the factor and specific components because they are not defined in the same way as ACTE (that is, not defined by a derivative). An alternative way to find the factor and specific component of an asset's change on total tracking error is to first define the total factor and specific component of tracking error and then take derivatives of each with respect to the asset positions. The factor component of tracking error (squared) is given by <f{tf = ws(t-l)TBHt - b)l{t 1t - l)B*(t-h)Twa(t-l) (20.74) The nth asset's contribution to the factor component of tracking error is represented by the ?zth element of ACTEfactor (t) = I------------------------- ----------- J----------- <20-75* <f(t) and £<(£-l)xACTEfactor^) = cpaW (20.76) The specific component of tracking error is ha{tf = wa(t-l)TMt \t-l)ws(t-l) (20.77) It follows from equation (20.77) that the ?zth asset's contribution to the specific component of tracking error is represented by the nth element of ACTEspedfic (t) = -5--------- -'--5----- '- (20.78) o (t) and £<(*-DxACTEspedfic^) = 5^) (20.79) "=i Note that o*(t) * qf(t) + &(t) but rather o*(t)2 = qf (t)1 + b*(t)2. As done previously, we can define relative contributions to tracking error. RCTEfactor(^) = ^^ACTEfactor(^) and f^KCTEiactOTJt) = l (20.80) N RCTE£pedfic(r) = ^^ACTEspedficW and 5>CTEspedfic^) = l (20.81)