1/25/00 B/12/00 2/25/01 9/16/01 4/4/02 FIGURE 17.4 Example of Monte Carlo Methods to Explore Tracking Error Stresses first blush, it seems as though the portfolio has an overall risk profile that is closely aligned with the risk target. Common sense tells us, however, that the particular combination of assets held in the portfolio might exhibit quite different tracking error characteristics in different environments. The PACE forecast is derived by assuming that the underlying data have a half-life of about half a year. When estimating the covariance matrix15 that is at the heart of the risk forecast, data that are six months old are weighted half as much as current data, and data that are one year old are weighted about one-quarter of current data, and so on. So, more import is given to recent data than to aged data in forecasting risk. This key assumption means that the covariance matrix itself fluctuates over time not only because different data are used to estimate its components but also because the passage of time causes the import of any particular element in the matrix to have an ever smaller weight. To examine how a tracking error forecast might fluctuate over time, Figure 17.4 simulates the frequency distribution of the tracking error of the positions held at April 26, 2002, over the period from June 1998 until April 26, 2002. These positions, when introduced into the Monte Carlo engine, would have yielded an average tracking error forecast that would have peaked at 6.5 percent in late 1998 and mid-2000. At these times, the 98th percentile risk forecast reached levels of 7 percent. The risk monitoring professional should consider whether these ranges of tracking error that might occur during periods of stress fall within acceptable levels vis a vis the long-term target of 5 percent. If these levels of tracking error are deemed unacceptably large, an appropriate response might be to run the portfolio at a lower risk profile (say, 4 percent) such that there is reason to believe that the tracking error is less likely to reach unacceptably large levels during periods of stress.16 15Recall that the standard deviation (or tracking error) is calculated by the formula: Tracking error = [WTZW] '2 where Wis an Nx 1 matrix of weights applied to particular factors (e.g., risk factors, or market value of stock holdings, etc.) and X represents the Nx Ncovariance matrix associated with the returns of these factors. 1£Recall that tracking error is shorthand for the magnitude of earnings variability associated with a certain degree of statistical confidence. If this variability is unacceptably large, it may place the organization's overall strategic plan and goals at risk.