How is a conformal prediction interval different from a confidence interval?

A confidence interval describes uncertainty about a fixed quantity, such as a stock's average return. A conformal prediction interval is about the next individual outcome. Its width comes from the model's measured errors on held-out data, not from an assumed distribution, so it can be wrapped around any forecasting model.

Does a 90% conformal interval always contain 90% of stock returns?

No. The 90% holds on average across many forecasts, not for each stock, and only while new data resemble the calibration data. Markets do not always behave that way. Opulence Alpha's models are also refitted on the calibration months. Checked point-in-time over 2026, an earlier version held about 85–86% of outcomes in its bands. Recalibrating each month on recent outcomes lifted that to 88.3–88.6%. Coverage is measured, not assumed.

What is conformalized quantile regression (CQR)?

A form of conformal prediction introduced by Romano, Patterson and Candès (2019). Models estimate a low and a high quantile of the outcome. Errors on held-out data then widen or narrow that band until it reaches the stated coverage. Because the quantile models respond to each case, riskier stocks get wider bands than steadier ones.

FAQ · Conformal prediction

What is conformal prediction?

Reviewed against the platform's code on Sep 26, 2026

Conformal prediction turns any forecasting model into prediction intervals with a stated coverage. The model's errors on held-out calibration data decide how wide each interval must be so that, on average, a chosen share of outcomes (say 90%) falls inside it. It assumes no normal or other distribution. The one assumption is that new data resemble the calibration data.

Why it matters

A point forecast of +3% says nothing about whether −10% is plausible. Intervals built from a model's own assumptions are often too narrow for stock returns, which have fat tails and changing volatility. Conformal prediction swaps the assumption for a measurement: each interval is as wide as the model's held-out errors say it must be, and you can check afterwards whether it held.

How it works

In split conformal prediction, a model is fitted on one stretch of data and scored on a separate, later calibration set. Each new interval is widened by a high quantile of those calibration errors. A small-sample correction then gives at least 90% coverage on average when the data are exchangeable (Vovk, Gammerman and Shafer, 2005). Conformalized quantile regression starts from low and high quantile models, so riskier cases get wider bands (Romano, Patterson and Candès, 2019). Because markets shift, adaptive conformal inference adjusts its working level after each miss or hit (Gibbs and Candès, 2021).

How Opulence Alpha applies it

Opulence Alpha's return-range model uses conformalized quantile regression. Gradient-boosted trees (XGBoost) estimate the 5th, 50th and 95th percentiles of each stock's return relative to the average stock, over 1, 5, 21 and 63 trading days. A conformal correction then widens or narrows each band towards 90% coverage, in proportion to its width. It is fitted on the latest six months of known outcomes (twelve months at 63 days), using models trained only on earlier data. The models in use are afterwards refitted on all the data, so the 90% is a target to check against later outcomes, not a certainty. The Fair Value page sets aside names whose cash-flow value falls below the three-month model's price range.

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Related concepts

Probabilistic forecastingProbabilistic forecasting publishes a distribution of possible returns, with calibrated intervals, instead of one expected number — so a position can be sized from its uncertainty.Walk-forward validationWalk-forward validation tests a strategy the way it would have been used: fit on the past only, test on the next unseen period, then roll forward and repeat.Information coefficientThe information coefficient (IC) measures how well a signal ranks stocks: its correlation with the returns that followed, across stocks each date, averaged.

All concepts →Sector behaviour in every market regime →

Questions

How is a conformal prediction interval different from a confidence interval?: A confidence interval describes uncertainty about a fixed quantity, such as a stock's average return. A conformal prediction interval is about the next individual outcome. Its width comes from the model's measured errors on held-out data, not from an assumed distribution, so it can be wrapped around any forecasting model.
Does a 90% conformal interval always contain 90% of stock returns?: No. The 90% holds on average across many forecasts, not for each stock, and only while new data resemble the calibration data. Markets do not always behave that way. Opulence Alpha's models are also refitted on the calibration months. Checked point-in-time over 2026, an earlier version held about 85–86% of outcomes in its bands. Recalibrating each month on recent outcomes lifted that to 88.3–88.6%. Coverage is measured, not assumed.
What is conformalized quantile regression (CQR)?: A form of conformal prediction introduced by Romano, Patterson and Candès (2019). Models estimate a low and a high quantile of the outcome. Errors on held-out data then widen or narrow that band until it reaches the stated coverage. Because the quantile models respond to each case, riskier stocks get wider bands than steadier ones.

References

Vovk, V., Gammerman, A. & Shafer, G. (2005). Algorithmic Learning in a Random World. Springer.
Romano, Y., Patterson, E. & Candès, E. (2019). Conformalized Quantile Regression. Advances in Neural Information Processing Systems (NeurIPS) 32.
Gibbs, I. & Candès, E. (2021). Adaptive Conformal Inference Under Distribution Shift. Advances in Neural Information Processing Systems (NeurIPS) 34.

Educational content about research methods. Not investment advice.