Spectral Alpha: Trading Signals from Fourier Risk Coefficients

The Spectral Fenton Distribution compresses a portfolio's loss distribution into 130 parameters: 128 Fourier coefficients plus a location and scale anchor. PCA on the coefficient time series reveals that distributional dynamics are effectively 3-dimensional: \(z_1(t)\) captures the risk level (97.8\% of variation, \(r = 0.998\) with VaR), \(z_2(t)\) captures asymmetry shifts, and \(z_3(t)\) captures tail weight changes (Nagy, 2026f). In a controlled simulation of 500 trading days with an embedded volatility crisis, we show these spectral coordinates are predictive trading signals. A momentum strategy on \(z_1\) achieves a Sharpe ratio of 1.50 (bootstrap 95\% CI: [0.82, 2.18]), outperforming mean-reversion (\(-0.92\)), breakout (0.96), and cross-mode (vol-skew divergence, \(-0.16\)) strategies. The breakout detector fires at the onset of the crisis (\(z_1 = -52.7\sigma\) on day 300), providing early warning. The combined strategy achieves Sharpe 1.28 with a maximum drawdown of 11.8\%. These results suggest that the spectral coefficient space --- originally designed for risk measurement --- contains exploitable structure for alpha generation: the same 130 numbers that price risk also predict returns.