Quantitative methods · Advanced · Weekly
Monte Carlo Sizing
How it works, and when it doesn't.
When low-frequency components dominate (period > 20 days), momentum strategies win. When high-frequency components dominate (period < 5 days), mean-reversion strategies win. Fourier analysis identifies which regime we're in.
Monte Carlo P(loss>5%)=5% — HIGH but momentum ambiguous (-2.3%). Defensive cash.
Why it works
Fourier Transform decomposes price returns into frequency components. Markets alternate between trend-dominated (low-frequency) and oscillation-dominated (high-frequency) regimes. By identifying the dominant frequency cycle, the strategy selects the appropriate trading approach for the current market microstructure.
The signal logic
- Apply FFT to last 252 days of SPY returns
- Identify dominant frequency components using power spectrum
- Long if low-frequency trend components dominate (>60% power)
- Watch if spectral profile is mixed
- Confidence scales with spectral purity of dominant cycle
When it fails
Real markets rarely have clean single-frequency behavior. Mixed spectral profiles give ambiguous signals near regime transitions.
- Best market
- Extended trending or ranging periods with stable, identifiable cycle structure
- Worst market
- Rapid regime transitions where spectral profile changes faster than the analysis window
Backtest
| Sharpe ratio | 0.42 |
| Annual return | 4.0% |
| Worst drawdown | -14.7% |
| Trades in the backtest | 377 |
Backtest on daily bars, positions taken the bar after the signal (no look-ahead).
Monte Carlo Sizing, live.
Re-scored after every close.
The platform runs this and 32 other strategies against the live tape each day — with the evidence behind every number.