of portfolio risk having a property that when all positions are increased by a constant factor, then the portfolio risk increases by that factor. This is true, for example, for all three of the measures of portfolio risk we have mentioned-VaR, volatility, and tracking error.1 The portfolio decomposition is a very useful tool for identifying the significant hot spots in a portfolio. When these hot spots represent intended exposures, when the relative sizes make sense, and when the exposures are not too concentrated, then the investor can feel comfortable. Very often, however, the hot spots will reveal unintended risks or concentrations of risk that need to be reduced in size. We will give examples of the use of the portfolio decomposition in Chapter 13. This chapter on risk management began by emphasizing that risk management is not designed to minimize risk. In the investment world risk management should not be a constraint, but rather a quality control. A sensible approach to risk management is to view it as an important source of investment return. SUMMARY Portfolios should have both an asset allocation benchmark, which determines the overall level of risk, and long-run expected return and a risk budget, which is a plan for how the asset allocation is implemented. The basic role of risk management is to measure the adherence to this plan. The risk management function should identify any areas that are not on track. Many of the tools of risk management from the securities and banking industries have been usefully imported to the investment world, but there are many contrasts in approach, which reflect important differences in the objectives and horizons of investors as opposed to traders. The decomposition of risk is a particularly useful risk management tool because it highlights the hot spots, the most important sources of risk, in the portfolio. !For a more complete discussion of this decomposition of risk, see the Litterman paper, "Hot Spots and Hedges," published as part of the Risk Management Series at Goldman Sachs, October 1966.