The Black–Litterman Approach: A Tale of Subjective Views

Paolo Sironi

A man who wants the truth becomes a scientist; a man who wants to give free play to his subjectivity may become a writer; but what should a man do who wants something in between?

Robert Musil (1880–1942)

In this chapter we present an optimisation model (the Black–Litterman approach) that embeds asymmetric information and the market equilibrium portfolio (the Capital Asset Pricing Model). We give investors’ views and discuss the posterior distribution of portfolio returns.

INTRODUCTION

In 1991 Fisher Black and Robert Litterman published their work on asset allocation which they had built for in-house use at Goldman Sachs. Their Bayesian portfolio construction model was widely considered a step forward from the original mean–variance approach and made use of three novel ideas:

• 1. information about financial returns is asymmetrical and can be divided into long-term market equilibrium (eg, CAPM) and short-term investors’ views;
  2. both sets of information are uncertain and can be described by means of probability distributions;
  3. a complete set of expected excess returns can be estimated by combining the investor ’s views with the market equilibrium, which becomes