Conditional Monte Carlo Simulation

Abstract

There are two popular methods for assessing the exposure of a portfolio or a trading strategy to the risks posed by extreme events: scenario analysis, which is based on subjectively defined market scenarios, and Monte Carlo simulation which is based on an objectively determined probability distribution of outcomes. This article explains how to combine the two approaches to estimate return distributions conditional on subjectively defined “imprecise market scenarios.” The strategies compared include: buy-and-hold, buy-and-hold with put protection, stop loss rule, and stop loss rule with buy-back level. VaR-like measures and full return distributions are estimated for neutral, bull, bear, and whipsaw market scenarios. The main technical tool is a simple Markov chain Monte Carlo algorithm. Useful practical guidelines are given for using this algorithm in various situations.