returns). If excess returns are normally distributed, 67 percent of all outcomes lie within the benchmark's returns plus or minus one standard deviation. VaR is sometimes expressed as dollar value at risk by multiplying the VaR by assets under management. In this manner, the owner of the capital is able to estimate the dollar impact of losses that could be incurred over a given period of time and with a given confidence level. To achieve targeted levels of dollar VaR, owners of capital allocate capital among asset classes (each of which has its own VaR). An owner of capital who wishes to incur only the risks and returns of a particular asset class might invest in an index fund type product that is designed to replicate a particular index with precision. To the extent that the owner wishes to enjoy some discretion around the composition of the index, he or she allows the investment managers to hold views and positions that are somewhat different than the index. The ability to take risks away from the index is often referred to as active management. Tracking error is used to describe the extent to which the investment manager is allowed latitude to differ from the index. For the owner of capital, the VaR associated with any given asset class is based on the combination of the risks associated with the asset class and the risks associated with active management.1 The same premise holds for the VaR associated with any combination of asset classes and active management related to such asset classes. By now it is apparent that risk-whether expressed as VaR or tracking error- is a scarce resource in the sense that individuals and organizations place limits on their willingness to accept loss. For any given level of risk assumed, the objective is to engage into as many intelligent profit-making opportunities as possible. If risk is squandered or used unwisely, the ability of the organization to achieve its profit objectives is put at risk. If excessive levels of risk are taken vis a vis budget, the organization is risking unacceptably large losses in order to produce returns that it neither expects nor desires. If too little risk is taken vis a vis budgeted levels, return expectations will likely fall short of budget. The point here is that the ability of an organization to achieve its risk and return targets may be put at risk anytime that risk capital is used wastefully or in amounts inconsistent with the policies established by such organization. With the above as context, we now delve into the concepts and methods be- fore formally, the return of the portfolio (R) invested in a particular asset class can be described as follows: where Ko refers to the return of the index or benchmark. The term in parenthesis is often referred to as active or excess return. From this expression, one can see that the variance of the portfolio's return (V') can be reduced to: V = Variance (Excess return) + Variance (Benchmark) + 2(Covariance between excess return and benchmark return) The standard deviation of the portfolio is of course the square root of the variance.