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FRM Part II · FRM Exam Part II · Portfolio Construction

An analyst applies Black-Litterman with a prior covariance of equilibrium returns tau times Sigma. The analyst increases tau from 0.05 to 0.50 while keeping the views and view uncertainty matrix Omega unchanged. What is the most likely effect on the posterior returns?

Raising tau increases uncertainty about the equilibrium prior, so with view uncertainty unchanged the views get relatively more weight. The posterior returns therefore move further toward the view-implied returns and away from equilibrium returns.

  1. AThey move closer to the equilibrium returns because the prior is more certain
  2. BThey move further toward the view-implied returns because confidence in the prior declines relative to the viewsCorrect
  3. CThey are unchanged because tau only scales the covariance matrix Sigma of asset returns
  4. DThey converge to the risk-free rate as uncertainty rises

Explanation

Tau scales the uncertainty of the prior mean. A larger tau means the prior is less precise, so with Omega fixed the views receive greater relative weight and the posterior shifts toward them. The option claiming the prior becomes more certain reverses the effect.

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