Three Modes for Simulated Risk: A Data-Driven Spectral Basis for Portfolio Loss Distributions

The Spectral Fenton Distribution represents a portfolio loss distribution with 128 Fourier coefficients. Under the deterministic simulated protocol reported here (5 assets, 250 trading days, seed 42), a single principal component captures 97.81% of observed coordinate variation and three components capture 99.9996%. Three coordinates provide a 43x per-day coefficient compression with a maximum relative VaR reconstruction error of 0.0416%. A basis fitted on days 1-200 has a maximum relative VaR error of 0.0189% on days 201-250. The dominant mode is strongly associated with simulated VaR; economic interpretations of the remaining modes are tentative. The coordinates provide a descriptive reduced-order representation, not a calibrated detector or an empirical claim about real portfolios.