How Risk Managers Should Fix TEV and VaR Constraints in Asset Management

Many investors assign part of their funds to asset managers of mutual funds who are given the task of beating a benchmark. Asset managers usually face a constraint on maximum Tracking Error Volatility (TEV), imposed by the risk management office to keep the risk of the portfolio close to that of the selected benchmark. However, many admissible portfolios still have problems in mean-variance terms, for example because of a too high variance. To overcome this problem Jorion (2003) also fixes a constraint on variance, while Alexander and Baptista (2008) fix a constraint on Value-at-Risk (VaR). Moreover, a minimum TEV should be imposed to force the asset manager to perform a real active strategy, as proposed in Riccetti (2012). In this paper, I determine an optimal value for the set of bounds composed by minimum TEV, maximum TEV and maximum VaR. In particular, concerning maximum VaR, I develop a strategy which imposes to asset managers a set of portfolios that contains as much as possible "efficient constrained TEV" portfolios and, at the same time, as less as possible non-efficient ones. With this aim, I show that a bound on maximum VaR is usually better than a bound on maximum variance.