The Contribution of a Constituent Time Period-Asset Pair: Longitudinal Decompositions
提出一种纵向风险分解方法，将投资组合风险拆解为每个时间段-资产对的独立贡献，并扩展到均值、夏普比率、基准组合和因子模型，对资产配置者和投资经理有实用价值。
Cross-sectional decompositions are well described for some common risk measures, enabling the attribution of risk across assets. Similar decompositions in the time series or jointly in the cross section and time series remain unarticulated. The author presents a very straightforward longitudinal risk decomposition using portfolio volatility as the risk metric. This decomposition expresses portfolio risk as the sum of mutually exclusive and cumulatively exhaustive contributions from each constituent time period-asset pair. It allows the isolation of contributions conditioned on arbitrary criteria and the aggregation of the contributions of flexible groupings of constituent assets, time periods, or both, into their combined contributions additively. For completeness, the author also decomposes means and Sharpe ratios and then extends the analysis to benchmarked portfolios and factor models. The utility of these decompositions is discussed both broadly and in some specific applications using real-world examples. Asset allocators, consultants, and portfolio managers alike should find in these decompositions a host of powerful uses in portfolio analysis and decision-making.