Volatility Drag and the Perpetual Borrowing Option: The Admissible Financing Boundary

Modern Portfolio Theory specifies optimal portfolio composition but is largely silent on financing policy through time. This silence has a calculable cost. Under geometric Brownian motion, a risky portfolio compounds at its arithmetic return less one-half variance per unit time. This paper designates that unrecovered cost Itô’s Zeta and asks whether it can be recovered through an admissible financing policy. The paper introduces Spiral Theory as a framework for financing a chosen risky portfolio after adverse market outcomes. Unused borrowing capacity is modeled as a perpetual American-style financing option: the continuing ability to borrow against assets rather than sell them, reduce exposure, or interrupt compounding. Applying McKean’s optimal-exercise framework, the paper defines McKean’s Alpha as the portion of Itô’s Zeta recovered through financing. The central claim is that no financing leaves Zeta unrecovered, while unlimited financing leads to ruin. The economically relevant object is therefore the admissible region between unrecovered volatility drag and ruin. That admissible financing boundary is Spiral Theory. The framework distinguishes portfolio construction from financing policy: Modern Portfolio Theory asks what portfolio should be held; Spiral Theory asks how that chosen portfolio should be financed through time. The paper characterizes the admissible region through seven points, A through G, spanning no financing through certain ruin. Simulation evidence across 5,000,000 paths and 100 independent seeds shows full recovery, with McKean’s Alpha approximately equal to Itô’s Zeta, at volatility of 15 percent or below across all borrowing rates tested, with near-zero ruin probability. Long-horizon bootstrap analysis using 10,000 resamplings yields a 95 percent confidence interval for the McKean’s Alpha to Itô’s Zeta ratio of 1.0000 to 1.0004. The simulation evidence supports the conjecture that Itô’s Zeta equals McKean’s Alpha and equals one-half variance exactly, although the analytical proof remains open. Spiral Theory is distinguished from Merton and Kelly by sequence. Merton and Kelly are first-mover rules that optimize in anticipation of volatility drag. Spiral Theory is a second-mover rule that responds after deviation from the arithmetic benchmark is observed. The paper proposes that Itô’s Zeta and McKean’s Alpha be reported explicitly alongside expected arithmetic return in investment policy statements, financial plans, and performance reports.