Simulation is a widely used technique for portfolio risk assessment and management. Portfolio exposure to different factors is often evaluated over multiple scenarios, and portfolio risk measures such as value-at-risk are estimated. Generating meaningful scenarios is an art as much as a science, and presents a number of modeling and computational challenges.
This chapter reviews the main ideas behind Monte Carlo simulation and discusses important issues in its application to portfolio management, such as the number of scenarios to generate and the interpretation of output.
5.1 Monte Carlo Simulation: A Simple Example
As we explained in Chapter 2, the analysis of risk is based on modeling uncertainty, and uncertainty can be represented mathematically by probability distributions. These probability distributions are the building blocks for simulation models. Namely, simulation models take probability distribution assumptions on the uncertainties as inputs, and generate scenarios (often referred to as trials) that happen with probabilities described by the probability distributions. They then record what happens to variables of interest (called “output variables”) over these scenarios, and let us analyze the characteristics of the output probability distributions (see Exhibit 5.1). In the financial context, inputs may be interest rate levels, market returns, and so on, and the output variable can be a portfolio return or the return on a financial instrument. ...