Investors’ Direct Stock Holdings and Performance Evaluation for Mutual Funds

Investors need performance measures particularly as a means for funds selection inthe process of ex-ante portfolio optimization. Unfortunately, there are various performancemeasures recommended for different decision situations. Since an investor may be uncertainwhich kind of decision problem is best apt to describe his personal situation the question ari-ses up to which extent funds rankings react sensitive with respect to changes in performancemeasurement. To be more precise, an investor with mean-variance preferences is consideredwho is trying to identify the best fund f* out of a set consisting of F funds and to combine thisone optimally with the direct holding of a broadly diversified (reference) portfolio P of stocksas well as riskless lending or borrowing. For an investor just starting to acquire risky securi-ties all three fractions of the various assets in question as part of his overall portfolio can beconsidered variable, while there also might be investors with already given direct holdings ofstocks amounting to a certain fraction of their total wealth which cannot or shall not be alte-red. For both situations different adequate performance measures have been suggested byBreuer/Gürtler (1999, 2000) and Scholz/Wilkens (2003). We analyze theoretically as well asempirically possible deviations in resulting funds rankings for the two decision situationsdescribed previously. While there are indeed only loose theoretical relationships between theperformance measures under consideration, empirical evidence suggests almost identicalfunds rankings. As a consequence, potential investors need not bother much about whethertheir situation is best described by an already fixed or a still variable amount of direct stockholdings. Moreover, traditional performance measures like the Sharpe ratio or the Treynorratio will in general lead to reasonable funds selection in both situations.