Markowitz efﬁciency and size effect: evidence
from the UK stock market
Published online: 28 July 2013
Ó Springer Science+Business Media New York 2013
Abstract Academics and practitioners have frequently debated the relationship between
market capitalization and expected return. We apply the Markowitz efﬁcient frontier
approach to develop a portfolio performance measure that compares the return of a port-
folio to its optimal return, using data from the UK stock market over the period 1985–2012.
Our results show that there is a negative relationship between portfolio size and portfolio
return during the period under study. When comparing actual portfolio return with
achievable return for the same level of risk, we ﬁnd that as the portfolio size expands,
underperformance of the portfolio increases, i.e. the larger the portfolio size, the greater the
underperformance. This indicates that Markowitz efﬁciency is difﬁcult to achieve, par-
ticularly in large portfolios. Changing model parameters leads to alternative efﬁcient
frontiers that impact upon the measurement of performance. However, the use of alter-
native efﬁcient frontiers does not affect our result of the size effect on the relative per-
formance of portfolios. Our study shows that the size effect is present over the full period.
Our ﬁndings also suggest that the excess returns found in small portfolios are likely to be
associated with higher levels of diversiﬁable risk in comparison with larger portfolios.
Furthermore, in contrast to other studies, we ﬁnd no evidence to support the size reversal
effect in the data.
Keywords Size effect Á Efﬁcient frontier Á Minimum-variance portfolio Á Size
JEL Classiﬁcation G01 Á G11 Á G12
T. Hwang Á S. Gao (&) Á H. Owen
Edinburgh Napier Business School, Edinburgh Napier University,
Craiglockhart Campus, Edinburgh EH14 1DJ, UK
Rev Quant Finan Acc (2014) 43:721–750