O-i- CMO-i- O-i- CMO-i- CM-i- ----------- Active Daily Return -------- +ve 2" Tracking Error _ -ve 2* Tracking Error FIGURE 17.3 Model Validation ing professional should also explore how tracking error might behave in more unusual circumstances.13 There are many ways to examine how a portfolio might behave during periods of stress. One technique is historical simulation. To apply this approach, one takes today's positions and applies historical price changes to them to see what the earnings impact would have been had such positions been held fixed over a period of time. A shortfall of this method is that observed history produces only one set of realized outcomes. A more robust approach would allow us to examine the myriad outcomes that are probabilistically implied by the one set of outcomes that actually occurred. To examine these implied paths, Monte Carlo methods are commonly applied. Figure 17.4 graphs the results of a Monte Carlo simulation for a sample equity portfolio that was prepared to study how tracking error forecasts fluctuate depending on the environment used to estimate the risk forecast.14 Note that as of April 26, 2002, for this portfolio, the PACE risk model projected a tracking error of 5.08 percent per annum. The tracking error target for this portfolio was 5 percent. So, at 13It is often true that a three standard deviation scenario is more draconian than that value that is implied by multiplying a one standard deviation loss by three. This result occurs for two reasons: (1) Many products have nonlinear payoff structures (i.e., embedded options); and (2) the global stresses that are present in a three standard deviation scenario are qualitatively different than those which are present in a one standard deviation scenario. As an example, counterparty credit risk increases in more unusual environments. 14It is beyond the scope of this chapter to delve in depth into the calculation methodology behind Monte Carlo methods. Rather we present an output of a Monte Carlo analysis to give the reader a sense as to the types of insights it might provide.