Speed and dimensions of trading

Boris Gnedenko and Igor Yelnik

Abstract

How much risk does an investment portfolio turn over in a given period of time? In other words, how aggressively does it trade in terms of changing exposure to underlying risks? Surprisingly, the investment community still lacks a consistent definition that measures this important portfolio property. We argue that conventional portfolio turnover, which quantifies trading intensity in nominal terms, does not serve this purpose well enough. We introduce an alternative measure that we call risk-based portfolio turnover, which, loosely speaking, represents the overall risk traded. We also suggest a notion of effective number of trades (ENT), which targets a related but different question: how often does a portfolio make bets? Finally, we decompose trading activity by orthogonal axes and introduce the notion of effective number of trading dimensions (ENTD). Both ENT and ENTD are invariant to linear transformations in a space of portfolio assets, which makes these two metrics important intrinsic portfolio characteristics. The paper is complemented with the R code for computing all of the above measures.