MMRL · Drawdown-Constrained Kelly & Private-Markets Research

Rigor under constraint.

The mathematics of how much risk a mandate can carry — and what to do as the cushion closes.

Market Microstructure Research Lab is an independent, non-commercial initiative dedicated to the quantitative analysis of risk-constrained capital allocation: how much risk a portfolio can carry under a drawdown mandate, parameter uncertainty, or untradeable exposure, and what policy is optimal given that constraint.

Research

Drawdown-Constrained Capital Allocation

Optimal leverage and position sizing when capital faces a hard drawdown barrier and the edge itself is estimated, not known. Develops the Bayesian Grossman–Zhou rule and dynamic de-risking (DDR) policies that nest the classical Grossman–Zhou model as a limiting case, and benchmarks them against the true HJB optimum across GBM, regime-switching, Student-t, jump-diffusion and GARCH environments.

Tail Risk & Estimation Uncertainty in Position Sizing

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.

Illiquid & Mandate-Constrained Portfolio Design

For allocators holding an untradeable private-markets sleeve under a drawdown mandate: derives the maximum allocation to illiquid assets the mandate can actually sustain, and shows how capital calls draining the liquid sleeve — faster than distributions replenish it — can make a mandate structurally infeasible regardless of manager skill. Extends to semi-liquid funds — interval and tender-offer funds, non-traded BDCs — where a quarterly repurchase cap acts as a speed limit on redemptions, and characterises which gate designs are run-proof.

Working papers

How Close Is Bayes GZ to the True Optimum? A Validated Two-Channel Decomposition of the Drawdown-Constrained Kelly Gap — WP·2026·004, forthcoming December 2026. We close an open question from Sukhov (2026c) on the optimality of the Bayesian Grossman–Zhou drawdown-constrained Kelly rule. Correcting a dropped HJB term, we show the linear rule is exact at the barrier but not at the peak, decompose the gap into shape and amplitude channels, and propose a validated, no-extra-cost replacement rule.

Speed Limits for Liquidity: Queues, Gates, and Runs in Semi-Liquid Funds — WP·2026·006, September 2026. Semi-liquid funds — non-traded BDCs, interval and tender-offer funds — repurchase shares each quarter at NAV up to a cap and ration excess requests pro rata. When does the cap prevent a run, and when does the queue it creates sustain one?

Drawdown Mandates and Untradeable Wealth: An Allocation Ceiling for Private Markets — WP·2026·005, August 2026. Institutional investors increasingly write maximum-drawdown mandates on portfolios that contain a large, untradeable private-markets sleeve. Within long-only, bounded-leverage policies no rule can satisfy such a mandate — so how much private-markets exposure can it actually carry?

The Bayesian Grossman–Zhou Rule: Drawdown-Constrained Kelly Betting with Parameter Uncertainty — WP·2026·003, June 2026. The Kelly criterion assumes that expected returns are known. Real investors must choose leverage before the edge is known with confidence — under drawdown limits that can end a strategy after a small loss from peak. Learning and survival are usually studied separately; this paper combines them.

Dynamic De-Risking under Drawdown Constraints: Structural Properties and Heuristic Rules for Kelly Betting — WP·2026·002, April 2026. The classic Kelly criterion prevents absolute bankruptcy, but ignores 'practical ruin' triggered by drawdown limits (e.g. mandate revocation).

Bayesian Kelly Criterion with Parameter Uncertainty: A Robust Framework for Position Sizing Under Estimation Risk — WP·2026·001, March 2026. The classical Kelly criterion provides an optimal solution for position sizing by maximizing the expected logarithmic growth rate of capital — but its practical application is severely limited by parameter uncertainty.

Researcher

Sergei Sukhov, Founder & Lead Researcher. Independent quantitative researcher working on drawdown-constrained capital allocation — how much risk a mandate can carry when part of the portfolio is illiquid or subject to structural constraints, and how to size positions and de-risk without violating that mandate.