  Index tracking is a popular form of asset management. Typically, a quadratic
function is used to define the tracking error of a portfolio and the look back
approach is applied to solve the index tracking problem. We argue that a
forward looking approach is more suitable, whereby the tracking error is
expressed as expectation of a function of the difference between the returns of
the index and of the portfolio. We also assume that there is an uncertainty in
the distribution of the assets, hence a robust version of the optimization
problem needs to be adopted. We use Bregman divergence in describing the
deviation between the nominal and actual distribution of the components of the
index. In this scenario, we derive the optimal robust index tracking strategy
in a semi-analytical form as a solution of a system of nonlinear equations.
Several numerical results are presented that allow us to compare the
performance of this robust strategy with the optimal non-robust strategy. We
show that, especially during market downturns, the robust strategy can be very
advantageous.
