SHORT-HORIZON PRICE DIRECTION IS NOT PREDICTABLE: A NEGATIVE RESULT

Author: Cooper E. (jcooperkai)
Venue: Independent research note
Year: 2026

ABSTRACT

A common assumption among retail traders is that short-horizon price direction
carries exploitable signal. This note tests that assumption directly on 258,737
real one-minute bars spanning roughly 180 days, using walk-forward validation
with no lookahead, and metrics implemented from scratch rather than taken from a
library. Direction over a fifteen-minute horizon is not predictable: walk-forward
AUC is 0.5105 against a 0.5 baseline, and the Brier score improves on a
coin-flip by 0.00004. The result is reported because it rules out an entire
strategy class, and because negative results of this kind are rarely published.

1. SETUP

Data: 258,737 one-minute bars of real market data, roughly 180 days. Windows are
non-overlapping and fifteen minutes long. Each window's label is simply whether
the close exceeded the open.

Features, computed strictly from history before the window opens: multi-scale
momentum over 1, 5, 15, 30 and 60 minutes; realised volatility over two scales;
sign persistence; a volume trend ratio; time-of-day encoded as sine and cosine;
and a sixty-minute drift term. Thirteen features in total.

Validation is expanding-window walk-forward across six folds, purged by one
window so no training sample overlaps a test window. The model is logistic
regression written from scratch. Brier score, AUC and expected calibration error
are also implemented from scratch, so no library convention is silently assumed.

2. RESULT

  Metric   Model     Baseline    Verdict
  Brier    0.24996   0.25000     +0.00004 improvement
  AUC      0.5105    0.5         essentially no skill
  ECE      0.0096    --          well calibrated, but calibrated at ~0.5

11,497 out-of-sample windows were tested. The model is well calibrated in the
sense that its confidence matches its accuracy -- but the value it is confident
about is a coin flip. Calibration without discrimination is not signal.

3. WHAT SURVIVES

The instrument is a binary option struck at the window-open price. At minute t
inside the window, its driftless fair value is

  f(t) = Phi( ln(S_t / K) / (sigma * sqrt(tau)) )

with sigma a trailing one-minute realised volatility estimate and tau the time
remaining. Measured against realised settlement, this fair value is calibrated
(ECE ~= 0.02) and increasingly decisive as tau falls: AUC 0.603 at 14 minutes
remaining, 0.759 at 10, 0.883 at 5, 0.953 at 2, and 0.977 at 1.

This is not alpha. It is the option's delta, and any efficient quote observes the
same spot and prices it identically. The only tradeable residual is the extent to
which a quoted mid LAGS this fair value, or misprices volatility.

4. BOUNDING THE RESIDUAL

Modelling a mid as the fair value lagged by L and shrunk toward 0.5 by a
favourite discount d, and trading only when the disagreement exceeds the
half-spread, produces a measurable edge surface. With no lag and no discount --
an efficient mid -- the edge is zero and no trade fires. That control matters:
it demonstrates the measurement cannot manufacture profit from an efficient
quote.

Both L and d are live-measurable quantities, not free parameters. Establishing
them requires recording quotes against spot over real elapsed time, and cannot
be obtained from historical bars.

5. WHY PUBLISH A NULL

Two harness defects were found and fixed before these numbers were trusted. A
clamp asymmetry, in which fair value was left unclamped while the modelled mid
was clamped, manufactured a spurious one-to-two cent gap on near-certain
contracts and turned an efficient-mid control into a large fictitious profit.
Unbounded Kelly reinvestment across tens of thousands of sequential windows
produced figures with no economic meaning. Both were caught by insisting that the
zero-edge control return exactly zero.

The discipline generalises: any backtest should contain a configuration in which
profit is impossible, and that configuration should be checked first.

REFERENCES

[1] G. Brier. Verification of forecasts expressed in terms of probability, 1950.
[2] F. Black, M. Scholes. The pricing of options and corporate liabilities, 1973.
[3] M. Lopez de Prado. Advances in Financial Machine Learning, 2018.
