error. Both of these tools are designed to produce estimates of risk-adjusted returns, where risk is defined in standard deviation or tracking error space. In theory, two different estimates of standard deviation (or tracking error) could be used for these ratios-actual levels of standard deviation as well as forecasted levels. In our judgment, both are relevant. There are occasions where the realized risk- the risk actually observed by the investor-is materially different from the potential risk forecasted by a risk model.24 In the Monte Carlo analysis in Figure 17.4 we saw how stress tests can be used to provide a picture of how identical holdings can have quite different return and risk characteristics depending on the environment. If the estimates of potential risk capture these stressed scenarios, potential risk might well exceed realized risk. A favorable Sharpe or information ratio calculated using realized risk might be much less attractive when expressed in potential risk space. Over time, if the risk model is accurate, the realized risk will center on the potential risk. The Sharpe and information ratios incorporate the following strengths: II They can be used to measure relative performance vis a vis the competition by identifying managers who generate superior risk-adjusted excess returns vis a vis a relevant peer group. RMUs and investors might specify some minimum rate of acceptable risk-adjusted return when evaluating manager performance. II They test whether the manager has generated sufficient excess returns to compensate for the risk assumed. II The statistics can be applied both at the portfolio level as well as for individual industrial sectors and countries. For example, they can help determine which managers have excess risk-adjusted performance at the sector or country level. The Sharpe and information ratios incorporate the following weaknesses: II They may require data that may not be available for either the manager or many of his competitors. Often an insufficient history is present for one to be conclusive about the attractiveness of the risk-adjusted returns. II When one calculates the statistic based on achieved risk instead of potential risk, the statistics relevance depends, to some degree, on whether the environment is friendly to the manager. Tool #4-Alpha versus the Benchmark This tool regresses the excess returns of the fund against the excess returns of the benchmark. The outputs of this regression are: 11 An intercept, often referred to as "alpha," or skill. II A slope coefficient against the excess returns of the benchmark, often referred to as "beta." 24Risk models attempt to measure potential risk. Ultimately, the true potential risk is not knowable. We only see its footprints over time in the form of realized risk. Still, even this realized risk is only one outcome of an infinite number of outcomes that were in theory possible.