Risk Limited Asset Allocation with a Budget Threshold Utility Function and Leptokurtotic Distributions of Returns

Battle Count: 280

Highly relevant to quantitative trading. The paper provides a remarkably simple, interpretable, and implementable trading rule (three-state: long/short/flat) that directly addresses position sizing under risk constraints. The 'risk cost' concept (στ(κ) or Ks) provides an intuitive threshold for when to trade versus stay flat. The finding that leptokurtosis barely affects the optimal policy is practically significant, suggesting Normal distribution assumptions are adequate for this framework. The final algorithm (Equation 13) is immediately deployable as a holding function for traders. However, it is a single-asset, single-horizon model, limiting direct application to complex portfolio management.

Extremely low implementation complexity. The final practical algorithm (Equation 13) requires only: (1) an estimate of expected return α, (2) an estimate of standard deviation s, (3) a position limit L, and (4) a constant K≈0.4. The decision rule is a simple threshold comparison: if |α| > Ks, take position L in the direction of α; otherwise, hold zero. No iterative optimization, no matrix operations, no complex numerical methods are needed. The theoretical derivation involves Gamma functions and partial moments, but the final result is trivially implementable.

The paper provides a complete analytical derivation with all equations, the proof of Theorem 1, and explicit parameterizations of the GED and utility function. The final practical algorithm (Equation 13) is extremely simple to implement. However, no code or dataset is provided, and the empirical calibration of K≈0.4 is referenced to the author's prior work rather than included directly. The theoretical result is fully self-contained and reproducible from the equations given.