Durability Explorer — Leverage × Drift × Volatility

Durability Explorer

Leverage is durable when the incremental drift from levering up exceeds the incremental drag it introduces. This tool plots excess compound growth ΔR(L) = R(L) − R(1) as a function of leverage. The region where ΔR(L) > 0 is the productive band. The growth-maximizing leverage L* is the continuous-time Kelly fraction: L* = (μ − r) / σ².

Model

R(L) = Lμ − ½L²σ² − (L−1)(r_f + s) − AUM
Volatility drag (½L²σ²) is intrinsic to geometric compounding and scales quadratically with leverage
Financing drag ((L−1) × r) is the cost of borrowed capital; (L−1) dollars borrowed per dollar of equity at rate r = r_f + s
AUM fee is a flat annual charge on Jr equity

Assumptions

Analytical curve assumes constant drift (μ), volatility (σ), and risk-free rate (r_f)
Daily rebalancing to maintain constant leverage L
Empirical overlay uses historical BTC daily prices (2015–2025) with time-varying r_f
No liquidation, no transaction costs