Fin Generative Portfolio

Classical portfolio optimization minimizes a single risk metric — variance, VaR, or CVaR — subject to return constraints. This produces portfolios that are optimal in one dimension but unconstrained in all others: two portfolios with identical VaR can have radically different skewness, kurtosis, or tail structure. We propose generative portfolio design: specifying the entire loss distribution shape as the optimization target, then solving the inverse spectral problem to find portfolio weights that produce it.

The Spectral Fenton Distribution (Nagy, 2026a) represents any portfolio of correlated lognormal assets by 128 Fourier-cosine coefficients \(\{A_k\}_{k=0}^{127}\). The forward map \(\mathcal{F}: \mathbf{w} \mapsto \{A_k\}\), computed by the Eigen-COS algorithm, is differentiable in the portfolio weights. We formulate the inverse problem as constrained nonlinear least squares — \(\min_{\mathbf{w}} \lVert \mathcal{F}(\mathbf{w}) - A_k^*\rVert_2^2\) subject to \(\sum w_i = 1\), \(w_i \geq 0\) — and solve it via Sequential Least Squares Programming (SLSQP).

Three applications are demonstrated: (i) distribution matching — replicate a target portfolio's risk profile with different assets, achieving 0.015% relative \(L_2\) coefficient error and \(< 10^{-4}\) VaR difference; (ii) targeted tail reduction — reduce the high-frequency spectral energy (which encodes tail risk) while preserving the distribution body; and (iii) spectral risk budgeting — decompose each asset's contribution to each Fourier mode, revealing which assets drive which frequencies of the risk profile. For a 5-asset portfolio, the full inverse solve takes \(\sim\)5 seconds; the spectral risk budget requires \(n+1\) forward evaluations (\(\sim\)50 ms total). We show that mean-variance, mean-CVaR, and distributionally robust optimization are recovered as special cases corresponding to constraints on progressively more spectral modes.