Demos
Interactive, in-browser — they run on the page, no install.
The estimators
Thurstone portfolio · live race in the browserThe Thurstone race: clone a stock
Weights are the winning probabilities of a race among the assets. Add a near-duplicate of a Dow name and drag its correlation: the race de-duplicates the pair continuously, equal weight is blind to it, and minimum variance takes large opposite positions whose sign flips under a 0.1% input change. Runs the estimator's forward pass on 131,072 common-seed scenarios, live.
Schur-complementary · HRP to minimum varianceOne slider from HRP to minimum variance
The Schur γ coupling on 28 Dow names: drag γ and watch the
weights deform continuously from HRP toward minimum variance, over a Fiedler-seriated
correlation heatmap. Includes the turnover cost of the dendrogram this construction
replaces, measured over 700 weekly rebalances.
The geometry of choice
The race maximizes ability minus an entropy that knows the correlation. Merge two of three assets with a slider: softmax's triangle never moves (Luce's axiom in geometric form), while the race's attainable set collapses from a triangle to a segment and its maximum-entropy portfolio drifts to the two-horse limit (¼, ¼, ½). Computed live.
Tail consistency · beyond the second momentTwo clusters, one covariance
Two five-name clusters with the same correlation matrix and the same marginals — one of them crashes together. Minimum variance and the Gaussian race treat them identically at every slider position, provably; the race driven by the simulation itself gives the crash-together cluster up to a quarter less weight.
High dimension · n/T past 1Five hundred assets, T days
Shrink the estimation window on a known-truth market and watch sample minimum variance pass from best-on-page (1.4× the true minimum at n/T = 0.25) to 91× at n/T = 0.99 to rounding noise once the covariance is singular — while the low-rank race holds flat at 3.3×, long-only, no inverse taken. The race runs live in the browser.
Dependence, tails, and 2008
Implied correlation · live Kalshi marketsTetrachoric correlation: World Cup edition
Spin a cloud of bivariate-normal draws until the "both reach the final" corner matches the market, and you have backed out an implied correlation. Then rank every pair of teams by how much their runs to the final co-move.
Portfolio overlay · real Dow dataTail-sensitive Black–Litterman
Drag the tail-view confidence φ and watch a crash-proofing overlay shade the Dow names that crash together more than their correlation implies — reverse optimization with a view on dependence, not returns.
Credit · default contagionBowling Alone: Do Copula Models Washout?
Companies are pins in a bowling rack; a shock cascades whole sectors into joint default. The correlation matrix settles, yet the joint-default tail blows past the Gaussian copula that matches every pairwise probability and marginal — the 2008 lesson, live.