The Sherman-Morrison-Markowitz Portfolio

Battle Count: 67

Highly relevant to quantitative trading and portfolio management. The paper provides a theoretically optimal solution for multi-period portfolio construction, directly applicable to practitioners who backtest over multiple periods and optimize unconditional Sharpe ratios. The connection between conditional Markowitz portfolios and the optimal multi-period solution via a simple rescaling factor (1+μ⊤Σ⁻¹μ)⁻¹ is practically actionable. The Kelly criterion connection and leverage overlay application are directly relevant to trading strategy implementation. However, the practical impact is noted to be small in typical cases.

The core formula is simple: replace Σ⁻¹μ with (Σ+μμ⊤)⁻¹μ = (1/(1+μ⊤Σ⁻¹μ))Σ⁻¹μ, which is just a scalar rescaling of the Markowitz portfolio. However, practical implementation requires estimating conditional second moment matrices A₂(x), which is non-standard. The neural net recipe adds significant complexity. The constrained case requires solving a linear system for hedge coefficients. The discrete feature case is straightforward to implement.

The paper is primarily theoretical with closed-form solutions. Numerical examples are provided (two-state discrete example, linear conditional expectation model with Monte Carlo simulation), but no code or data repository is provided. The mathematical derivations are self-contained and verifiable. The neural net recipe is described only at a high level without implementation details.