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Portfolio Stress: how Neo measures book-level tail risk

When you ask Neo to stress your whole book, it answers one question: in a stressed regime, how large is the book's downside, and which position drives it? It returns a single stressed Expected Shortfall for the book, and a breakdown of that number into per-position contributions that sum to 100%.

This page is the model card. It explains the model and, just as importantly, why it is built the way it is.

Why not a Gaussian copula​

The obvious way to couple several positions is a Gaussian copula. Neo does not use it, on purpose.

A Gaussian copula has zero tail dependence for any correlation below one: it treats joint extremes as effectively independent — precisely when they are not. This is the property behind the Gaussian copula's role in the 2008 crisis ("The Formula That Killed Wall Street", Salmon, Wired, 2009): it priced correlated defaults as if catastrophes did not cluster.

DeFi collateral returns do the opposite of independent in a crisis. Depegs, liquid-staking-token slashing, and liquidation cascades are fat-tailed and they co-occur. A portfolio tail-risk model has to carry tail dependence, or it understates exactly the scenario the report exists to describe.

The model, in plain terms​

Neo builds the book's stressed loss from two pieces, kept honest separately:

Heavy-tailed marginals​

Each position gets a heavy-tailed loss distribution anchored to the risk engine's precomputed Expected Shortfall for that pool. The engine's figure sets the level of the loss; a heavy-tailed (Generalized-Pareto) shape restores the tail beyond that anchor, so the model stays fat-tailed where a thin bell would understate the extreme.

A Student-t copula for dependence​

The positions are coupled with a Student-t copula, which has positive tail dependence — it models positions co-crashing together. As its degrees of freedom rise it collapses to the Gaussian case, so nothing is lost by choosing it: the thin-tailed model is just the limit of the family Neo uses. Neo reports the average pairwise tail-dependence as a headline number: how strongly your positions co-crash.

Dependence estimated robustly​

The dependence structure is estimated from Kendall's tau — a rank-based concordance measure — rather than Pearson correlation. Pearson assumes a finite variance and a characteristic scale, both unreliable for power-law collateral returns, where a zero correlation is not independence. Kendall's tau depends only on the dependence structure and needs no finite second moment.

What you get back​

  • A single stressed Expected Shortfall for the book — the average loss in the tail set of simulated outcomes.
  • Per-position contributions that sum to 100% — each position's share of the book's tail loss, computed as an Euler allocation (the unique additive attribution of a coherent risk measure). This tells you which position drives the tail, not just how big the tail is.

The simulation is seeded and reproducible: the same book and snapshot produce the same numbers.

How to read it​

  • The headline ES is a modeled stress index, not a probability or a forecast.
  • The contribution breakdown is the actionable part: it ranks your positions by how much they drive the book's downside, which is often not the same ranking as position size.
  • Real extremes can exceed the modeled tail. The model is built to be honest about fat tails, not to promise a ceiling.

For single-pool reviews, see Risk Review Methodology (D1–D8).