【基金量化研究系列】基金绩效归因模型——Brinson多期归因模型

注：本文暂未完成，预计完成时间5/17，敬请期待

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1. 引言

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2. Brinson单期归因模型

2.1 模型框架

	wp	wb
rp	组合收益：wp rp	择股收益：wb rp
rb	择时收益：wp rb	基准收益：wb rb

2.2 公式推导

R E = ∑ i = 1 n w i p r i p − ∑ i = 1 n w i b r i b = ∑ i = 1 n ( w i p r i p − w i b r i b ) = ∑ i = 1 n ( w i p r i b − w i b r i b + w i b r i p − w i b r i b + w i p r i p − w i p r i b − w i b r i p + w i b r i b ) = ∑ i = 1 n ( w i p − w i b ) r i b + ∑ i = 1 n w i b ( r i p − r i b ) + ∑ i = 1 n ( w i p − w i b ) ( r i p − r i b ) = R A + R S + R I R_{E}= \sum_{i=1}^{n}w_i^pr_i^p - \sum_{i=1}^{n}w_i^br_i^b \\ = \sum_{i=1}^{n} (w_i^pr_i^p - w_i^br_i^b) \\ = \sum_{i=1}^{n} (w_i^pr_i^b - w_i^br_i^b+ w_i^br_i^p-w_i^br_i^b+ w_i^pr_i^p- w_i^pr_i^b - w_i^br_i^p + w_i^br_i^b) \\ = \sum_{i=1}^{n} (w_i^p - w_i^b)r_i^b + \sum_{i=1}^{n} w_i^b(r_i^p-r_i^b) + \sum_{i=1}^{n}( w_i^p- w_i^b)(r_i^p- r_i^b )\\ =R_A + R_S + R_I RE​=i=1∑n​wip​rip​−i=1∑n​wib​rib​=i=1∑n​(wip​rip​−wib​rib​)=i=1∑n​(wip​rib​−wib​rib​+wib​rip​−wib​rib​+wip​rip​−wip​rib​−wib​rip​+wib​rib​)=i=1∑n​(wip​−wib​)rib​+i=1∑n​wib​(rip​−rib​)+i=1∑n​(wip​−wib​)(rip​−r