10 The Black-Litterman Model
This chapter covers
- The motivation for and methodology of the Black-Litterman Model for asset allocation
- Implementing the Black-Litterman model in Python
- Examples of the model in action, including one with cryptocurrency as an asset class
In Chapter 8, we learned how to use convex optimization to build portfolios. The key inputs to these optimization problems were the expected returns of the assets, and the covariance matrix of asset returns. We saw that the portfolios obtained via optimization could be very sensitive to the expected returns inputs.
The Black-Litterman model, developed by Fischer Black and Robert Litterman while working at Goldman Sachs in the early 1990s, aims to address the sensitivity of portfolio optimization to its inputs while still allowing the user the flexibility to express opinions about the future returns of the assets in the portfolio. In this chapter, we’ll cover both the theory and implementation of the Black-Litterman model.
10.1 Equilibrium returns
Chapter 3 showed multiple different ways of estimating expected returns. Of course, each method will result in different values. Then in Chapter 8 we saw that portfolio optimization can be highly sensitive to expected returns - portfolios built using different methods of estimating expected returns can be wildly different. In Chapter 8, we showed that we could use constraints to keep the optimized portfolio “close” to a reference portfolio.