Determining the tracking error and value-at-risk of an active portfolio when combined with a passive portfolio with value-at-risk constraint

Abstract

When an asset manager manages a portfolio, he usually imposes a TE or a VaR limit on his portfolio to control portfolio risks. However, a portfolio may be divided into different portions. In our research, we consider a portfolio that consists of an active portion and a passive portion. Having a VaR budget of an entire portfolio, we propose methods to determine TE and VaR limit on the active portfolio and illustrate them by using real data. In the empirical part, some problems can occur when we relax certain theoretical assumptions such as (1) stocks in an investment universe can be different from stocks in a benchmark (2) there is a restriction on short-selling. Moreover, risk measures derived from the analysis part are "ex-ante," but calculation methods for monitoring are "ex-post." Therefore, we need to consider these limitations when using the proposed limit on TE and VaR of an active portfolio in real life.