Research has shown that adding constraints to total portfolio volatility can substantially improve the performance of managed portfolios. Although other work has considered constant tracking-error volatility frontiers, in this study tracking error was allowed to vary but the risk aversion was fixed. The resulting optimal portfolios have several desirable properties.

This paper examines some properties of portfolio insurance that are linked to the risk aversion and the prudence of the investor. We provide explicit conditions to measure portfolio sensitivity to downside risk. We also characterize the degree of portfolio insurance by means of the ratio of absolute prudence to absolute risk aversion.

This paper examines whether the risk-adjusted performance attribution process is consistent with portfolio optimisation under tracking-error constraints. Since Mina (2003), Bertrand (2005, 2008b) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process. This paper analyses and discusses the information ratio decomposition proposed by Menchero (2007) in the light of the analysis of risk-adjusted performance attribution developed by Bertrand (2005). It is also shown that only optimisation under the tracking-error constraint alone is consistent with the risk-adjusted performance attribution process. Indeed, as soon as additional constraints (for example, on total risk) are introduced, the component information ratios of the decisions are no longer the same or equal to the information ratio of the whole portfolio. This means that no equilibrium between expected return and relative risk has been reached.

This paper examines wether risk attribution process is consistent with portfolio optimizations under tracking-error constraints. Since Mina (2003), Bertrand (2005) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process. This article presents an extension of our previous work on risk attribution to others portfolio optimization contexts. It is shown that only optimization under the tracking-error constraint alone is consistent with the risk attribution process. Indeed, as soon as additional constraints (e.g. on total risk) are introduced, the risk attribution method conflicts with the performance attribution process, preventing us from legitimating all the optimal decisions taken by a portfolio manager.