Can a Portfolio of Farmed Signals Harvest a Factor Premium?
From a pile of signals to a portfolio
88 cross-sectional signals 45 market-timing rules 8 themes Oct 2003–Jan 2024, monthly, net of 10bp
The question
The main farming page asks of each signal: does this predict returns on its own? Most of the library fails that test after correcting for the size of the search, and a reasonable response is that single signals were never the point. Weak, imperfectly correlated edges are supposed to add up. That is the whole argument for multi-factor portfolios.
So this study takes the argument seriously. It asks three things:
- What did the farm actually find? A map of the library by theme, data source and origin.
- Do the signals diversify each other? Correlation structure and the effective number of independent bets.
- Does a combination harvest a premium, and is it a factor premium? Five blends, each regressed on market, size, value and momentum factors built from the same panel.
Two rules keep the blends honest. Every signal keeps the sign its idea agent committed to before the backtest; nothing is flipped because it lost money. And the catalog keeps every idea that was implemented, regardless of how it performed, so “all live signals” is not a set chosen by outcome. Near-duplicates (|correlation| above the novelty threshold) are excluded so one bet is not counted twice. The two adaptive blends size month t using returns through month t−1 only.
1. What the farm found
The catalog’s own categories are coarse: a third of the library was filed as “other”. Sorting by what the signal actually does gives eight cross-sectional themes, plus the market-timing rules, which are a different kind of strategy altogether (a time-varying market exposure rather than a long/short stock book).
| Theme | Signals | Median Sharpe | Positive | Theme blend Sharpe | Best single signal | Data used |
|---|---|---|---|---|---|---|
| Value | 5 (2 textbook) | +0.19 | 100% | +0.46 |
retained_vs_contributed_capital_value (+0.38)
|
price 60%, fundamental 60%, macro 20% |
| Momentum | 3 (1 textbook) | -0.08 | 33% | +0.09 |
momentum_12_1 (+0.27)
|
price 67%, macro 33%, fundamental 33% |
| Quality | 26 (2 textbook) | +0.09 | 65% | +0.16 |
gross_profitability (+0.92)
|
fundamental 92%, price 38%, macro 15% |
| Investment | 6 (2 textbook) | +0.35 | 83% | +0.63 |
payout_funding_gap (+0.82)
|
fundamental 67%, price 33%, macro 17% |
| Low risk | 10 (2 textbook) | +0.11 | 70% | +0.14 |
macro_systematic_variance_share (+0.57)
|
price 90%, macro 90%, fundamental 30% |
| Seasonality | 17 | -0.57 | 12% | -0.76 |
predicted_dividend_month_premium (+0.41)
|
price 100%, fundamental 18% |
| Reversal & attention | 7 | -0.10 | 29% | -0.23 |
quiet_strength_low_attention_high (+0.22)
|
price 100%, macro 43% |
| Macro exposure | 14 | -0.09 | 29% | -0.28 |
oil_beta_trend_interaction (+0.10)
|
macro 100%, price 93%, fundamental 50% |
| Market timing | 45 (2 textbook) | -0.01 | 49% | +0.16 |
stagflation_supply_shock_timing (+0.52)
|
macro 73%, price 49%, fundamental 22% |
The shape of the library says something about how the idea agent searches. It went deepest where the accounting data is richest: 26 quality and earnings-quality ideas, nearly all built on fundamentals. The second-largest cluster is calendar seasonality (17 ideas), built mostly from price data, and it is the worst-performing theme in the library. Only 12% of those signals have a positive Sharpe, and their 1/N blend runs at -0.76. Many are variations on published calendar anomalies (same-month return persistence, tax-loss selling around the turn of the year), and on this universe and period, net of costs, they lost steadily. Reversing their signs now would be exactly the after-the-fact decision the study refuses to make.
Value and investment are the only themes where a clear majority of ideas work. They are also small and close to the textbook: 4 of their 11 signals are the reference anomalies the harness ships with.
2. How different are they?
The library is genuinely diverse. The average absolute correlation between two signals’ returns is 0.17. Themes are weak clusters: two signals from the same theme correlate +0.054 on average, barely more than two from different themes (+0.004). The eigenvalues of the correlation matrix put the library at about 15 effective independent bets out of 88. That is plenty of room to diversify.
The exception is on the right: the quality and investment blends correlate 0.71. Low accruals, conservative payouts and restrained asset growth describe the same kind of company, and the returns agree.
3. Diversification converges — to the average
This chart is the key to everything that follows. Blending does exactly what it promises: the spread of outcomes collapses, from a 10th–90th percentile range of -0.59 to 0.40 for one signal to a single number for all 88, and volatility falls from 12.3% to 2.3% a year. But diversification removes noise. It does not add edge. It converges on the average signal, and in this library the average signal loses money after costs. The median line slopes gently down: the more signals you blend, the more certainly you get the library’s mean, which is -0.17 Sharpe.
4. Five ways to combine
| Blend | Sharpe | Ann. return | Ann. vol | Max drawdown | Sharpe pre / post 2012 |
|---|---|---|---|---|---|
|
Equal weight 1/N across every cross-sectional book |
-0.17 | -0.4% | 2.3% | -18.2% | -0.34 / -0.13 |
|
Theme parity 1/N across the eight theme blends, so 26 quality ideas count once |
0.05 | 0.1% | 2.4% | -13.5% | 0.08 / 0.04 |
|
Inverse vol each book weighted by 1 / trailing 36-month volatility |
-0.31 | -0.6% | 1.7% | -19.5% | 0.18 / -0.51 |
|
Trailing winners 1/N across books with a positive trailing 60-month mean; cash if none |
0.22 | 0.9% | 4.6% | -14.9% | 0.27 / 0.19 |
|
Integrated score one decile book on the average cross-sectional rank of every signal |
0.36 | 4.0% | 13.3% | -45.7% | 0.57 / 0.31 |
- Equal weight lands at -0.17, as the diversification curve predicted.
- Theme parity caps each theme at one-eighth of the book, so the 26 quality ideas no longer outvote the 5 value ideas. That lifts Sharpe to +0.05, which is still zero for practical purposes.
- Inverse vol is the worst of the five (-0.31). The lowest-volatility books in this library are disproportionately the losing ones (the calmest third has a median Sharpe of -0.22, the most volatile third +0.01), so risk parity scales the losers up.
- Trailing winners holds only books whose trailing five-year mean is positive (a median of 39 of 88 at any time). It recovers +0.22. That is consistent with factor momentum, but it is not distinguishable from zero (t = 0.99).
- Integrated score is the only blend that clears the others comfortably, at +0.36. It is also a different animal. Averaging ranks before trading lets opposing views on a stock cancel out, so the book concentrates on names most signals agree on. It runs at 13.3% volatility against 2.3% for the return blend, with a -45.7% maximum drawdown and one-way turnover of 1.22 a month (the median single signal turns over 0.59).
4 of the 5 blends are weaker after 2012 than before, in line with the evidence that anomalies decay once published. The exception is equal weight, which loses less in the second half, though losing less is not the same as working.
5. Whose premium is it?
A blend that earns something might be harvesting new return, or it might be a roundabout way to own the factors everyone already knows. Regressing each blend on market, size, value and momentum separates the two.
| Blend | β MKT (t) | β SMB (t) | β HML (t) | β UMD (t) | Alpha / yr | Alpha t | R² |
|---|---|---|---|---|---|---|---|
| Equal weight | -0.02 (-3.2) | -0.10 (-8.1) | +0.16 (7.5) | +0.11 (5.5) | -0.7% | -1.75 | 56% |
| Theme parity | -0.02 (-2.4) | -0.11 (-7.0) | +0.19 (6.8) | +0.10 (5.4) | -0.2% | -0.49 | 53% |
| Inverse vol | -0.02 (-3.4) | -0.07 (-7.1) | +0.13 (8.0) | +0.06 (3.4) | -0.7% | -2.07 | 46% |
| Trailing winners | -0.02 (-1.5) | -0.19 (-5.7) | +0.17 (4.7) | +0.25 (9.1) | +0.4% | 0.57 | 62% |
| Integrated score | -0.21 (-6.9) | -0.50 (-6.7) | +0.95 (8.7) | +0.59 (8.0) | +4.6% | 2.36 | 60% |
How to read this. Betas are loadings on the factor long/short portfolios (t-stats in brackets, Newey-West). Alpha is the return the four factors do not explain; it is the part of the premium that is actually the library’s own.
The loadings are the clearest result on the page. Every blend is long value, long momentum and short small caps, with t-stats between 3 and 9, and the four factors explain 46–62% of every blend’s variance. Individually the signals looked diverse. In aggregate the library leans the way the academic literature leans, because that is where the idea agent most plausibly learned what a good signal looks like.
So the blends do harvest factor premia, in the sense that they load on them. The problem is what those premia paid over this window:
| Factor | Ann. return | Sharpe | t-stat (NW) |
|---|---|---|---|
| MKT Market (equal-weighted universe) | 9.0% | 0.54 | 2.45 |
| SMB Size: small minus big | -2.4% | -0.20 | -0.96 |
| HML Value: low minus high price/book | 0.1% | 0.06 | 0.24 |
| UMD Momentum: winners minus losers | 0.9% | 0.13 | 0.59 |
Over Oct 2003–Jan 2024, value was flat, momentum barely positive and size negative; only the market paid. A portfolio that loads on HML and UMD collects roughly nothing from those loadings. That is why the return blends have alphas near zero or below: equal weight -0.7% a year (t = -1.75), inverse vol t = -2.07.
The integrated book is the exception, with alpha of +4.6% a year (t = 2.36). Look at its betas, though: an HML loading of 0.95 and a UMD loading of 0.59, several times the return blends’. Integrating scores turned a mild, diluted factor tilt into a concentrated one. The alpha clears t = 2 only narrowly, and it is the best of five combinations tried, before any correction for having tried five.
By theme: which ideas are factors in disguise?
The themes load where their names say they should. The value blend is a value tilt (HML +0.61); quality and investment are value plus momentum; low risk is short value, and the macro-exposure blend loads on momentum. After the factors, investment and low risk keep a significant positive alpha (t ≥ 2), and seasonality and reversal & attention carry a significant negative one. The negative alphas are not a factor story: seasonality and reversal barely load on anything (R² 15% and 20%). They are losses of their own.
Across single signals, 9 of 88 have a factor-adjusted alpha with t ≥ 2 and 20 have t ≤ −2. A search with no skill would put about two in each tail.
Textbook versus invented
| 1/N blend of | Signals | Sharpe | Alpha / yr | Alpha t | R² |
|---|---|---|---|---|---|
| Textbook references | 9 | 0.47 | +2.6% | 2.98 | 70% |
| Agent-invented | 79 | -0.36 | -1.0% | -2.50 | 42% |
Split the library by who wrote the signal and the picture sharpens. The 9 textbook references, blended 1/N, earn Sharpe 0.47 with a factor-adjusted alpha t-stat of 2.98. The 79 agent-invented signals, blended the same way, earn -0.36 with alpha t = -2.50: significantly negative after the factors. As a portfolio, the farm’s inventions subtract value. The positive premium in the library comes from the ideas it was seeded with.
Do the blends add anything to the factors?
The formal version of the question is spanning: if you can already hold the four factors, does adding a blend raise the best achievable Sharpe?
| Investable set | Max Sharpe (in-sample) | Gain over factors |
|---|---|---|
| The four factors alone | 0.93 | +0.00 |
| Factors + equal weight | 1.02 | +0.10 |
| Factors + theme parity | 0.93 | +0.01 |
| Factors + inverse vol | 1.08 | +0.15 |
| Factors + trailing winners | 0.94 | +0.01 |
| Factors + integrated score | 1.07 | +0.15 |
| Factors + all eight theme blends | 1.81 | +0.89 |
The best single blend adds +0.15 to the factors’ 0.93. Adding all eight theme blends at once reaches 1.81, but that number should not be trusted. It comes from an in-sample optimiser choosing twelve weights with hindsight, free to short the seasonality theme it now knows lost money. That is the sign flip the rest of the page refuses, done by an optimiser instead of by hand.
6. The timing sleeve
The 45 market-timing rules are a separate kind of strategy, so they stay out of the blends above. Blended 1/N they earn Sharpe 0.06 at 1.7% volatility. The factors explain only 7% of that, with a market beta of +0.03 and alpha t = -0.56. They are uncorrelated with the factors, which is useful in principle, but there is no premium to harvest.
What this adds up to
Combining signals works exactly as advertised on risk and not at all on return. The farmed library is diverse enough to diversify, about 15 independent bets, and blending it produces smooth, low-volatility return streams. But a blend converges on the average signal, and the average farmed signal does not earn its trading costs. What the blends do reliably hold is the classic factors: long value, long momentum, short size, and that accounts for 46–62% of their variance. That is a factor premium the combination genuinely harvests, and over Oct 2003–Jan 2024 it was worth very little.
The best result on the page, the integrated score book, is the one that concentrates those factor bets most. It earns a marginal alpha, and it wins a five-way comparison in which it was the most aggressive entrant.
What this does not show. The common window starts in October 2003 because the adaptive blends need history to estimate from; single-signal results on the main page use the full sample. The factors are equal-weighted tercile spreads built from this panel, not the Fama-French series, so they share this universe’s liquidity filter and exclude the smallest stocks. Costs are a flat 10bp on traded notional. The integrated book and the seasonality signals trade the most, so a realistic cost model would hurt them the most. And the theme labels are a keyword mapping written for this page; a different taxonomy would move the theme-level numbers, though not the library-wide blends.
Reproduce
python scripts/run_combination_study.py # ~10 min, writes runs/combination/
python -c "from llm_alpha.reporting.combination_page import build; build()"The blending rules live in src/llm_alpha/backtest/combination.py, where each adaptive rule has a test that shocks one month and checks that no earlier month moves.