Journal of Risk

How risk managers should fix tracking error volatility and value-at-risk constraints in asset management

Luca Riccetti

  • A consistent set of limits that risk management offices should impose is determined.
  • A limit on maximum VaR is usually better than a limit on maximum variance.
  • The set of limits includes lower and upper limits on TEV, and upper limit on VaR.


Investors usually assign part of their funds to asset managers, who are given the task of beating a benchmark. Asset managers usually face a constraint on maximum tracking error volatility (TEV), which is imposed by the risk management office. In the mean-variance space, Jorion, in his 2003 paper "Portfolio optimization with tracking-error constraints", shows that this constraint determines an ellipse containing all admissible portfolios. However, many admissible portfolios have problems in mean-variance terms, for example, because of an overly high variance. To overcome this problem, Jorion also fixes a constraint on variance, while, in their 2008 paper "Active portfolio management with benchmarking: adding a value-at-risk constraint", Alexander and Baptista fix a constraint on value-at-risk (VaR). In this paper, I determine an optimal value for a set of limits composed of the lower limit on TEV, the upper limit on TEV and the upper limit on VaR. To fix the upper limit on VaR, I use the TEV constrained efficient frontier developed in Palomba and Riccetti's 2013 paper "Asset management with TEV and VAR constraints: the constrained efficient frontiers", which is the set of portfolios that is on Jorion's ellipse and not dominated from the mean-variance perspective. In particular, I develop a strategy to impose on asset managers a set of portfolios that contains as many TEV constrained efficient portfolios and as few inefficient portfolios as possible. Moreover, I show that a limit on maximum VaR is usually better than a limit on maximum variance.


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