Pitfalls in VAR based return decompositions: A clarification

Based on Chen and Zhao's (2009) criticism of VAR based return decompositions, we explain in detail the various limitations and pitfalls involved in such decompositions. First, we show that Chen and Zhao's interpretation of their excess bond return decomposition is wrong: the residual component in their analysis is not "cashflow news" but "interest rate news" which should not be zero. Consequently, in contrast to what Chen and Zhao claim, their decomposition does not serve as a valid caution against VAR based decompositions. Second, we point out that in order for VAR based decompositions to be valid, the asset price needs to be included as a state variable. In parts of Chen and Zhao's analysis the price does not appear as a state variable, thus rendering those parts of their analysis invalid. Finally, we clarify the intriguing issue of the role of the residual component in equity return decompositions. In a properly specified VAR, it makes no difference whether return news and dividend news are both computed directly or one of them is backed out as a residual.