![]() ![]() ![]() The unknown model parameter is the expected return μ. Σ is the covariance from historical asset returns. Local FunctionsĮnd Appendix: Black-Litterman Model Under a Bayesian Framework Assumptions and ViewsĪssume that the investment universe is composed of k assets and the vector of asset returns r is modeled as a random variable, following a multivariate normal distribution r ~ N ( μ, Σ ). This is because the investment analyst has a strong view that MSFT will outperform IBM. For example, when you compare the Black-Litterman result with the plain mean-variance optimization result, you can see that the Black-Litterman result is more heavily invested in MSFT than in IBM. Also, the weights among the assets in the Black-Litterman model agree with the investment analyst views. ![]() The allocation from the Black-Litterman model is more diversified, as the pie chart shows. When you use the values for the blended asset return and the covariance from the Black-Litterman model in a mean-variance optimization, the optimal allocations reflect the views of the investment analyst directly. AssetName Mean_Variance Mean_Variance_with_Black_Litterman ![]()
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