Case Studies: Probabilistic Scenario Optimisation

Paolo Sironi

However beautiful the strategy, you should occasionally look at the results.

Winston Churchill (1874–1965)

We demonstrate numerical application of PSO, review the data set (securities, risk factors, statistics) and compare multi-period optimisation with risk-averse and risk-mitigating profiles and multi-period and single-period optimisation with a risk-tolerant profile.

INTRODUCTION

In this chapter we present a set of optimal asset allocations identified by means of PSO. The set of investment opportunities is made up of 42 distinct securities (funds, Treasury notes, financial and corporate bonds) that cover the same risk factors represented by the market indexes introduced in the previous chapter, dedicated to the case studies of mean–variance and Black–Litterman optimisations. We generated Monte Carlo multi-variate stochastic scenarios over time to shock the market risk factors and derive the potential return distributions of these real products.

The investment horizon

We set the investment horizon to five years, as a subset of the total length of the 10Y multi-period Monte Carlo simulations performed with an uneven time-step discretisation to show higher