Optimality and Diversifiability of Mean Variance and Arbitrage Pricing Portfolios

54 Pages Posted: 3 Dec 2009

See all articles by M. Hashem Pesaran

M. Hashem Pesaran

University of Southern California - Department of Economics; University of Cambridge - Trinity College (Cambridge)

Paolo Zaffaroni

Imperial College Business School

Date Written: November 2009

Abstract

This paper investigates the limit properties of mean-variance (mv) and arbitrage pricing (ap) trading strategies using a general dynamic factor model, as the number of assets diverge to infinity. It extends the results obtained in the literature for the exact pricing case to two other cases of asymptotic no-arbitrage and the unconstrained pricing scenarios. The paper characterizes the asymptotic behaviour of the portfolio weights and establishes that in the non-exact pricing cases the ap and mv portfolio weights are asymptotically equivalent and, moreover, functionally independent of the factors conditional moments. By implication, the paper sheds light on a number of issues of interest such as the prevalence of short-selling, the number of dominant factors and the granularity property of the portfolio weights.

Keywords: large portfolios, factor models, mean-variance portfolio, arbitrage pricing, market (beta) neutrality, well diversification

JEL Classification: C32, C52, C53, G11

Suggested Citation

Pesaran, M. Hashem and Zaffaroni, Paolo, Optimality and Diversifiability of Mean Variance and Arbitrage Pricing Portfolios (November 2009). CESifo Working Paper Series No. 2857, Available at SSRN: https://ssrn.com/abstract=1516222

M. Hashem Pesaran (Contact Author)

University of Southern California - Department of Economics

3620 South Vermont Ave. Kaprielian (KAP) Hall 300
Los Angeles, CA 90089
United States

University of Cambridge - Trinity College (Cambridge) ( email )

United Kingdom

Paolo Zaffaroni

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

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