Review of Quantitative Finance and Accounting, 10 (1998): 75–94
© 1998 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
Benchmark Invariancy, Seasonality and APM-Free
Portfolio Performance Measures
Department of Finance, Concordia University
University of Quebec at Montreal (UQAM)
MINH CHAU TO
GReFi at Ecole des H.E.C.
Abstract. The Jobson-Korkie (1981) Z score and the positive period weighting (PPW) score of Grinblatt and
Titman (1989) are applied to various benchmarks of market and mimicking portfolios to study the benchmark
invariancy problem. Signiﬁcantly different portfolio performance inferences are found for a sample of 146 equity
mutual funds depending on the mean-variance efﬁciency of the portfolio benchmarks (mimicking portfolios
versus market indices). Portfolio performance inferences are affected signiﬁcantly by the number of factors,
nonsynchronous trading adjustment, and the sizes of the ﬁrms used for factor extraction. The returns of the
portfolio benchmarks exhibit signiﬁcant monthly seasonalities, which, in turn, signiﬁcantly inﬂuence mutual
fund performance inferences.
Key words: Benchmark choice, portfolio performance inferences, seasonality, robustness
Investigations of mutual fund performance involve a joint test of the adequacy of both the
benchmark and the performance measure. Lehmann and Modest (1987), Grinblatt and
Titman (1988), amongst others, ﬁnd that inferences about mutual fund performance are
not robust across different benchmarks and performance measures.
While market indexes are generally used as portfolio benchmarks, empirical tests sug-
gest that they are not mean-variance (E-V) efﬁcient.
For such comparisons, abnormal
performances may be identiﬁed for funds that use passive (buy-and-hold) strategies. When
the APT is exact, Grinblatt and Titman (1987) demonstrate that a global portfolio of
mimicking portfolios is globally E-V efﬁcient, and that each mimicking portfolio is
locally E-V efﬁcient. Lehmann and Modest (1985b) observe that minimum idiosyncratic
risk mimicking (MIRM) portfolios generate the best (empirical) estimators of the eco-
nomic forces that move all assets.
However, construction choices (such as the number of
factors, nonsynchronous trading adjustment, and so forth) may lead to a benchmark
While some portfolio performance measures require speciﬁc information about the
forecasts of managers,
others require the determination of the appropriate asset pricing
@ats-ss3/data11/kluwer/journals/requ/v10n1art5 COMPOSED: 11/05/97 10:39 am. PG.POS. 1 SESSION: 8