Simulate productive bands on single-stock equities and crypto assets
Productive Band Explorer
Simulate productive bands on single-stock equities and crypto assets. Adjust drift, volatility, and leverage to visualize where leveraged derivatives thrive or decay. The productive band is the range of leverage where R(L) − R(1) > 0. The growth-maximizing leverage L* = (μ − r) / σ².
Model
R(L) = Lμ − ½L²σ² − (L−1)(rf + 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 = rf + s