.8 and 1.3. The red zone is defined as ratios below .7 or above 1.8. . . . the predefined green, yellow, and red zones provide clear expectations for the asset management division portfolio managers. When portfolios move into the yellow or red zone, which will happen every so often, it may be time for a discussion of what is going on. We never expect portfolio management, or risk monitoring, to be reduced to a formula, but these types of quantitative tools have proved to be useful in setting expectations and in providing useful feedback which can foster better quality control of the investment management process. Tool #2-Attribution of Returns A commonly used tool to measure the quality of returns is performance attribution. This technique attributes the source of returns to individual securities and/or common factors. Recall that when analyzing the risk profile of a portfolio, we discussed techniques (e.g., risk decomposition) to measure the extent to which the implied risks in a portfolio are consistent with expectations and manager philosophy. So, too, when examining the actual returns of a portfolio, we are concerned that the returns were sourced from those themes where the manager intended to take risk and that such returns are consistent with the risks implied by the ex ante risk analysis. One form of attribution, commonly called variance analysis, shows the contribution to overall performance for each security in the portfolio. Figure 17.7 is an excerpt of this kind of analysis for a stock portfolio. This same kind of analysis can be performed at the industry, sector, and country levels, essentially by combining the performance of individual securities into the correct groupings. The RMU professional can use this analysis to ascertain whether the portfolio tended to earn returns in those securities, industries, sectors, and countries where the risk model indicated that the risk budget was being spent. To the extent that the manager thinks of risk in factor space as opposed to security-specific space, the attribution process can be performed on this basis. Namely, the attribution process captures the weightings in various risk factors on a periodic basis and also accumulates the returns to such factors in order to produce a variance analysis expressed in factor terms. As a general rule, it is most meaningful to attribute returns on the same basis that ex ante risk for such returns is measured. For managers who think in factor terms, factor risk analysis and factor attribution will likely be more meaningful. For managers who think about risk in terms of individual securities, risk forecasting and attribution at the security level will likely be more relevant. This is not to say that risk should not be measured using a range of models. The point here is that portfolio managers will likely find most meaningful those techniques that measure and describe risk in the same manner that they internalize these issues. Once again, this argues for having a range of risk and attribution models in order to achieve the most robust understanding. Tool #3-The Sharpe and Information Ratios The Sharpe ratio divides a portfolio's return in excess of the risk-free rate by the portfolio's standard deviation. The information ratio divides a portfolio's excess