Measuring the risk of 10,000 stocks is actually no harder than measuring the risk of five—the math stays exactly the same.
March 25, 2026
Original Paper
The Universal Risk Representation Theorem: Breaking the Curse of Dimensionality
SSRN · 6334498
The Takeaway
It is a standard belief that larger portfolios are exponentially harder to monitor and require massive data sets to manage risk accurately. This theorem proves that the 'curse of dimensionality' in finance is actually an artifact of how we run simulations, not a fundamental constraint of the market.
From the abstract
How many parameters does it take to compute every coherent risk measure for a portfolio of n assets? We prove the answer is Θ(log(1/ε)/ log ρ)-independent of n. For any portfolio whose sum density has analyticity radius ρ > 1, this many Fourier coefficients suffice (upper bound, constructive via the Eigen-COS method) and are necessary (lower bound, information-theoretic via Fourier mode counting). The bounds match, establishing the exact rate. A 5-asset portfolio and a 10,000-asset portfolio req