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ADR-0006: τ = 0.05 (He-Litterman convention)

  • Status: Accepted
  • Date: 2026-05-23

Context

The Black-Litterman τ scalar reflects uncertainty in the prior. The literature is genuinely inconsistent: He-Litterman (1999) and Idzorek (2005) use small τ (0.025–0.05); Meucci (2010) uses τ = 1 ("tau-less convention") and absorbs the scaling into Ω.

Decision

Default to τ = 0.05 (He-Litterman convention). This is the value used in the reference reproduction test (He-Litterman 1999 Table 7).

Decision drivers

  • Reproducibility: the He-Litterman 1999 numbers depend on τ = 0.05.
  • Reference compatibility: PyPortfolioOpt uses the same convention.
  • Idzorek's confidence-implied Ω procedure assumes the He-Litterman convention.

Considered options

  • Option A: τ = 0.05 He-Litterman default. Chosen.
  • Option B: τ = 1 Meucci tau-less default. Rejected: would break reproduction test.
  • Option C: τ = 1/T derived from data. Rejected: introduces an additional hyperparameter dependency.

Consequences

  • Documentation states the convention loudly.
  • The tau argument is exposed for user override.
  • TauScaleError raised if τ ≤ 0 or τ > 1.
  • He, G. & Litterman, R. (1999). "The Intuition Behind Black-Litterman Model Portfolios."
  • Walters, J. (2014). "The Black-Litterman Model in Detail." SSRN #1314585.
  • Meucci, A. (2010). "The Black-Litterman Approach: Original Model and Extensions."