Abstract

Markowitz's celebrated mean-variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counter-intuitive asset allocation weights; this has been referred to as the "Markowitz optimization enigma". The speaker first reviews different approaches in the literature to address these difficulties, and in particular the Black-Litterman approach that has received much recent interest. He then explains the root cause of this enigma and proposes a new approach to resolve it. Connections of the speaker's approach to that of Black and Litterman are also discussed.

About the speaker

Prof Tze Leung Lai received his PhD in Mathematical Statistics from Columbia University in 1971. He stayed on the faculty until he moved to Stanford University in 1987, where he is currently Professor of Statistics, of the Institute for Computational and Mathematical Engineering, and by courtesy, of Health Research and Policy. He is also Director of Financial Mathematics Program and the Financial and Risk Modeling Institute at Stanford, and Co-director of the Biostatistics Core of the Cancer Institute and the Center of Innovative Design at the School of Medicine.

Prof Lai won the Committee of Presidents of Statistical Societies Award in 1983 and the Abraham Wald Prize in Sequential Analysis in 2005. He is an elected Member of Academia Sinica, where he has been an Advisory Committee member of the Institute of Statistical Science since 1992. He is also an Advisory Committee member of the Department of Statistics and Actuarial Science and of the Institute for Mathematical Research at The University of Hong Kong, and of the Statistics Center at Peking University and the Mathematical Sciences Center at Tsinghua University. He has published nine books, 275 papers, and has supervised sixty PhD students.

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