Investors' direct stock holdings and performance evaluation for mutual funds

Investors need performance measures particularly as a means for funds selection in the process of exante portfolio optimization. Unfortunately, there are various performance measures recommended for different decision situations. Since an investor may be uncertain which kind of decision problem is best apt to describe his personal situation the question arises up to which extent funds rankings react sensitive with respect to changes in performance measurement. To be more precise, an investor with mean-variance preferences is considered who is trying to identify the best fund f* out of a set consisting of F funds and to combine this one optimally with the direct holding of a broadly diversified (reference) portfolio P of stocks as well as riskless lending or borrowing. For an investor just starting to acquire risky securities all three fractions of the various assets in question as part of his overall portfolio can be considered variable, while there also might be investors with already given direct holdings of stocks amounting to a certain fraction of their total wealth which cannot or shall not be altered. For both situations different adequate performance measures have been suggested by Breuer/Gürtler (1999, 2000) and Scholz/Wilkens (2003). We analyze theoretically as well as empirically possible deviations in resulting funds rankings for the two decision situations described previously. While there are indeed only loose theoretical relationships between the performance measures under consideration, empirical evidence suggests almost identical funds rankings. As a consequence, potential investors need not bother much about whether their situation is best described by an already fixed or a still variable amount of direct stock holdings. Moreover, traditional performance measures like the Sharpe ratio or the Treynor ratio will in general lead to reasonable funds selection in both situations.