Capital
Misallocation

The
Multiplicative
Indictment

The Causal Barbell: Part 1

How much alpha does your hedge fund need to beat the index? You supply the assumptions. The arithmetic does not negotiate.

Market — feeds every tab

Defaults

These are starting values. Move any slider; the indictment is yours.

  • 10-year hold
  • 1.5-and-20, pod-level netting on, pass-through skipped
  • ½σ² variance drag — conservative if the book is left-tailed
  • Monte Carlo seed 20260910, 10,000 shared draws
  • Cascade impact k = 0.09
  • Shiller real total returns, 1871–2023

Tab 1 · Fee decomposition

This book needs 6.0% annual alpha to match the index

Net geometric
7.8%
Unlevered beta
7.7%
Total fee load
3.5%
Wealth ratio
1.00×
10-year terminal vs. index
This book
6.0%
0.5× net · 0.75× short
Unlevered, no short
2.5%
Net 1.0×, borrow 0, same fee contract

Move net exposure to 1.0. The extra 3.4% is beta this book does not own. Borrow sits inside the short rebate, so it is not a second charge.

From gross alpha to net geometric

Dashed line is unlevered-beta geometric — the index match. Last bar lands at net geometric.

Net geometric vs. unlevered beta

Fee integral — transfer vs. deadweight

Total fees extracted
53%

Transfer — cumulative fees as % of initial capital.

Foregone compounding
76%

Deadweight — fees compounded at the equity rate, less excess delivered.

The ½σ² drag formula is a second-order approximation, exact under lognormality. Under negative skew (which this essay argues is endemic to long-short), the true drag is larger. This makes the break-even alpha estimate conservative. See Tab 3's skew slider for the higher-order correction.