Portfolio Choice with Model Misspecification: A Foundation for Alpha and Beta Portfolios

92 Pages Posted: 3 Dec 2015 Last revised: 12 Jul 2016

See all articles by Raman Uppal

Raman Uppal

EDHEC Business School; Centre for Economic Policy Research (CEPR)

Paolo Zaffaroni

Imperial College Business School

Date Written: July 5, 2016

Abstract

Our objective is to investigate the effect of model misspecification on mean-variance portfolios and to show how asset-pricing theory and asymptotic analysis (for large number of assets) can be used to provide powerful solutions to mitigate misspecification. The starting point of our analysis is the Arbitrage Pricing Theory (APT). We extend the APT to show that it can capture not just small pricing errors that are independent of factors, but also large pricing errors from mismeasured or missing factors. Our key insight is that, instead of treating misspecification directly in the mean-variance portfolio, it is better to first decompose the portfolio into components that correspond to the two components of returns in the APT: a ``beta'' portfolio that depends on factor risk premia and an ``alpha'' portfolio that depends only on pricing errors. For the beta portfolio, we treat misspecification using asymptotic analysis: as the number of assets increases, we show that the weights of the alpha portfolio dominate those of the beta portfolio, leading to an expression for mean-variance portfolio weights that is immune to beta misspecification. For the alpha portfolio, we treat misspecification by imposing the APT restriction on alphas, which serves both as an identification condition and a shrinkage constraint. Finally, we demonstrate that our approach achieves an out-of-sample Sharpe ratio that is more than double that of the equally weighted portfolio.

Keywords: Active and passive portfolios, pricing errors, managerial skill, factor models, mean-variance portfolio, global-minimum-variance portfolio, estimation error, robust estimation

JEL Classification: G11, G12, C58, C53

Suggested Citation

Uppal, Raman and Zaffaroni, Paolo, Portfolio Choice with Model Misspecification: A Foundation for Alpha and Beta Portfolios (July 5, 2016). Available at SSRN: https://ssrn.com/abstract=2697866 or http://dx.doi.org/10.2139/ssrn.2697866

Raman Uppal (Contact Author)

EDHEC Business School ( email )

58 rue du Port
Lille, 59046
France

Centre for Economic Policy Research (CEPR)

90-98 Goswell Road
London, EC1V 7RR
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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