Long-only allocation as the winning probabilities of a correlated race.
Abilities calibrate the race to a benchmark; the tilt re-runs it under the
estimated dependence, so the portfolio is a controlled perturbation of the
benchmark. It is free of the duplication paradox, tail-consistent when the race
is driven by a downside-dependent simulation, and solves an implied
convex-regularizer objective with a smoothness (low-turnover) bound. Built on the
thurstone package.
Read the PDF →
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Source
Splitting credit among correlated contributors without double counting.
The probability that a competitor wins a noisy race is a rule for attributing
credit. It is a probability share, symmetric, differentiable in the abilities, and
redundancy-aware: contributors that move together split a single share instead of
each taking a full one. It updates online and costs O(Mn) in one
Monte-Carlo pass, with no coalition enumeration. It is not a Shapley value; Shapley
measures coalitional cooperation, this measures selection relevance.
Read the PDF →
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Source
Which portfolio rules survive out of sample, after costs.
Eleven online constructions backtested over thousands of random subsets of U.S.
stocks, mapped against two axes: the number of names and the cost of trading. Three
regions. Few names and cheap trading, classic minimum-variance wins. Many names and
cheap trading, factor-model minimum-variance wins, by a margin that grows with the
number of names. Above about five to ten basis points of trading cost, inverse-variance
weighting wins everywhere, because turnover rather than estimation error is what
hurts.
Read the PDF →
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Source
Robust, inversion-light allocation along a smooth Fiedler seriation.
A one-parameter (gamma) bridge between hierarchical risk parity and
minimum variance, ordered by Fiedler seriation rather than a dendrogram, so the
hierarchy and the weights are a smooth function of the covariance. The idea first
appeared as a blog post; the theory and experiments are in the paper, with background,
bibliography, and a literature map at
schur.microprediction.org.
Paper (arXiv 2411.05807) →
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Original blog
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Background & map
The flat-partition bridge: NCO at γ=0, the global optimum at γ=1.
Block inversion writes the unconstrained minimum-variance portfolio as one problem per
cluster on a Schur-complemented block. Conditioning each cluster on one knot from every other
cluster, in the manner of a Vecchia approximation, is exact under a rank-one model of
cross-cluster dependence. Under estimation error the optimal γ can be strictly interior,
with exact examples. Theory lives in the schur repo; the engine here is
SchurBridge.nco_to_min_variance.
SSRN 7480738 →
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PDF
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Demos
HERC's budget rule is already the optimizer's; what it lacks is two Schur complements.
Damping the two complements by γ and η gives a square with HERC at one corner and
the global optimum at the opposite corner. The inner dial makes Stevens' identity a
one-parameter path with a closed form and an explicit long-only frontier, and on an
equicorrelated cluster it is the straight segment from inverse variance to cluster minimum
variance. Under estimation error the best point is often inside, with a sign criterion and
exact examples. The engine here is SchurBridge.herc_to_min_variance.
PDF →
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Which Schur is which
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All roads lead to minimum variance