Tail Risk & Estimation Uncertainty in Position Sizing

The question

Connects a known result in Bayesian nonparametrics — posterior inconsistency of the tail index under Dirichlet-process mixture priors — to constrained Kelly sizing. Unconstrained Kelly turns out consistent despite the inconsistent tail estimate; a drawdown- or VaR-constrained fraction is not, and its error is indexed by extrapolation depth into the tail rather than by sample size.

Tail-Risk Transmission Identity

ξ

tail index

L

extrapolation length beyond the observed data

κ(y_p)

limited-liability saturation factor

Working papers

No paper in this area has been posted yet. The work is in progress; write to the Lab for the current draft.