  Active portfolio management tries to incorporate any source of meaningful
information into the asset selection process. In this contribution we consider
qualitative views specified as total orders of the expected asset returns and
discuss two different approaches for incorporating this input in a
mean-variance portfolio optimization model. In the robust optimization approach
we first compute a posterior expectation of asset returns for every given total
order by an extension of the Black-Litterman (BL) framework. Then these
expected asset returns are considered as possible input scenarios for robust
optimization variants of the mean-variance portfolio model (max-min robustness,
min regret robustness and soft robustness). In the order aggregation approach
rules from social choice theory (Borda, Footrule, Copeland, Best-of-k and MC4)
are used to aggregate the total order in a single ``consensus total order''.
Then expected asset returns are computed for this ``consensus total order'' by
the extended BL framework mentioned above. Finally, these expectations are used
as an input of the classical mean-variance optimization. Using data from
EUROSTOXX 50 and S&P 100 we empirically compare the success of the two
approaches in the context of portfolio performance analysis and observe that in
general aggregating orders by social choice methods outperforms robust
optimization based methods for both data sets.
