Local Risk Decomposition for High-frequency Trading Systems

In the present work we address the problem of evaluating the historical performance of a trading strategy or a certain portfolio of assets. Common indicators such as the Sharpe ratio and the risk adjusted return have significant drawbacks. In particular, they are global indices, that is they do not preserve any local information about the performance dynamics either in time or for a particular investment horizon. This information could be fundamental for practitioners as the past performance can be affected by the non-stationarity of financial market. In order to highlight this feature, we introduce the local risk decomposition (LRD) formalism, where dynamical information about a strategy’s performance is retained. This framework, motivated by the multi-scaling techniques used in complex system theory, is particularly suitable for high-frequency trading systems and can be applied into problems of portfolio optimization.