#!/usr/bin/env python3 """ PRIORS No.1 — The Pattern That Wasn't A runnable, dependency-free demonstration of overfitting / selection bias. What it shows: if you test enough random "strategies" against pure noise and keep the one with the best in-sample Sharpe, it will look brilliant on the data it was chosen from — and collapse on data it has never seen. This is SYNTHETIC data. It is an illustration of a statistical trap, NOT a strategy, a backtest of any real approach, or any representation of performance. Run: python3 priors-01-overfitting.py Out: priors-01-results.md + 02-insample-outofsample-chart.svg Pure standard library. Deterministic (fixed seed) so anyone gets the same result. """ import random import math import statistics SEED = 254 T = 504 # ~2 trading years SPLIT = 252 # first year = in-sample, second = out-of-sample N = 1000 # number of random strategies we "search" over ANN = math.sqrt(252) def sharpe(returns): if len(returns) < 2: return 0.0 sd = statistics.pstdev(returns) if sd == 0: return 0.0 return (statistics.mean(returns) / sd) * ANN def main(): random.seed(SEED) # The market is pure noise: zero expected return. There is NO edge to find. market = [random.gauss(0, 0.01) for _ in range(T)] # Each "strategy" is a random sequence of long/short bets, fixed in advance. strategies = [] for _ in range(N): pos = [random.choice((-1, 1)) for _ in range(T)] ret = [pos[t] * market[t] for t in range(T)] strategies.append((sharpe(ret[:SPLIT]), ret)) # Keep the single best strategy BY IN-SAMPLE SHARPE — i.e. we "discover" it. strategies.sort(key=lambda x: -x[0]) best_is_sharpe, best_ret = strategies[0] best_oos_sharpe = sharpe(best_ret[SPLIT:]) # Context: the whole population, and the top-10 winners out-of-sample. all_is = [s for s, _ in strategies] top10_oos = sorted(sharpe(r[SPLIT:]) for _, r in strategies[:10]) median_is = statistics.median(all_is) top10_lo, top10_hi = top10_oos[0], top10_oos[-1] # Equity curve of the "winner" across the full period (cumulative return). eq, run = [], 0.0 for r in best_ret: run += r eq.append(run) # ---- honest write-up ------------------------------------------------- md = f"""# Priors No.1 — results (reproducible) Synthetic illustration of overfitting. Not a strategy or any performance claim. - Strategies searched: **{N}** (each a random sequence of long/short bets) - Market: **pure noise**, zero expected return — there is no real edge to find - Period: {T} days, split {SPLIT} in-sample / {T-SPLIT} out-of-sample - Seed: {SEED} (deterministic) | Metric | Sharpe | |---|---| | Best strategy — **in-sample** (the number that would sell it) | **{best_is_sharpe:.2f}** | | Same strategy — **out-of-sample** (what was actually left) | **{best_oos_sharpe:.2f}** | | Median strategy — in-sample | {median_is:.2f} | | Top-10 in-sample winners — out-of-sample (they scatter) | {top10_lo:.2f} to {top10_hi:.2f} | The best in-sample Sharpe of ~{best_is_sharpe:.1f} was produced by luck alone, from searching {N} random bets against noise. Out-of-sample it is ~{best_oos_sharpe:.1f}. The honest number was never the {best_is_sharpe:.1f}. It was the {best_is_sharpe:.1f} *penalized for how many times we went looking.* """ with open("priors-01-results.md", "w") as f: f.write(md) # ---- chart (SVG built from the real numbers) ------------------------- write_svg(eq, best_is_sharpe, best_oos_sharpe) print(md) print("wrote priors-01-results.md and 02-insample-outofsample-chart.svg") def write_svg(eq, is_sharpe, oos_sharpe): X0, X1, Y0, Y1 = 200, 1460, 290, 720 # plot box lo, hi = min(eq), max(eq) pad = (hi - lo) * 0.12 or 1.0 lo, hi = lo - pad, hi + pad def px(i): return X0 + (X1 - X0) * (i / (len(eq) - 1)) def py(v): return Y1 - (Y1 - Y0) * ((v - lo) / (hi - lo)) split_x = px(SPLIT) is_pts = " ".join(f"{px(i):.1f},{py(v):.1f}" for i, v in enumerate(eq[:SPLIT+1])) oos_pts = " ".join(f"{px(i):.1f},{py(v):.1f}" for i, v in enumerate(eq) if i >= SPLIT) svg = f''' PRIORS No.1 · ANTHERA The pattern that wasn't {N} random strategies vs pure noise. This is the best one — by luck. THE PRESENT · UNSEEN DATA → IN-SAMPLE OUT-OF-SAMPLE in-sample Sharpe {is_sharpe:.1f} — looks brilliant out-of-sample Sharpe {oos_sharpe:.1f} — nothing was there ANTHERA CAPITAL synthetic data · illustration of overfitting · not a strategy or performance ''' with open("02-insample-outofsample-chart.svg", "w") as f: f.write(svg) if __name__ == "__main__": main()