Case Studies: Mean–Variance and Black–Litterman

Paolo Sironi

What can be asserted without evidence can also be dismissed without evidence.

Christopher Hitchens (1949–2011)

We present a numerical application of mean–variance and Black–Litterman, conduct a review of the data set (market indexes, statistics) and compare the mean–variance optimisation with Black–Litterman optimisation.

INTRODUCTION

In this chapter we present two exercises corresponding to the mean–variance and Black–Litterman portfolio optimisations, which start from the same market data inputs: the statistical properties of a set of 31 market indexes that correspond to broader asset classes. These market indexes have been chosen to represent 42 distinct investment opportunities (funds, Treasury notes, financial and corporate bonds), which are direct inputs to the probabilistic scenario optimisation that is covered in the next chapter, so that we can make an intuitive comparison between different methods. The Black–Litterman approach requires us to indicate the market portfolio as the initial asset allocation. Thus, a synthetic non-traded index (indicated as the Global Market Index) has been engineered from the chosen market indexes.

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