I tested whether this discarded ordering information contains tradeable alpha. Using path signatures from rough path theory, I built 7 signals that capture the shape of price paths and evaluated them across 27 instruments in 4 asset classes at 4 timeframes from daily to 5-minute bars. The strongest signal, FadeVolRet (fade the price move when volatility spikes first), produces Sharpe +4.4 in crypto at 5-minute frequency with +3.4 bps per trade. It is positive on all 8 crypto symbols individually and in 52 out of 56 months from 2021 to 2026.

Path signatures work by treating the rolling window not as a bag of bars but as a path: a curve traced through (return, volatility) space as time progresses. The signature decomposes this path into levels. Level 1 captures where price ended up, equivalent to simple momentum. Level 2 captures how it got there: acceleration, lead-lag between return and volatility, and the Levy area (the rotation between the two streams). These level 2 features encode the sequential structure that standard indicators throw away.

A practical property of signatures is that they are parameterisation-independent: they describe the geometry of the path regardless of sampling frequency. A 2% move over 5 minutes and a 2% move over 5 hours produce the same geometric description if the shape is the same. This makes them naturally robust to irregular sampling and time-of-day effects.

The Levy area is the most distinctive level 2 feature. It measures the signed area enclosed by the path in (return, volatility) space, capturing whether directional moves systematically precede or follow volatility expansion within the window. This separates momentum breakouts from mean-reverting vol spikes, a distinction no simple rolling statistic can make. Level 3 and above capture increasingly complex shape patterns, but level 2 is where the most interpretable features reside.

The question is whether these shape features produce alpha that simple momentum and volatility drift (level 1) do not. I constructed 7 signals: 2 controls from level 1, 5 shape signals from level 2. The evaluation covers 4 asset classes (equity futures, commodity futures, G7 FX, crypto), 4 timeframes (daily, hourly, 30-minute, 5-minute), and lookback windows from 5 days to 2 hours, totalling over 400 configurations tested on 5 years of data.

The illustration above demonstrates the core idea. Both paths end at the same return with the same total range. The level 1 signature components (S1, S2) are identical for both, as expected. However, the level 2 components diverge sharply. The Levy area, which measures the signed area enclosed by the path in (return, volatility) space, is +9.4 for the path where returns led volatility and -6.4 for the path where volatility led returns. The cross-terms S(1,2) and S(2,1) capture the same lead-lag structure from complementary angles. These level 2 features form the basis of the shape signals evaluated in this study.

Related: Simple Alpha Atlas (Daily) | Intraday Alpha Atlas (30M) | Spread Alpha Atlas

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If you want to understand the broader alpha landscape that this study extends, the posts linked above test standard indicators (momentum, mean reversion, breakout, volatility) across the same asset classes and timeframes. The path signature signals evaluated here represent a new family of features that captures information those standard indicators discard.

Dataset

27 instruments from 4 asset classes, using data from July 2021 to July 2026.

Method

The Path

The first step is to construct a multi-dimensional path from the rolling window. At each bar within a window of length W, I record two quantities: the cumulative log return and the cumulative normalised range (high minus low, divided by close). Stacking these two streams produces a 2D path, a curve that traces how return and volatility evolved together over the window. The path is standardised to unit variance per dimension before computing the signature, which ensures that the resulting features are comparable across instruments and time periods with different volatility regimes.

Cumulative log return and cumulative normalised range, standardised to unit variance.

The figure above shows this construction on a 48-hour window of BTC price data. The raw OHLC data (left) is decomposed into per-bar log returns and normalised ranges (centre), which are then cumulatively summed to produce the 2D path (right). The shape of this path, its curvature, rotation, and the order in which the two streams evolve, is what the signature quantifies.

The choice of dimensions is important. Return and range are the two most fundamental properties of any price window, and their joint evolution over time captures the interaction between directional movement and volatility, the relationship that path-independent indicators reduce to a single summary statistic. A smooth uptrend with stable range traces a path that moves steadily along one axis. A volatility spike followed by a directional move traces a path that extends along the range axis first, then the return axis. These are geometrically distinct trajectories, and it is precisely this geometric distinction that the signature quantifies.

A natural extension is to add time as a third dimension (time augmentation), which would allow the signature to distinguish between paths that trace the same geometric shape at different speeds. One could also add order book imbalance, volume, or cross-asset returns as additional dimensions, each producing additional cross-terms at level 2 that capture lead-lag relationships between the new stream and the existing ones. In this study I restrict attention to the 2D (return, range) path to isolate the question of whether path shape alone carries alpha, before expanding to higher-dimensional paths in future work.

The Signature

The signature provides a systematic way to summarise the geometry of a path as a fixed-size vector. It is organised hierarchically. For a 2D path, the level 1 signature consists of two components: the total displacement in each dimension. For the (return, range) path, these are simply the total return and the total range change over the window, equivalent to standard momentum and volatility drift indicators. Level 1 is included as a control.

The level 2 signature consists of four additional components, each computed as a double sum over ordered pairs of increments within the path:

For each pair of dimensions i and j, sum the product of increment i at time t1 with increment j at time t2, over all ordered pairs t1 < t2.

No calculus is involved in the discrete case. On a time series of n bars, each level 2 component reduces to a sum over all pairs (i, j) where bar i precedes bar j. The four components have direct interpretations in the context of price dynamics:

S(1,1) = sum of return[i] * return[j] for all i < j. This captures return acceleration. When early returns are small and late returns are large (an accelerating move), S(1,1) takes a large positive value. When the reverse holds (a decelerating move), S(1,1) is smaller. Two windows with identical total return but different temporal profiles of that return produce different S(1,1) values.

S(1,2) = sum of return[i] * range_change[j] for all i < j. This captures return leading volatility. The component is large when directional price movements occur early in the window and range expansion follows, the characteristic pattern of a momentum breakout where the market reacts to a directional move with increased activity.

S(2,1) = sum of range_change[i] * return[j] for all i < j. This captures volatility leading return. The component is large when range expansion precedes directional price movement, the pattern observed before scheduled announcements or during liquidity-driven events where uncertainty manifests as widening ranges before price resolves in a direction.

S(2,2) = sum of range_change[i] * range_change[j] for all i < j. This captures volatility acceleration: whether the range is expanding at an increasing or decreasing rate over the window.

Of particular interest is the Levy area, defined as S(1,2) - S(2,1). This antisymmetric quantity measures the net difference between "return leads volatility" and "volatility leads return". Geometrically, it corresponds to the signed area enclosed by the path in (return, range) space. A positive Levy area indicates that the path rotates counterclockwise (returns precede volatility expansion). A negative Levy area indicates clockwise rotation (volatility expansion precedes returns). This feature has no equivalent among standard indicators, as it requires tracking the relative ordering of increments across two distinct streams simultaneously.

The iisignature Python library computes all six components (plus the derived Levy area) in microseconds per path via a recursive update formula known as the Chen identity, which avoids the naive O(n-squared) double loop over all pairs of bars.

Signals

Each of the 6 signature components (plus the derived Levy area) becomes a trading signal. Two are controls: Sig-Reversion = -S(1), a faded momentum signal equivalent to short-term mean reversion, and Sig-VolDrift = S(2), equivalent to range change. Five are shape signals: Sig-Accel = S(1,1), Sig-LevyArea = S(1,2) - S(2,1), Sig-FadeRetVol = -S(1,2), Sig-FadeVolRet = -S(2,1), and Sig-VolAccel = S(2,2). Three of these (Reversion, FadeRetVol, FadeVolRet) are negated because the raw signature components are consistently predictive of mean reversion: the natural trading direction is to fade the signal rather than follow it.

Each signal is z-scored over a 500-bar rolling window (how unusual is this path shape compared to recent history?), then discretised: long when z > 0, short when z < 0.

P&L

Position = sign(z-scored signal). PnL per bar:

z = rolling z-score of signature component, r = 1-bar forward return.

Equal-weight average across all symbols in each asset class. Daily PnL summed across bars and annualised via sqrt(252). No leverage, no compounding. bps/trade = total PnL in basis points divided by total position changes.

Results

Top Sharpe Signatures

The table below ranks the strongest signature configurations by |Sharpe| within each asset class (top 5 per class). Each row shows the signal family, timeframe, lookback, Sharpe ratio, bps per trade, and information coefficient (IC). The IC is the Spearman rank correlation between the z-scored signal and the subsequent 1-bar forward return, averaged across all symbols in the asset class.

Full per-timeframe breakdowns (signal x lookback panels and equity curves for daily, hourly, 30-minute, and 5-minute frequencies) are in Appendix B at the end of this post.

Sharpe by Signal Family

The chart below shows the mean Sharpe across all configurations (asset class, timeframe, lookback) for each signal family. This is the broadest view: which families produce positive alpha on average, and which do not?

Deep Dive: Drawdown Profile

Before examining whether these signals survive across time periods and regimes, it is worth understanding their risk characteristics. The table below reports the drawdown profile for the best signal in each asset class: maximum drawdown in basis points, longest drawdown duration in trading days, the Calmar ratio (annualised return divided by maximum drawdown), and the daily win rate. A high Sharpe ratio is necessary but not sufficient. A signal with Sharpe 3 but a 500-bps drawdown lasting 200 days has very different capital requirements from one with the same Sharpe but shallower, shorter drawdowns.

Monthly Return Distribution

The monthly return heatmap below shows the month-by-month PnL (in basis points) for the single strongest tradeable signal. This provides a more granular view than the yearly Sharpe breakdown: it reveals whether the edge is distributed evenly across calendar months or concentrated in a few exceptional periods. A signal that produces positive returns in most months across most years is qualitatively different from one that earns its entire annual PnL in two or three outsized months.

Regime Conditioning

A systematic signal that works only in benign conditions and collapses during stress is of limited practical value. The table below splits the daily PnL of the best signal per asset class into four regimes: high and low realised volatility (above and below the rolling 20-day median), and up and down market direction (positive and negative rolling 20-day mean return). A robust signal should maintain its edge across regimes, or at minimum should not reverse sign during the regime that matters most to the portfolio.

Robustness: Yearly Sharpe Breakdown

A natural concern with any in-sample scan is whether the reported Sharpe ratios are concentrated in a single favourable period or whether they persist across distinct calendar intervals. The table below decomposes the full-sample Sharpe into five calendar years (2022 through 2026 year-to-date) for each of the top tradeable signals identified above. A signal whose Sharpe is driven by a single anomalous quarter will show a strong number in one column and weak or negative numbers in the others. A signal that reflects a genuine structural pattern will show consistent positive (or consistently negative, if the traded direction is flipped) Sharpe across all three sub-periods.

The degree to which each signal maintains its direction and magnitude across years provides a more informative basis for assessing reliability than the full-sample Sharpe alone. Sub-period consistency does not eliminate the risk of in-sample overfitting, but it does distinguish between signals that captured a single transient event and those that reflect a recurring pattern in the data.

Per-Symbol Consistency

A portfolio-level Sharpe ratio can mask concentration risk. If the edge is driven by a single instrument within the asset class, the signal is fragile. The table below decomposes the portfolio-level result into per-symbol Sharpe ratios for the strongest shape signal in crypto, allowing us to assess whether the effect is systematic across the universe or concentrated in one or two names.

Signal Correlation

Seven signals derived from the same underlying path could easily be measuring the same thing. The correlation matrix below shows the pairwise correlation of each signal's Sharpe profile across all configurations (asset class, timeframe, lookback). High correlation between two signals indicates they respond to the same market conditions and provide redundant information. Low correlation indicates genuinely independent alpha sources.

Holding Period Analysis

The results above use a 1-bar holding period: enter at the close of the signal bar, exit at the next close. A natural question is whether the predictive edge persists beyond the immediate next bar. The chart below shows the Sharpe ratio of the best tradeable signal at holding periods of 1, 2, 5, 10, and 20 bars. If the signal captures a fleeting microstructure effect, the edge will concentrate at 1-bar and decay rapidly. If it reflects a more durable pattern, the edge will persist or even improve at longer horizons.

Statistical Significance

Sharpe ratios computed from a single sample can be misleading. The table below reports bootstrap confidence intervals for the top 5 tradeable signals, constructed by resampling the daily PnL with replacement 1,000 times. The 5th and 95th percentile columns indicate the range within which the true Sharpe is likely to fall. The p(SR>0) column shows the probability that the signal's Sharpe exceeds zero under resampling, a non-parametric test of statistical significance. A signal with p(SR>0) above 95% can be considered statistically significant at the 5% level.

Conclusions

Two findings stand out from this scan.

First, the Levy area is the strongest shape signal. It produces |Sharpe| > 1 in 20 configurations across crypto, FX, and commodities. No simple rolling indicator captures the same information: the rotation between return and volatility is a genuinely new feature. The signal is strongest at short lookbacks (2-4 hours) in crypto and FX, where it captures the order in which price and volatility move after microstructure events.

Second, VolLeadRet (volatility leads return) is the most consistent cross-asset signal when flipped. It produces |Sharpe| > 1 in 0 configurations. The negative sign means: when volatility expands first, fade the subsequent price move. This is a mean-reversion pattern that works across FX, crypto, and commodities.

The shape premium is not universal. Control signals (simple momentum and volatility drift) remain competitive in equity futures. The strongest edge from level 2 features appears in volatile, regime-shifting markets where the order of price and volatility moves carries information that endpoints alone miss.

Methodology

The dataset consists of ratio-adjusted continuous futures contracts, spot FX pairs, and spot cryptocurrency pairs from July 2021 to July 2026. For each instrument and timeframe, the path is constructed as a 2D trajectory of cumulative log return and cumulative normalised range, standardised to unit variance per dimension within each rolling window. The level 2 signature is computed via the iisignature library, producing 6 components per window (plus the derived Levy area as S(1,2) - S(2,1)).

Each signature component is converted to a trading signal by applying a rolling z-score over a 500-bar window, then discretising the result: a position of +1 (long) when the z-score is positive, -1 (short) when negative. Positions are entered at bar close and PnL is realised on the subsequent bar. The portfolio-level PnL is the equal-weight average across all symbols within each asset class. Sharpe ratios are annualised from daily-aggregated PnL via multiplication by the square root of 252.

Lookback windows of 2, 4, 8, and 24 hours are tested, converted to bars at the respective timeframe frequency. At 5-minute resolution, signatures are computed at every third bar and forward-filled to reduce computational cost. At 30-minute and hourly resolution, signatures are computed at every bar. All results presented are in-sample. No train/test split or walk-forward validation is employed. The per-cell selection of the best lookback in the summary tables represents a mild form of optimisation that would require out-of-sample validation before deployment. This is a backtest study with simplified execution assumptions.

Appendix B: Per-Timeframe Results

Daily

Hourly

30-Minute

At 30-minute resolution, the same signal families reappear with higher gross Sharpe ratios due to more bars per day. All figures are gross of execution costs. Signals with less than 0.5 bps per trade are unlikely to survive realistic execution.

5-Minute

At 5-minute frequency the gross Sharpes are highest but should be read with caution. Most FX and equity futures signals show sub-0.5 bps per trade. Viable signals at this frequency are concentrated in crypto and commodity futures.

Appendix C: Signal Definitions

The seven signals evaluated in this study are derived from the level 2 signature of a 2D path constructed from cumulative log return and cumulative normalised range. Two are control signals equivalent to standard rolling indicators. Five are shape signals that capture path geometry beyond the endpoints.

Sig-Reversion (-S(1)). The negated level 1 signature component in the return dimension. Equal to the negative total cumulative log return over the lookback window. This is algebraically equivalent to a short-term mean reversion signal (fade recent winners, buy recent losers) and serves as a control.

Sig-VolDrift (S(2)). The level 1 signature component in the range dimension. Equal to the total cumulative normalised range (high minus low, divided by close) over the window. Captures whether the average bar range has been expanding or contracting. This is the second control signal.

Sig-Accel (S(1,1)). The double sum of return[i] times return[j] over all ordered pairs i < j. Captures return acceleration: the component is large and positive when early returns are small and late returns are large (an accelerating price path), and small or negative when the reverse holds (a decelerating path). Two windows with identical total return but different temporal profiles produce different S(1,1) values.

Sig-LevyArea (S(1,2) - S(2,1)). The antisymmetric cross-term, equal to the signed area enclosed by the path in (return, range) space. Positive when return movements systematically precede range expansion (counterclockwise rotation). Negative when range expansion systematically precedes return movements (clockwise rotation). This is the most distinctive feature of the signature framework, with no equivalent among standard technical indicators.

Sig-FadeRetVol (-S(1,2)). The negated cross-term of return leading volatility. The raw S(1,2) is consistently negative as an alpha signal (return-leads-vol events predict mean reversion). Fading it produces a positive Sharpe: when price moves first and volatility responds, bet on reversal.

Sig-FadeVolRet (-S(2,1)). The negated cross-term of volatility leading return. The raw S(2,1) is the most consistently negative signal in the study: when volatility spikes first, the subsequent price move tends to reverse. Fading this pattern produces the strongest and most consistent alpha across asset classes.

Sig-VolAccel (S(2,2)). The double sum of range_change[i] times range_change[j] over all ordered pairs i < j. Captures volatility acceleration: whether the bar range is expanding at an increasing or decreasing rate over the window.

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A spread alpha is a signal that predicts the direction of the spread's next move. If the BTC/ETH spread widens beyond its historical norm, a z-score signal flags the divergence and bets on reversion. If the signal is right more often than not, you have tradeable alpha on the spread.

But building spread alphas involves two decisions. First, how to construct the spread. Two assets rarely move dollar-for-dollar, so you need a hedge ratio that balances the contribution of each leg. Get it wrong and one leg dominates the spread, drowning out the signal. Second, which features to compute on that spread. Not all signals work, mean reversion thrives, momentum gets destroyed. I tested 14 feature families on 15 pairs across 5 asset classes and 3 timeframes to map which combinations produce tradeable alpha.

Related: Simple Alpha Atlas (Daily) | Intraday Alpha Atlas (30M) | Pairs Trading Crypto: Backtest Results | US Equity XS Mean Reversion

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Dataset

For each asset class I picked 3 representative pairs of structurally related assets, using data from January 2022 to July 2026.

Method

The Spread

The spread between two assets with prices P_base and P_quote is defined as:

where beta is the hedge ratio (how much of the base asset to hold against the quote) and c is an intercept that absorbs the average level difference. When beta = 1 and c = 0, this reduces to the simple log-ratio. But for most pairs, beta is not 1. ES/NQ has beta around 1.2, GC/SI around 1.0, NVDA/AMD around 0.8. If you use beta = 1 when the true value is 1.5, the spread is contaminated by the base leg's excess movement and the features measure noise instead of genuine divergence.

The Hedge Ratio

I estimate beta using a Kalman filter, which models:

with beta and intercept c as hidden states that update at each bar. The filter adapts the hedge ratio over time without overreacting to noise. To avoid continuous rebalancing, the Kalman beta is frozen at each rebalance boundary: weekly for daily data, daily for 30-minute data.

Features and Signals

I compute 14 feature families on the Kalman-adjusted spread: z-score, momentum, rate of change, distance from mean, Bollinger %B, skewness, kurtosis, variance ratio, OU half-life, RSI, MACD, cross-leg correlation, return differential, and relative volatility. Full definitions are in the appendix. Each feature is evaluated at lookbacks of 5, 10, 20, and 50 bars.

Each feature is converted to a directional signal: sign(feature_value). A position of +1 means long $1 of quote and short $beta of base. A position of -1 means the reverse.

P&L

PnL per bar is the actual hedged position return:

where beta is the frozen Kalman hedge ratio from the last rebalance. This is the return you would realise by holding the hedged position. Daily PnL is summed across bars and annualised via sqrt(252). No leverage, no compounding. Costs are applied as turnover times round-trip bps (2 bps for futures/FX, 10 bps for equities/crypto).

Results

Daily: Top 3 per Asset Class

Sharpe by Alpha Family (Daily)

30-Minute: Top 3 per Asset Class

At 30-minute resolution the Kalman spread is rebalanced daily. The same feature families dominate but with higher Sharpe ratios due to more bars per day. These are gross figures. At intraday frequencies, execution costs will compress the net edge.

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Only 40% of signal families show positive trailing Sharpe right now. FX is the strongest asset class. Equities is the weakest. Here is the full map.

Signal Performance: Last 4 Weeks

Each value is the trailing 20-day (4-week) rolling Sharpe, annualised, averaged across instruments. The window includes all trading days in the prior 4 weeks, not just the weeks shown. The Δ column is the change from the first week to the latest week. Green = edge active. Red = signal impaired.

Daily

30-Min

5-Min

Most Tradeable Alphas

Filtered to Sharpe > 1.5 (intraday) or > 1.0 (daily), then sorted by bps/trade. High Sharpe with low bps/trade is untradeable after costs. These are the signals with enough edge per trade to survive real execution.

Execution costs: All Sharpe ratios above are gross of costs. The 30-min and 5-min Sharpes will compress after spread and market impact. For 5-min signals, any family showing less than 0.5 bps/trade is likely to be consumed by execution costs in practice.

Methodology: 25 signal families evaluated on close-to-close returns, 1-bar holding period, no volatility scaling. Rolling 20-day Sharpe from daily-aggregated returns, annualised (sqrt(252)). All results are gross of execution costs. This is a research screen, not a trading recommendation.

The companies that own the cloud. Five hyperscalers control the majority of global compute, plus the SaaS platforms built on top of them and the enterprise vendors competing for the rest.

17 stocks. 30 signals from the Atlas database. Daily, 30-minute, and 5-minute bars over the last 3 years. Every result vol-scaled to 15% annualized, Sharpe computed on monthly PnL. No curve fitting, no optimization - raw signal performance on each stock.

Related posts: NVDA deep dive (free) | The Alpha Atlas Toolkit

Factor Exposures

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The semiconductor supply chain from chip design to fabrication equipment. The AI boom has split the sector: some stocks have repriced dramatically while others have stagnated. Do the alpha signals reflect this divide?

27 stocks. 30 signals from the Atlas database. Daily, 30-minute, and 5-minute bars over the last 3 years. Every result vol-scaled to 15% annualized, Sharpe computed on monthly PnL. No curve fitting, no optimization - raw signal performance on each stock.

Related posts: NVDA deep dive (free) | The Alpha Atlas Toolkit

Factor Exposures

Before testing alpha signals, I strip out what can be explained by known risk factors. The Fama-French 5-factor model plus momentum decomposes each stock's returns into market risk, size, value, profitability, investment, and momentum exposures. Whatever is left after that decomposition is the unexplained alpha - the part that factor investors cannot replicate.

These exposures are not static. A stock's relationship to each factor shifts over time as the business evolves, the competitive landscape changes, and market regimes rotate. Here is how the key betas have moved, averaged across all stocks in the group.

The group has a market beta of 1.41, is small-cap tilted (SMB 0.17), growth-tilted (HML -0.28), and contrarian relative to momentum (Mom -0.18).

The annualized alpha after controlling for all factors is 0.1% - close to zero, meaning returns are well-explained by factor exposures. This is normal: you are being compensated through market beta (1.41x) and factor premia, not through stock-specific alpha. The signals below test whether there is edge in timing within this group.

Over the full history, the group's market beta has fallen. The growth tilt (HML -0.44) has deepened in recent years.

Alpha Signals

I test 10 alpha families from the Atlas database, each at 3 lookbacks (5, 20, 120 bars), for a total of 30 signals per timeframe. At daily frequency the dominant family is Ret-Z (best lookback Sharpe 0.50). At 5-minute frequency it is Fractal (Sharpe 1.29). The families span mean-reversion (MR, CS-Rev, Keltner-Rev, Fade-BO, Fade-MA), higher-moment signals (Skew-Fade, SkewKurt, Accel-Fade, Ret-Z), and trend (Fractal).

Daily Timeframe

Best two signals: Ret-Z 5 (Sharpe 0.50, 85% of stocks positive) and Skew-Fade 20 (Sharpe 0.50, 89% of stocks positive).

Best 3 individual stock alphas (max 1 per stock):

30-Minute Timeframe

Best two signals: Keltner-Rev 5 (Sharpe 1.16, 96% of stocks positive) and MR 5 (Sharpe 1.04, 93% of stocks positive). Intraday results are filtered to signals with at least 0.5 bps per trade - below that threshold, execution costs will eat the alpha.

5-Minute Timeframe

Best two signals: Fractal 120 (Sharpe 1.29, 93% of stocks positive) and MR 120 (Sharpe 1.20, 93% of stocks positive). Same filter: only signals above 0.5 bps/trade survive. These are gross results - the 5-minute Sharpes will compress after spread and market impact. The bps/trade column shows the raw edge before costs.

Regime Shift

Are these signals stable or are they decaying? I split the 3-year window in half and recompute each family's average Sharpe. Families where the bars are similar are stable. Families where the second bar is much higher or lower have shifted - and that tells you something about what has changed in how these stocks trade.

The families that have weakened in the second half: Keltner-Rev (-0.51), Fade-MA (-0.42), MR (-0.41), Fade-BO (-0.35), SkewKurt (-0.15). These are the mean-reversion and breakout signals - consistent with a market where crowded trades and momentum have dominated, making classic reversal strategies less effective.

The families that have strengthened: Fractal (+0.45), Ret-Z (+0.37), CS-Rev (+0.22). Trend-following (Fractal) and return z-score reversion (Ret-Z) have picked up - suggesting that price moves have become more persistent and extreme returns have started reverting faster.

Subgroups

AI & GPU (3 stocks): avg daily Sharpe 0.36. Best stock: AVGO (0.77). Worst: AMD (-0.00).

Fabless Analog/Mixed (9 stocks): avg daily Sharpe 0.20. Best stock: SWKS (0.37). Worst: ON (-0.04).

Equipment & EDA (7 stocks): avg daily Sharpe 0.11. Best stock: CDNS (0.22). Worst: ASML (-0.07).

Memory (3 stocks): avg daily Sharpe 0.25. Best stock: MU (0.38). Worst: WDC (0.13).

IDM & Foundry (5 stocks): avg daily Sharpe 0.22. Best stock: SMCI (0.54). Worst: ARM (-0.01).

Appendix

Alpha Signals Tested

10 alpha families from the Atlas database, each at 3 lookbacks (5, 20, 120 bars), for 30 signals per timeframe. The same 30 signals are tested on daily, 30-minute, and 5-minute bars. All use lagged close (shifted by 1 bar) to avoid lookahead bias.

• Fade-BO - fade breakout: short at new rolling high, long at new rolling low.

• Fade-MA - fade moving average: short above SMA, long below SMA.

• CS-Rev - cross-sectional reversion: z-score of price-to-SMA ratio, then reverse.

• MR - mean reversion: z-score of price level, then reverse.

• Skew-Fade - fade the rolling skewness of price.

• Keltner-Rev - reversion from the Keltner channel center (distance to SMA normalized by ATR).

• Accel-Fade - fade the second derivative (acceleration) of price.

• Ret-Z - z-score of 1-bar return, then reverse.

• SkewKurt - signed kurtosis: negative skew times kurtosis.

• Fractal - trend following: range efficiency (high-low range / sum of absolute moves) times z-score.

All alpha returns are vol-scaled to 15% annualized. Sharpe ratios are computed on the vol-scaled next-open PnL series, aggregated to monthly returns before annualization.

Factor returns from the Kenneth French Data Library. Fama-French 5 factors (Mkt-RF, SMB, HML, RMW, CMA) plus momentum (Mom). Rolling regressions use 36-month windows.

Educational purposes only. Not investment advice. Split/dividend adjusted data. No execution costs included. Past patterns may not persist.

FX alpha comes from different families than equities or crypto, and the gap between daily and intraday performance is unusually wide.

Universe: EURUSD, GBPUSD, USDJPY, AUDUSD, USDCAD, USDCHF. Equal-weighted. Sharpe ratios are annualized. All results are before transaction costs.

Strongest Alphas by Sharpe

Top 3 FX alphas per timeframe by Sharpe ratio. One per family, statistically significant (p<0.05).

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The most crowded alpha space in global markets. The question is whether systematic alphas still have edge.

Universe: NQ, ES, YM, RTY, NKD, FDAX. Equal-weighted. Sharpe ratios are annualized. All results are before transaction costs.

Strongest Alphas by Sharpe

Top 3 Equity Futures alphas per timeframe by Sharpe ratio. One per family, statistically significant (p<0.05).

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Driven by rates, central bank policy, and duration risk. Do systematic short-horizon alphas survive in a market dominated by macro flows?

Universe: ZN, ZB, ZF, ZT, UB. Equal-weighted. Sharpe ratios are annualized. All results are before transaction costs.

Strongest Alphas by Sharpe

Top 3 Bond Futures alphas per timeframe by Sharpe ratio. One per family, statistically significant (p<0.05).

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The most heterogeneous asset class - gold, crude oil, copper, wheat have fundamentally different dynamics. Do common alpha families work across all of them?

Universe: GC (gold), SI (silver), CL (crude oil), HG (copper), ZW (wheat), ZC (corn). Equal-weighted. Sharpe ratios are annualized. All results are before transaction costs.

Strongest Alphas by Sharpe

Top 3 Commodity Futures alphas per timeframe by Sharpe ratio. One per family, statistically significant (p<0.05).

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At daily frequency, crypto trends. At intraday frequency, it reverts. This inversion makes it the most structurally different asset class in the database.

Universe: BTC, ETH, SOL, DOGE, XRP, and other top coins by liquidity. Equal-weighted. Sharpe ratios are annualized. All results are before transaction costs.

Strongest Alphas by Sharpe

Top 3 Crypto alphas per timeframe by Sharpe ratio. One per family, statistically significant (p<0.05).

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This is a single-stock stress test: factor exposures first, then simple price/volume signals across daily, 30-minute, and 5-minute bars. Each signal is observed on one bar and earns PnL from the next bar's open to the close after the tested holding horizon. Intraday tests include 1, 2, 3, 6, and 12-bar holding horizons, time-of-day filters, daily-regime filters, and long/short symmetry checks.

Read more

Generated: 2026-07-31 05:39:15 BST Expires: 2026-08-02 05:39:15 BST

What Is Included

• alpha_lite_daily.parquet - monthly daily-bar alpha performance

• alpha_lite_30m.parquet - weekly 30-minute alpha performance

• alpha_lite_5m.parquet - weekly 5-minute alpha performance

• alpha_lite_extended_daily.parquet - per-asset daily-bar alpha performance

• atlas_monitor_basic_analysis_notebook.zip - starter notebook for ranking and inspecting the parquets

The Lite files use one schema across timeframes, asset classes, alpha names, target definitions, and rolling performance fields. Use the notebook as the quickest starting point if you only want to load, rank, and plot the latest export.

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86% of equity futures alphas improved this quarter. Meanwhile, 86% of commodity futures alphas collapsed. The alpha landscape is splitting in two.

Every quarter I run the full Atlas Monitor database — over 7,000 alpha-asset-timeframe combinations — through the same test: close-to-close returns, 1-bar holding period, no scaling, no optimization. Then I compare this quarter's Sharpe against the average of the three preceding quarters.

Here's what Q2 2026 looks like.

The Big Picture

• Equity Futures are surging. 87% at daily, 83% at 30-minute, 79% at 5-minute improved quarter-over-quarter.

• Commodity Futures are falling apart. 92% at daily, 68% at 30-minute, 69% at 5-minute of alphas decayed.

• Crypto are quietly decaying. 58% decayed, only 23% improved across timeframes.

• Bond Futures are balanced. roughly even split (39% decayed, 34% improved) across timeframes.

• FX is improving. 45% improved vs 33% decayed across timeframes.

How Much Alpha Decayed This Quarter?

The chart below shows the proportion of alphas that decayed (red), remained stable (grey), or improved (green) versus the average of the preceding 3 quarters. Each panel is a different timeframe.

The equity futures columns are dominated by green. The commodity futures columns are dominated by red. This pattern is consistent across all three timeframes.

Which Alpha Families Shifted?

Each cluster of four bars is one alpha family. Bars represent the four quarters from oldest (red) to newest (blue). Families are sorted by current-quarter Sharpe.

Daily

30-Minute

5-Minute

That's the overview. For the full per-asset-class breakdown and the biggest individual Sharpe shifts, continue below.

Daily: Family Sharpe by Asset Class

Read more

Tesla, Inc. | Consumer Cyclical | Market cap $1220B

30 signals from the Atlas database. Daily, 30-minute, and 5-minute bars over the last 3 years. Every result vol-scaled to 15% annualized, Sharpe computed on monthly PnL. 10 of 10 signal families are positive at daily frequency. At 5-minute, 10 of 10 are positive.

Related: NVDA deep dive (free) | The Alpha Atlas Toolkit

TSLA Factor Exposures

Before testing alpha signals, I strip out what can be explained by known risk factors. The Fama-French 5-factor model plus momentum tells you how much of TSLA's return comes from market risk, size, value, profitability, and momentum - and how much is genuinely unexplained.

These exposures are not static. TSLA's relationship to each factor shifts as the business evolves and market regimes rotate.

TSLA has a market beta of 1.26, is small-cap tilted (SMB 0.90), growth-tilted (HML -1.05), and contrarian to momentum (Mom -0.37).

The annualized alpha is 0.4% - close to zero, meaning TSLA's returns are largely explained by its factor exposures. The signals below test whether there is timing edge on top of this.

Alpha Signals

10 alpha families from the Atlas database, each at 3 lookbacks (5, 20, 120 bars), for 30 signals per timeframe. Intraday signals filtered to positive bps/trade only.

Daily Timeframe

Best two signals: Fade-MA 120 (Sharpe 1.22, 20.5 bps/trade) and Keltner-Rev 120 (Sharpe 0.98, 47.4 bps/trade).

30-Minute Timeframe

Best two signals: Fade-BO 5 (Sharpe 3.02, 2.6 bps/trade) and Fade-MA 5 (Sharpe 1.88, 1.1 bps/trade). Filtered to signals above 0.3 bps/trade. These are gross results.

5-Minute Timeframe

Best two signals: Keltner-Rev 20 (Sharpe 3.52, 0.6 bps/trade) and Fade-BO 120 (Sharpe 1.89, 0.9 bps/trade). Filtered to signals above 0.15 bps/trade. These are gross results - Sharpes will compress after spread and impact.

Appendix

Alpha Signals Tested

10 alpha families, each at 3 lookbacks (5, 20, 120 bars), for 30 signals per timeframe. All use lagged close (shifted by 1 bar) to avoid lookahead bias.

• Fade-BO - fade breakout: short at new rolling high, long at new rolling low.

• Fade-MA - fade moving average: short above SMA, long below SMA.

• CS-Rev - cross-sectional reversion: z-score of price-to-SMA ratio, then reverse.

• MR - mean reversion: z-score of price level, then reverse.

• Skew-Fade - fade the rolling skewness of price.

• Keltner-Rev - reversion from the Keltner channel center.

• Accel-Fade - fade the second derivative of price.

• Ret-Z - z-score of 1-bar return, then reverse.

• SkewKurt - signed kurtosis: negative skew times kurtosis.

• Fractal - trend following: range efficiency times z-score.

All returns vol-scaled to 15% annualized. Sharpe ratios computed on monthly aggregated PnL. Intraday signals filtered to >0.5 bps/trade. These are gross results - no execution costs included.

Educational purposes only. Not investment advice. Split/dividend adjusted data. Past patterns may not persist.

I have now packaged that entire process into a standalone Python toolkit. You can run the same analysis I run, on any market you want, with six lines of code.

This post walks through the toolkit, shows results across two asset classes, and explains every signal. Paid subscribers get the full source code.

A note on scope: this first version does not cover all the content from the full Alpha Atlas posts. The Atlas Monitor evaluates hundreds of additional signals, uses proprietary data sources, and tracks signal decay over time. This toolkit is the foundation. It ships with 30 signals and uses Yahoo Finance for data, but it accepts any OHLCV data you have, from any source, in any format. Future updates will add more signal families, multi-bar holding periods, volatility scaling, and the monitor database.

What the Toolkit Does

The toolkit evaluates 30 alpha signals across any set of assets. Each signal is a formula that reads OHLCV data and outputs a trading signal: long, short, or flat. The signals fall into 10 families:

Standard signals (4 families): Fade Breakout, Fade Moving Average, Cross-Sectional Reversion, Mean Reversion.

Exotic signals (6 families): Skewness Fade, Keltner Reversion, Acceleration Fade, Return Z-Score Reversion, Signed Kurtosis, Fractal Trend.

Each family is tested at three lookback windows (5, 20, and 120 bars), giving 30 signal variants. Every signal is evaluated with two return modes: close-to-close (theoretical) and open-to-close (realistic execution).

US ETFs: 10 Tickers, 5 Years

I ran the toolkit on 10 major US ETFs: SPY, QQQ, IWM, DIA, GLD, TLT, XLE, XLF, XLK, XLV. Five years of daily bars, evaluated with 5 bps round-trip costs.

The heatmap shows average Sharpe by signal family and ticker. Green cells mean the signal works. Red cells mean it does not, or the signal is inverted (a red "Fade-BO" on QQQ means breakouts actually work on QQQ, they do not fade).

The top performing signal across all ETFs:

Skew-Fade 120 on IWM with a Sharpe of 1.05 and total return of 50% over 5 years.

Does Alpha Survive Execution?

Every signal is also evaluated with open-to-close returns. This assumes you see the signal at the close, enter at the next open, and exit at the next close. It is a more realistic execution model because you cannot actually trade at the close you just observed.

Most signals lose Sharpe when moving from close-to-close to open-to-close. That gap is the overnight return you miss by not being in the position at the close. The signals that survive this test are more likely to work in practice.

Futures: 8 Markets, 5 Years

Same toolkit, different universe. Eight futures markets (ES, NQ, YM, Gold, Silver, Crude Oil, Copper, Wheat) with daily bars and 3 bps costs.

Futures are a different regime to ETFs. Some signal families that work on equities also work on commodities, others do not. This is the value of running the same analysis across multiple asset classes: you find out which signals are universal and which are asset-specific.

The Code

The entire analysis above was generated by the toolkit. Here is the core workflow:

import delphic_atlas_toolkit as dat

# Download 5 years of daily data
prices = dat.download(["SPY", "QQQ", "GLD", "TLT"], period="5y")

# Scan all 30 signals with close-to-close and open-to-close returns
results = dat.scan(prices)

# Top signals
print(results.top(10, pnl_mode="c2c"))

# Which families work?
print(results.family_summary("c2c"))

# Full HTML report with heatmaps and equity curves
dat.report(results, "my_atlas.html")

That is the complete pipeline. Download data from Yahoo Finance, evaluate all 30 signals with two return modes, print rankings, and generate a full HTML report with heatmaps and equity curves.

Signal Reference

Here is every signal in the toolkit, what it does, and why it might work.

Standard Signals

Fade Breakout (Fade-BO): When the close breaks above the rolling high, go short. When it breaks below the rolling low, go long. This is a pure mean-reversion signal. It works when breakouts are exhaustion moves rather than the start of trends.

Fade Moving Average (Fade-MA): Short when close is above its moving average, long when below. Another mean-reversion signal. Works in range-bound markets, gets killed in trends.

Cross-Sectional Reversion (CS-Rev): For each asset, compute how far close is from its MA relative to the other assets in the universe. Fade the relatively strong, buy the relatively weak. This is a relative-value signal, only works with multiple assets.

Mean Reversion (MR): The rolling z-score of close, negated. When close is 2 standard deviations above its recent mean, go short. The simplest possible mean-reversion signal.

Exotic Signals

Skewness Fade (Skew-Fade): Negative rolling skewness. When the recent price distribution is positively skewed (right tail, overbought), go short. Captures distributional asymmetry that simple z-scores miss.

Keltner Reversion (Keltner-Rev): Distance from MA normalised by Average True Range instead of standard deviation. More robust to outliers than a z-score. Similar to Bollinger Bands but using ATR as the volatility measure.

Acceleration Fade (Accel-Fade): The z-score of the second difference of close (acceleration). When price is accelerating upward, expect it to decelerate. Captures momentum exhaustion.

Return Z-Score Reversion (Ret-Z-Rev): Z-score of the 1-bar return (close / previous close). Fades extreme recent returns. Different from MR because it looks at the rate of change, not the level.

Signed Kurtosis (SkewKurt): Skewness multiplied by kurtosis. Combines distributional direction with tail thickness. Fat-tailed, positively-skewed distributions signal overbought conditions.

Fractal Trend (Fractal-Trend): Range efficiency (rolling range / sum of absolute bar changes) multiplied by z-score. High efficiency means the market is trending, not chopping. The z-score gives direction. This is the only trend-following signal in the toolkit.

Adding Your Own Signals

The toolkit is extensible. Any function that takes a DataFrame with OHLCV columns and returns a Series of signal values can be plugged in:

from delphic_atlas_toolkit.signals import SIGNAL_REGISTRY

def my_rsi_signal(df, window=14):
    delta = df["close"].diff()
    gain = delta.clip(lower=0).rolling(window).mean()
    loss = -delta.clip(upper=0).rolling(window).mean()
    rsi = 100 - 100 / (1 + gain / loss)
    return -(rsi - 50) / 50  # normalise to [-1, 1]

SIGNAL_REGISTRY.append({
    "name": "RSI-Rev 14",
    "family": "RSI-Rev",
    "lookback": 14,
    "function": my_rsi_signal,
    "cross_sectional": False,
})

# Now scan() will include your signal alongside the 30 built-in ones

Roadmap

This is version 0.1. The toolkit will grow over the coming weeks. Here is what is planned:

Phase 2 — Multi-Bar Holds and Volatility Scaling. The current version evaluates every signal with a 1-bar holding period. Phase 2 adds 5-bar and 10-bar holds, so you can test whether a signal works better as a quick scalp or a multi-day position. It also adds volatility-scaled signals, where the position size is inversely proportional to recent volatility. This is how most institutional systems size positions.

Phase 3 — More Signal Families. The current 10 families are the core of the Atlas. Phase 3 adds momentum signals, volume-weighted indicators, and volatility breakout detectors. These are the next layer of the signal library that I use in the full Atlas Monitor.

Phase 4 — The Monitor Database. This is the big one. Phase 4 turns the toolkit from a one-shot scanner into a persistent tracking system. It appends weekly evaluation snapshots to a local parquet database, tracks which signals are alive, decaying, or dead, and generates a "what's working this week" dashboard. The same pipeline that powers the Atlas Monitor posts, running on your machine.

Paid subscribers get every update as it ships. The repo is live and I push directly to it.

Getting the Toolkit

The entire toolkit is a single Python file. Save it, install four dependencies, and run:

pip install pandas numpy yfinance matplotlib
python delphic_atlas_toolkit.py

That is it. The script downloads 5 ETFs, scans all 30 signals, prints the rankings, and generates an HTML report. No git, no package install, no configuration.

Download the file:

Read more

This PDF pulls them together into one document. 100 pages. The point is not the individual rankings — those are in the posts. The point is what happens when you compare the same signal across horizons, markets, and feature types.

What's Inside

7 atlas families unified. The daily Alpha Atlas, the 30-minute Atlas, the 5-minute Atlas, the exotic extension, the stock Atlas, and the microstructure Atlas — side by side for the first time.

30 stock alphas across 1,500 US equities. Which signal families work at which frequency, and which ones flip sign when you change the horizon.

18 exotic alphas on 30-minute bars. Distributional shape, volatility envelopes, normalised return logic — the signals that beat textbook indicators.

12 microstructure features. Queue imbalance, microprice bias, adverse selection, depth gradient, OFI. Ranked by mean IC across 12 instruments from BTC to EUR/USD to S&P 500 futures.

The Thesis

Signal quality is not a static property of the formula. It depends on horizon, market design, and the way price discovery happens in that market. Same idea, different plumbing, different answer.

Mean reversion dominates at daily frequency. At 30 minutes, trend starts to compete. At 5 minutes, equities reverse sign while FX and bonds stay positive. The exotic signals — skewness, kurtosis, Keltner — fill the gaps where standard signals fail.

The microstructure layer is a different world. Queue imbalance at IC 0.066 across all instruments. Microprice bias at IC 0.100. These are the features that matter at the shortest horizons.

Key Numbers

• Top microstructure feature: microprice_bias_bps — mean |IC| of 0.100 across all instruments and horizons

• Strongest 1-second signal: ETH Perp queue_imbalance_top1 at IC 0.414

• Strongest 60-second signal: ZN (10Y Treasuries) microprice_bias_bps at IC 0.309

• Best per-asset features: BTC → queue imbalance. EUR/USD → microprice bias. ES → spread. Each market has its own dominant signal

A good atlas is not a list of winners. It is a map of where the same idea works differently when the market structure changes.

Related Research

• The Intraday Alpha Atlas (5-Minute) — 12 alphas across 5 asset classes

• The Daily Stock Alpha Atlas — 30 alphas across 1,500 US stocks

• The Exotic Alpha Atlas — beyond textbook signals

• The Atlas Monitor — 1,000+ signals tracked weekly for decay

• Crisis Alpha — which signals survive regime changes

Download the PDF

100 pages. Print it, bookmark it, search it. All signal rankings, equity curves, and performance tables from the entire Atlas series in one place.

Read more

30 signals from the Atlas database. Daily, 30-minute, and 5-minute bars over the last 3 years. Every result vol-scaled to 15% annualized, Sharpe computed on monthly PnL. 10 of 10 signal families are positive at daily frequency. At 5-minute, 10 of 10 are positive.

Related: NVDA deep dive (free) | The Alpha Atlas Toolkit

NVDA Factor Exposures

Before testing alpha signals, I strip out what can be explained by known risk factors. The Fama-French 5-factor model plus momentum tells you how much of NVDA's return comes from market risk, size, value, profitability, and momentum - and how much is genuinely unexplained.

These exposures are not static. NVDA's relationship to each factor shifts as the business evolves and market regimes rotate.

NVDA has a market beta of 1.66, is small-cap tilted (SMB 0.14), growth-tilted (HML -0.94), and contrarian to momentum (Mom -0.30).

The annualized alpha is 0.4% - close to zero, meaning NVDA's returns are largely explained by its factor exposures. The signals below test whether there is timing edge on top of this.

Alpha Signals

10 alpha families from the Atlas database, each at 3 lookbacks (5, 20, 120 bars), for 30 signals per timeframe. Intraday signals filtered to positive bps/trade only.

Paid subscribers get the full per-timeframe equity curves, signal details, and methodology below.

Daily Timeframe

Best two signals: Ret-Z 5 (Sharpe 1.15, 17.3 bps/trade) and Accel-Fade 20 (Sharpe 0.91, 21.0 bps/trade).

30-Minute Timeframe

Best two signals: Fade-BO 5 (Sharpe 2.65, 2.4 bps/trade) and Ret-Z 5 (Sharpe 1.86, 1.1 bps/trade). Filtered to signals above 0.3 bps/trade. These are gross results.

5-Minute Timeframe

Best two signals: Keltner-Rev 20 (Sharpe 3.01, 0.6 bps/trade) and Fade-BO 20 (Sharpe 2.18, 0.6 bps/trade). Filtered to signals above 0.15 bps/trade. These are gross results - Sharpes will compress after spread and impact.

Appendix

Alpha Signals Tested

10 alpha families, each at 3 lookbacks (5, 20, 120 bars), for 30 signals per timeframe. All use lagged close (shifted by 1 bar) to avoid lookahead bias.

• Fade-BO - fade breakout: short at new rolling high, long at new rolling low.

• Fade-MA - fade moving average: short above SMA, long below SMA.

• CS-Rev - cross-sectional reversion: z-score of price-to-SMA ratio, then reverse.

• MR - mean reversion: z-score of price level, then reverse.

• Skew-Fade - fade the rolling skewness of price.

• Keltner-Rev - reversion from the Keltner channel center.

• Accel-Fade - fade the second derivative of price.

• Ret-Z - z-score of 1-bar return, then reverse.

• SkewKurt - signed kurtosis: negative skew times kurtosis.

• Fractal - trend following: range efficiency times z-score.

All returns vol-scaled to 15% annualized. Sharpe ratios computed on monthly aggregated PnL. Intraday signals filtered to >0.5 bps/trade. These are gross results - no execution costs included.

Educational purposes only. Not investment advice. Split/dividend adjusted data. Past patterns may not persist.

The headline: cross-sectional reversion dominates everything. CS-Rev 5-bar is the top signal in 7 of 11 sectors at the 1-bar horizon, peaking at Healthcare 6.40 and Financial Services 2.11. At the 5-bar horizon (2.5 hours), Healthcare CS-Rev hits 5.60. At 20 bars (10 hours), Return Z-Score Reversion takes over with Healthcare reaching 6.56 - the atlas peak.

Every signal is direction-agnostic: if a strategy shows negative Sharpe, we trade the opposite side. Execution: signal at bar close, enter at next bar's open, exit N bars later at close.

1-Bar Holding Horizon (30 minutes)

• CS-Rev 5-bar wins 7 of 11 sectors. Healthcare (6.40), Financial Services (2.11), Energy (3.26), Basic Materials (2.08), Consumer (2.35), Industrials via 20-bar (1.80), Utilities (1.64). Cross-sectional reversion - buying sector losers, selling winners within each half-hour - is the dominant intraday force in equities.

• Technology is the outlier: Ret-Z Rev 20-day at 3.72. Tech stocks trend at the intraday scale. The flipped signal means trend-following (not fading) the 120-bar MA works. This aligns with tech's momentum-driven microstructure.

• Skew Fade shines in Comms (2.80) and Real Estate (1.68). Third-moment signals capture asymmetric mean-reversion patterns that CS-Rev misses in these sectors.

Read more

The headline: CS-Rev 5-bar dominates almost universally. It wins 10 of 11 sectors at 1-bar, peaking at Financial Services 2.11 and Energy 3.26. At 5 bars (25 minutes), CS-Rev stays dominant across all sectors. At 20 bars (100 minutes), Accel Fade emerges for Healthcare (2.70) and Tech (1.84) while CS-Rev remains strongest elsewhere.

Every signal is direction-agnostic: if a strategy shows negative Sharpe, we trade the opposite side. Execution: signal at bar close, enter at next bar's open, exit N bars later at close.

1-Bar Holding Horizon (5 minutes)

• CS-Rev 5-bar wins 10 of 11 sectors. Financial Services (2.11), Energy (3.26), Comms (2.80), Technology (3.72), Industrials (2.88), Healthcare (3.38), Consumer (3.27), Utilities (2.66), Real Estate (1.93). Cross-sectional reversion at 5-minute frequency is the single most dominant alpha pattern in the entire stock atlas series.

• Basic Materials is the outlier: Fade 5-day breakout at 2.76. The only sector where a standard breakout signal beats CS-Rev. Materials stocks exhibit classic breakout-fade microstructure even at 5-minute bars.

• Healthcare leads at 6.40. The hardest sector on daily bars (best 0.94) becomes the strongest on 5-minute bars. Intraday cross-sectional dynamics in banks and insurance stocks create massive alpha.

Read more

This post applies 18 exotic alphas from 6 non-standard signal families to the same 5 asset classes on 5-minute bars. Same rules: no optimization, no fitting, no lookahead, no transaction costs. All returns use open-to-close execution: signal computed at close_t, position entered at open_{t+1}, exited at close_{t+1}. This eliminates shared-variable bias between signal and return.

The question: does going from textbook to exotic buy you alpha, or just complexity?

Signal Definitions

18 alphas from 6 exotic families, each at three lookback horizons N ∈ {5, 20, 120} bars (~25 minutes, ~100 minutes, ~10 hours):

• Skewness Fade. Signal = −skewₙ(P). The rolling skewness of lagged close prices. Positive skewness means the right tail is fatter -prices have been making outsized moves upward. This alpha fades that asymmetry: sell when skew > 0, buy when skew < 0. At N=5 this captures micro-distribution shifts over 25 minutes; at N=120 it captures multi-session skewness regimes.

• Keltner Reversion. Signal = −(P − SMAₙ) / ATRₙ. The classic z-score mean reversion, but normalized by Average True Range instead of standard deviation. ATR uses the true range (max of |H−L|, |H−C₁|, |L−C₁|), which captures intrabar volatility and gaps that σ misses. Think of it as measuring distance from the SMA in ‘volatility envelope’ units rather than standard deviation units.

• Acceleration Fade. Signal = −zscoreₙ(Δ²P). The z-scored second finite difference of lagged close: Δ²P = (Pₜ₋₁ − Pₜ₋₂) − (Pₜ₋₂ − Pₜ₋₃). This is price curvature -positive when the move is accelerating upward (convex), negative when decelerating. The alpha fades unusual acceleration: bet that parabolic moves don’t sustain. At N=5, this fires on micro-parabolas within a single session.

• Return Z-Score Reversion. Signal = −zscoreₙ(rₜ₋₁) where rₜ₋₁ = Pₜ₋₁ / Pₜ₋₂. Classic MR z-scores the price level: “is the price far from its average?” This z-scores the return: “was the last return unusually large?” The two diverge in trends -price z-score stays high but return z-score resets quickly -and agree on spikes. This alpha is a pure return-space mean reversion signal.

• Signed Kurtosis Fade. Signal = −skewₙ × kurtₙ. The product of negated skewness and kurtosis. When the distribution is both skewed (directional asymmetry) and fat-tailed (extreme moves likely), the signal fires hardest. Positive skew + high kurtosis = strong short. Negative skew + high kurtosis = strong long. Normal kurtosis = weak signal regardless of skew. This is a third-moment × fourth-moment interaction - no standard alpha uses this combination.

• Fractal Regime Trend. Signal = (rangeₙ / pathₙ) × zscoreₙ. The ratio of the N-bar price range to the sum of absolute bar-to-bar moves is a fractal dimension proxy. High ratio ≈ price moved in a straight line (trending). Low ratio ≈ price zigzagged (choppy). Multiply by the z-score and you get a signal that trend-follows only when the market geometry says it’s actually trending. In choppy regimes the signal self-mutes. This is a regime-adaptive alpha with zero fitted parameters.

Applied identically to 30 instruments across 5 asset classes: equity index futures (ES, NQ, YM, NKD, FTSE, DAX), bond futures (TN, UB, US, ZN, ZF, ZT), commodity futures (GC, SI, CL, HG, ZW, ZC), G7 FX, and crypto (BTC, ETH, SOL, XRP, DOGE, ADA).

Period: January 2024 - February 2026. Sharpe ratios annualised from monthly returns. Up to ~225,000 bars per instrument (~150K for futures, ~225K for 24/7 crypto).

The Exotic Alpha × Asset Class Heatmap

Each cell: annualised Sharpe (left) and return per trade per unit bet (right) for one exotic alpha -asset class pair:

Left: annualised Sharpe. Right: RPT -return per trade assuming a ±1 unit position. Open-to-close execution: signal at bar close, enter next bar open, exit same bar close. No costs, no fitting, no lookahead.

What patterns emerge:

• Keltner Reversion is the dominant exotic family. It shares the same directional thesis as textbook MR (fade deviations from the moving average) but normalizes by true range. If ATR normalization produces higher Sharpes than σ normalization, it tells us that intraday volatility structure (gaps, intrabar range) contains information that standard deviation ignores.

• Skewness Fade separates asset classes. Markets with persistent skewness regimes (commodities trending, crypto trending) should show signal in the skewness family. Markets with symmetric microstructure (bonds, FX) may not. The heatmap reveals where distributional shape adds value beyond price levels.

• Acceleration Fade captures a different effect. The second derivative is orthogonal to both level (MR) and first-derivative (momentum) signals. Parabolic move fading should work best in markets prone to overshoot-and-correct dynamics -crypto and commodities during trend exhaustion.

• Return Z-Score vs Price Z-Score: the subtle difference. Return-space MR won’t flag a smooth, persistent trend (returns are normal, just consistently positive). It only fires on spikes. Compare its heatmap column with the textbook MR from the original Atlas to see where this distinction matters.

Best Exotic Alpha per Asset Class

The key comparison: how do these exotic winners stack up against the textbook winners from the original Atlas? If the best exotic alpha in an asset class beats the best textbook alpha, the added complexity pays for itself. If not, stick with the simpler signal.

Read more