-factor residual is 0.36 percentage points per year, against a median of -0.08 and a 5th-95th range from -1.86 to 2.21. [01][02]
Interpretation
That gap matters. The gross result ranks higher than the residual, yet neither percentile is a probability that the rule works.
Practical implication
Each shift preserves the signal's sequence and changes its alignment with returns. The residual rank offers limited evidence that factor-adjusted performance stands apart under this diagnostic. It does not establish durable alpha.
Limitations
The paths depend on one another, so 431 shifts are not independent trials. They are not out-of-sample: each rotation uses the full observed series, including future information, and is not tradable as a historical alternative. A calendar boundary can split a holding run. Costs are omitted. Nonstationarity and lack of exchangeability rule out formal significance. This disclosed construction is ours, not a replication of the random-path model in [03].
BlackRidge Research: Alpha Decay Dynamics06
BlackRidge
BlackRidge Research | Factor-model comparison
07 / 11
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.
Decline from prior peak (%)
12-month rule, net of 25 basis points per tradeBuy-and-hold market
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
216
−1.40
−4.39 … 1.58
11.29
January 2008 to December 2025
216
1.83
−3.21 … 6.87
9.38
Observation
The fixed 12-month rule charges 25 basis points per trade. Its annualized six-factor residual is −1.40% from January 1990 to December 2007, then +1.83% from January 2008 to December 2025. Each window spans 216 months. Approximate normal 95% intervals are [−4.39%, +1.58%] and [−3.21%, +6.87%] [01][02].
Interpretation
A single regression with factor interactions estimates the later-minus-earlier change at +3.23 percentage points. Its approximate normal 95% interval runs from −2.61 to +9.07 points. The interval includes zero. We use a six-lag Newey and West correction, with covariance carried across the window boundary.
Practical implication
Holding the lookback and transaction cost fixed prevents parameter retuning from explaining the contrast. Even so, the six-factor intercept depends on the chosen model. Other controls could produce another residual [01][02].
Limitations
McLean and Pontiff discuss attenuation after academic publication as one possible explanation for weaker return predictability. This analysis does not measure publication effects, identify a cause, or estimate a permanent decay rate [05].
BlackRidge Research: Alpha Decay Dynamics07
BlackRidge
BLACKRIDGE RESEARCH | FACTOR RETURNS
08 / 11
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.
Annual residual (percentage points per year)
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)
6
74.8
49
9.11
0.68
−2.66 … 4.03
9
79.4
41
9.62
0.24
−2.90 … 3.37
12
81.5
23
10.33
0.22
−2.90 … 3.34
18
83.6
21
9.45
−0.29
−3.26 … 2.67
Observation
The four rules share 432 monthly observations from January 1990 through December 2025, with 25 basis points charged per one-way change. Exposed time rises from 74.8% to 83.6% as the lookback lengthens, while changes fall from 49 to 21. Net CAGR ranges from 9.1% to 10.3%. Annual residual estimates run from −0.29 to 0.68 percentage points, and each six-lag 95% interval includes zero [01][02].
Interpretation
Model choice changes the reading. For the 12-month rule, a market-only regression estimates 2.22 percentage points of annual residual return. The six-factor specification gives 0.22. Its interval remains wide, and the residual is better read as model-dependent than as a stable property of the rule. Factor models have documented limits [04].
Practical implication
CAGR stays positive across these settings, but the table cannot establish return beyond factor exposures. The point estimates are small beside their uncertainty.
Limitations
These are neighboring settings, not the full search universe. Earlier trials are unknown, so a multiplicity-adjusted discovery claim is unavailable. The French data library notes a CIZ reconstruction from January 2025 and a risk-free provider change in June 2024 [01][02].
BlackRidge Research: Alpha Decay Dynamics08
BlackRidge
BLACKRIDGE RESEARCH | FACTOR MODEL
09 / 11
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.
Annualized residual estimate (percentage points per year)
Annualized estimate95% lower bound95% upper bound
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
0.22
−2.29 … 2.73
3
0.22
−2.71 … 3.15
6
0.22
−2.90 … 3.34
12
0.22
−2.77 … 3.21
Observation
Across 313 overlapping rolling windows of 120 months each, annualized estimates range from -3.84 to 4.39 percentage points. A positive estimate in one window is a point estimate, not evidence of a persistent premium. The windows share most of their observations, so they do not amount to 313 independent tests.
Interpretation
For the full sample, the 95% interval runs from -2.90 to 3.34 percentage points per year. Changing the Newey-West lag changes its width, but all four intervals include zero. The annualized estimate remains 0.22 percentage points.
Practical implication
A fixed market beta can miss changing exposure as a trading rule shifts its positions. The residual therefore describes what this six-factor specification leaves unexplained, rather than a stable measure of trading skill.
Limitations
Newey-West standard errors account for dependence up to a chosen lag. They do not adjust for unknown model selection or repair a misspecified factor model. Fama and French discuss documented limits of factor-model fit [04].
BlackRidge Research: Alpha Decay Dynamics09
BlackRidge
BlackRidge Research | Alpha decay dynamics
10 / 11
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.
0.22% net residual
0.22%
Annual six-factor intercept under the 25 bp cost scenario.
25 bp cost case
25
Declared implementation-cost scenario, not a measured trading cost.
432 months
432
January 1990 through December 2025.
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.
Observation
Model choice matters. The market-only intercept is 2.37% a year, falling to 0.36% under six factors. Costs erode it to 0.22%. The net 95% interval, −2.90% to 3.34%, spans zero [01][02][04].
Interpretation
A circular-shift test ranks the residual at the 66.4th percentile of 431 rotations [03]. That result does not establish absence of skill, nor does it show that all rules fail.
Practical implication
The two equal halves also disagree in point estimates: −1.40% versus 1.83% a year, but the interval for their difference stretches from −2.61% to 9.07%. Before calling live performance durable skill, test mandate-specific factor exposure against actual fills, spreads, slippage and financing [06]. Freeze the dated rule and complete experiment registry, then use an untouched future period and a timing diagnostic with a defensible null distribution.
Limitations
Factor models may omit priced risks, and publication can attenuate reported predictability [04][05]. This is a constructed US cash/equity illustration, not BlackRidge provider results or foreign-exchange evidence. Research only. Not personal investment advice.
BlackRidge Research: Alpha Decay Dynamics10
BlackRidge
DATA SOURCES / U.S. EQUITIES / MONTHLY
11 / 11
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].
The source reports monthly U.S. returns for six value-weighted portfolios formed on size and prior returns over months 2-12. Its momentum factor is the average return on the two high-prior-return portfolios minus that on the two low-prior-return portfolios.
Fama and French set out a five-factor asset-pricing model and discuss cases where it fails to account for average returns. We use the article for methodological context only. All results are recalculated from source files, not the paper's reported statistics.
McLean and Pontiff test whether publication is followed by weaker stock-return predictability. We use their paper as one possible explanation for attenuation. It does not establish a universal half-life, and we import no study percentages into the calculations here.
The authors analyze implementation costs across asset-pricing anomalies and show that cost-aware implementation can retain returns. Our 0, 10, 25, 50, and 100 basis-point cases are declared sensitivities, not estimates from this paper. Each switch-month return is reduced by the one-way full-sleeve charge.
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.
BlackRidge Research: Alpha Decay Dynamics11
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.
When you use a result that another publication established, cite that original work; it is linked in Sources. Cite this report for our synthesis, explanation or an identified recalculation. No link is required in return.
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