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382 RISK BUDGETING ACTE, an increase in this weight would mean making it less negative (e.g., going from -0.5 percent to


0). Since RCTE measures the relative change in risk, given a relative change in weight, a positive RCTE means that if the current active weight is: II Positive, an increase in this weight (making it more positive) would lead to an increase in tracking error. II Negative, a decrease in this weight (making it less negative) would lead to a decrease in tracking error. Similarly, a negative RCTE means that if the current active weight is: 11 Positive, an increase in this weight (making it more positive) would lead to a decrease in tracking error. II Negative, a decrease in this weight (making it less negative) would lead to an increase in tracking error. Table 20.6 summarizes the relationship between RCTE and ACTE. In addition to computing an asset's change on the total tracking error, we can, in the context of a linear factor model, measure an asset's change on the factor and specific components of total tracking error. From the decomposition of tracking error into factor and specific components, we have ACTE{t) = V(t\t-l)wa(t-l) Bi(t-h)Y.(t\t-l)Bi(t-h)Twa{t-l) A(t\t-T)wa(t-1) (20.73;   o*(f) o*{t)   Factor component Specific Equation (20.73) has the benefit of having the factor and specific contributions add up to the total contribution to tracking error. A disadvantage with using TABLE 20.6 Comparison of RCTE and ACTE Current Value Change in Active Weight Change in Tracking Error   RCTE Positive Negative ACTE Positive Negative Negative weight becomes more negative Increase Positive weight becomes more positive Increase Negative weight becomes more negative Decrease Positive weight becomes more positive Decrease Negative weight becomes less negative Increase Positive weight becomes more positive Increase Negative weight becomes less negative Decrease Positive weight becomes more positive Decrease