Drawdown Mandates and Untradeable Wealth
An Allocation Ceiling for Private Markets
By Sergei Sukhov · Market Microstructure Research Lab
Abstract
Institutional investors increasingly write maximum-drawdown mandates on portfolios that contain a large, untradeable private-markets sleeve. We show these commitments are mathematically incompatible: within the admissible class of long-only, bounded-leverage policies, none satisfies the mandate whenever the two sleeves are less than perfectly negatively correlated. In the Grossman–Zhou framework the mandate is enforceable because the investor can drive risky exposure to zero at the barrier; when part of the book cannot be sold, and cannot be hedged by the liquid sleeve, the diffusion coefficient of wealth has a strictly positive floor and the mandate is breached almost surely. We quantify the resulting second-best. Reparametrising the problem in terms of the controllable and uncontrollable volatility contributions (u, v) yields an exact law P(D > d) = (1 − d)^η and a ceiling on the attainable drawdown exponent that is exactly hyperbolic in the illiquid share, η*(v) = A/v − 1. We prove this ceiling is attained, uniquely, by a constant control over the class of drawdown-monotone feedbacks — a broad class of economically natural rules that do not increase risk as the drawdown deepens, containing the Grossman–Zhou, CPPI, fractional-Kelly and constant-proportion families — and we exhibit a non-monotone policy that beats it, which shows that mandates written on the frequency of breach are gameable, while a depth-weighted mandate cuts the gain from that manipulation roughly in half. Inverting the ceiling gives a closed-form maximum private-markets allocation under a frozen-share approximation: 12.4% at standard parameters, against reported allocations near 30%. A coupled-model diagnostic indicates the approximation is conservative, so the fully coupled ceiling is, if anything, lower. Finally, appraisal smoothing with Geltner inertia a inflates the perceived ceiling by exactly (1 + a)/(1 − a); at standard calibration this is by itself sufficient to account for most of the gap between the theoretical ceiling and reported allocations, though other explanations are not ruled out.
Keywords
- Private markets
- Drawdown mandates
- Allocation ceiling
- Illiquid assets
- Grossman–Zhou
- CPPI
- Appraisal smoothing
Cite this paper
Sukhov, S. (2026). Drawdown Mandates and Untradeable Wealth: An Allocation Ceiling for Private Markets. MMRL Working Paper WP-2026-005. SSRN. https://doi.org/10.2139/ssrn.7255538
@techreport{sukhov2026drawdown,
author = {Sukhov, Sergei},
title = {Drawdown Mandates and Untradeable Wealth: An Allocation Ceiling for Private Markets},
institution = {Market Microstructure Research Lab},
type = {MMRL Working Paper},
number = {WP-2026-005},
year = {2026},
month = aug,
doi = {10.2139/ssrn.7255538},
url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=7255538},
}