Quantitative Financial Risk Management: Theory and Practice

CHAPTER 5

Output Analysis and Stress Testing for Risk Constrained Portfolios

Jitka Dupačová Miloš Kopa

Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

INTRODUCTION

The main feature of the investment and financial problems is the necessity to make decisions under uncertainty and over more than one time period. The uncertainties concern the future level of interest rates, yields of stock, exchange rates, prepayments, external cash flows, inflation, future demand, and liabilities, for example. There exist financial theories and various stochastic models describing or explaining these factors, and they represent an important part of procedures used to generate the input for decision models.

To build a decision model, one has to decide first about the purpose or goal; this includes identification of the uncertainties or risks one wants to hedge, of the hard and soft constraints, of the time horizon and its discretization, and so on. The next step is the formulation of the model and generation of the data input. An algorithmic solution concludes the first part of the procedure. The subsequent interpretation and evaluation of results may lead to model changes and, consequently, to a new solution, or it may require a what-if analysis to get information about robustness of the results.

In this paper, we shall focus on static, one-period models. Accordingly, let us consider a common portfolio optimization ...