Conformal prediction is not one technique - it is a family of methods, each with its own strengths and weaknesses. Split Conformal, Mondrian, ACI, CQR - they all produce valid prediction intervals, but they behave very differently depending on the signal you feed them.
It is not an implementation detail. On the same alpha signal with the same data, switching from Split Conformal to ACI turns a Sharpe of -1.08 into +1.10. On another signal, that same switch destroys all the alpha. The conformal method matters as much as the alpha itself, and the right choice depends on what type of signal you have.
If you want the theory, Valeriy Manokhin literally wrote the book (Applied Conformal Prediction) and his Substack is the best running commentary on what practitioners get wrong. For a worked example, Vertox Quant walked through wrapping a neural-net vol forecaster in Split Conformal, CQR, and ACI for distribution-free interval estimation.
Both answer how to apply conformal prediction to a trained model. I wanted to answer a different question: which conformal method should you use, and does the answer depend on what type of alpha signal you have?
I took 18 raw alpha signals across four categories, applied six conformal methods to each, and measured which method-signal combinations produce tradeable Sharpe ratios. No gradient boosting. No neural network. Just the raw signal, a linear calibration, and conformal prediction on top. The answer is a taxonomy: stationary signals need Split, regime-switching signals need ACI, vol-conditional signals need Mondrian, and binary signals don't benefit from confidence filtering at all. Important caveat: all results in this post are in-sample. The taxonomy is a hypothesis to test out-of-sample, not a guaranteed recipe.
What Is Conformal Prediction?
Every alpha signal gives you a direction: go long or go short. Conformal prediction adds a prediction interval around the expected return - with a mathematical coverage guarantee that requires no distributional assumptions. The interval tells you how confident the signal is right now, on this trade.
It works with any model underneath. You hold out a calibration set, measure how wrong the model is on that set, and use those errors to build intervals on new data. The guarantee: the true value will fall inside the interval at least X% of the time, no matter what distribution the data comes from.
The Six Methods
Split Conformal is the baseline. Compute one quantile from the calibration residuals, apply it to every test trade. Static, simple, distribution-free. The fixed-width and normalized variants collapse to identical results with a linear model, and CQR (Conformal Quantile Regression) produces the same intervals too.
Mondrian calibrates per regime. It splits the calibration set into terciles by 60-day realised vol and computes a separate quantile for each group. The prediction intervals become regime-conditional - tighter in calm markets, wider in volatile ones.
Weighted Conformal applies exponential decay to calibration scores, so recent residuals count more than old ones. A soft, offline version of online adaptation.
ACI (Adaptive Conformal Inference) goes further - it adjusts the coverage target after every test observation based on whether the previous interval was correct. If the model starts miscovering, ACI widens intervals in real time. It tracks regime shifts as they happen.
In practice, with a linear base model, Split/CQR/Weighted produce nearly identical results. The real variation is between three distinct approaches: Split, Mondrian, and ACI.
Dataset
Universe: 24 US ETFs - SPY, QQQ, IWM, DIA (broad equity), XLF, XLE, XLK, XLV, XLI, XLU, XLP, XLY, XLC, XLB, XLRE (sectors), TLT, IEF, LQD (fixed income), GLD, SLV (metals), EEM, EFA (international), USO (energy), VXX (volatility).
Period: January 2010 to July 2026. Train: first 60% of dates. Calibration: next 20%. Test: final 20% (May 2023 to July 2026). All results shown are test-period only - no in-sample numbers.
Horizon: 5-day forward returns. All results are gross of costs. A 5-day hold on liquid ETFs implies roughly 2-4 bps round-trip - negligible relative to the signal magnitudes shown.
350,000+ signal-return observations in the test set across all 18 alphas.
I tested 18 raw alpha signals across four categories (stationary z-scores, higher-order statistics, event/threshold, and trend/momentum), applied each conformal method, and traded only the top 20% most confident signals. Full signal definitions, calibration steps, and the confidence filter are in the Appendix.
Results
Raw is the baseline (no filtering). Split, Mondrian, and ACI show the Sharpe after each method's top-20% confidence filter. Best Lift is the largest improvement over raw. Bold green values beat raw by more than +0.3 Sharpe.
Stationary z-scores: use Split
When: signal magnitude maps linearly to forward returns, stable across regimes.
Why: static calibration captures a constant relationship. No need for regime adaptation.
Results: MR_20: +0.57 → +1.31. MR_5: +0.51 → +1.20. Expect +0.5 to +0.8 lift.
Higher-order statistics: use Mondrian or ACI
When: the signal-return relationship changes with vol regime or market conditions.
Why: Split averages across regimes and dilutes the signal. Mondrian calibrates per regime; ACI adapts online.
Results: SkewFade_60: +0.26 with Split, +1.79 with Mondrian. AccelFade_20: -1.08 with Split, +1.10 with ACI. If the raw signal is already strong (SkewFade_20 at +2.45), don't bother.
Event/threshold signals: skip confidence filtering
When: the signal is binary (breakout/no breakout, spike/no spike).
Why: no meaningful magnitude for the confidence filter to rank. Top-20% filter becomes random selection.
Results: FadeBO_60: +0.53 with every method. VolShock_20 drops from +1.02 raw to +0.27. Exception: GapFade (-0.18 → +1.22 with ACI) because gap size is continuous.
Trend/momentum: use ACI
When: the signal works in trending markets and fails in mean-reverting ones.
Why: ACI tracks which regime is active and concentrates trades in the right windows. Note: Mom_5/Mom_20 have negative raw Sharpe because mean reversion dominates on this ETF universe - reversing them gives you the MR signals above. The value of ACI is detecting when momentum works, not the average direction.
Results: Mom_60: +0.02 → +2.54 with ACI (biggest lift). RangeBO_20: -0.30 → +1.03 with Mondrian. Caveat: the test period (2023-2026) includes a strong equity rally favouring momentum.
Cumulative P&L for the top 6 alpha-method combinations. Raw (blue) vs conformal-filtered (green).
Mom_20: -0.57 raw, +0.29 with Mondrian. Medium-term momentum goes from negative to slightly positive when calibrated per vol regime. The lift is modest but the direction reversal is notable.
The coverage guarantee is distribution-free and model-agnostic: it holds even with a linear calibration on raw signals. This is conformal prediction's core strength - the intervals are valid regardless of whether the underlying model is good or bad.
Full Results
Raw Sharpe, best conformal method, filtered Sharpe, and lift for all 18 signals.
Conclusions
Conformal prediction works, but only if you match the method to the signal. The wrong method doesn't just fail to help - it actively destroys alpha (AccelFade_20: +0.56 raw, -1.08 with Split, +1.10 with ACI). The practical question is not "should I use conformal prediction?" but "which method for this signal?"
What I would actually trade: MR_20 with Split Conformal. Stable signal, consistent +0.74 Sharpe lift, no regime dependency. ACI on momentum is the flashiest result, but needs to survive a sideways market first.
What this study does NOT show
These are in-sample results. The "test" set is the final 20% of a single historical window. There is no walk-forward validation, no multiple independent test periods, and no live trading. The taxonomy (Split for z-scores, ACI for momentum, Mondrian for skew) is a pattern observed once. It could be stable or it could be an artefact of this specific data period.
The Sharpe lifts are best-case. I'm showing the best method for each signal after seeing all six methods. In practice you'd have to choose the method before running the test, and you'd sometimes pick wrong. The reported lifts overstate what you'd capture live.
One universe, one horizon, one base model. All results are on 24 US ETFs with 5-day holds and a linear calibration. Different asset classes, shorter horizons, or nonlinear base models could produce entirely different method rankings. Don't assume the taxonomy transfers without retesting.
Conformal prediction doesn't create alpha. It filters when to act on alpha you already have. If the underlying signal is noise, conformal prediction will give you valid intervals around noise. The coverage guarantee holds either way - it just means your intervals are honestly wide.
What this study DOES show
The method choice matters. That finding is robust regardless of the specific Sharpe numbers. AccelFade_20 going from -1.08 with Split to +1.10 with ACI is not a rounding error that disappears with a different test window. The mechanism is clear: Split applies a static filter to a non-stationary signal, which is structurally wrong. ACI adapts, which is structurally right. Even if the exact lift changes out-of-sample, the direction of that result should persist.
The practical value is the framework: before applying conformal prediction, ask whether your signal-return relationship is stable, regime-dependent, or binary. That question has a correct answer independent of any backtest, and it determines which method to use.
Data: 24 US ETFs, Jan 2010 - Jul 2026, 60/20/20 train/cal/test split by date, 5-day forward returns. This is research, not investment advice.
Appendix: Signal Definitions and Calibration
The 18 Alpha Signals
The four categories are not arbitrary. They determine which conformal method works.
Category 1: Stationary z-scores. MR_5, MR_20, MR_60 (mean reversion), RetZ_5, RetZ_20 (return z-score reversion). Continuous signals where magnitude is directly informative: a z-score of -3 should predict a larger reversal than -0.5. The signal-return relationship is roughly linear and stable over time.
Category 2: Higher-order statistics. SkewFade_20, SkewFade_60 (rolling skewness fade), AccelFade_20 (acceleration fade), Keltner_20, Keltner_60 (ATR-normalized reversion). Continuous but non-linear or regime-dependent. Large skewness doesn't simply mean "bigger reversal" - it can mean trend exhaustion or regime shift depending on context.
Category 3: Event/threshold signals. FadeBO_20, FadeBO_60 (fade breakout), VolShock_20 (capitulation fade), GapFade (overnight gap fade). Binary or near-binary: the signal is either on or off. There is no "half breakout."
Category 4: Trend/momentum. Mom_5, Mom_20, Mom_60 (momentum z-scores), RangeBO_20 (range efficiency breakout). Signals that follow price direction rather than fading it.
Conformal Calibration
Step 1: Linear calibration. On the training set (first 60% of dates), fit a single coefficient: E[5-day forward return] = β × signal. One number.
Step 2: Conformal calibration. On the calibration set (next 20%), measure the normalized residuals: |actual return - predicted return| / |signal|. The 80th percentile becomes the conformal quantile q.
Step 3: Prediction intervals. On the test set (final 20%), each trade gets an interval: prediction ± q × |signal|.
Confidence Filter
Confidence = |prediction| / (interval width / 2). A narrow interval on a large predicted return is high confidence; a wide interval on a small prediction is low confidence. I trade only the top 20% most confident signals. Hit rates across all strategies are 49-56% - the alpha comes from asymmetric payoff magnitude, not win rate.