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SUMMARY:Portfolio Choice with Model Misspecification: A Foundation for Alp
 ha and Beta Portfolios - UPPAL Raman\, PhD  Professor - Speciality: Financ
 e\, EDHEC Business School
DTSTART:20151029T130000Z
DTEND:20151029T140000Z
UID:TALK61137@talks.cam.ac.uk
CONTACT:Cerf Admin
DESCRIPTION:Hedge funds such as Bridgewater Associates o↵er two kinds of
  portfolios: “alpha”portfolios (a strategy with both long and short po
 sitions with overall zero market risk)and “beta” portfolios (a long-on
 ly strategy with exposure to market risk)\; similarly\,sovereign wealth fu
 nds such as Norges Bank separate the management of their alpha and beta fu
 nds. Moreover\, hedge funds and sovereign funds hold a large number of ass
 ets in their portfolios\, ranging from several hundred to thousands (the p
 ortfolio of Norges Bank has over 9\,000 assets). In this paper\, we provid
 e a rigorous foundation for “alpha” and “beta” portfolio strategie
 s and characterize their properties when the\nnumber of assets is asymptot
 ically large and returns are given by the Arbitrage Pricing Theory (APT). 
 The APT is ideal for this analysis because it allows for alphas\, while st
 ill imposing no arbitrage. Our first contribution is to extend the interpr
 etation of the APT to show that it can capture not just small pricing erro
 rs that are independent of factors but also large pricing errors that aris
 e from mismeasured or missing factors. Our second contribution is to show 
 that under the APT\, the optimal mean-variance portfolio in the presence o
 f a risk-free asset can be decomposed into two components: an “alpha”\
 nportfolio that depends only on pricing errors and a “beta” portfolio 
 that depends only on factor risk premia and their loadings. We then demons
 trate that the alpha portfolio is the minimum-variance portfolio that is o
 rthogonal to the beta portfolio\, and vice versa\, `a l a Roll (1980). Thi
 s optimality property implies that the alpha and beta portfolios satisfy p
 roperties similar to those of the optimal mean-variance portfolio in terms
  of the relation between portfolio mean and variance. Moreover\, their opt
 imality implies that the squares of their Sharpe ratios sum to the square 
 of the Sharpe ratio of the optimal mean-variance portfolio. Our third cont
 ribution is to characterize alpha and\nbeta portfolios when the number of 
 assets is asymptotically large: in this setting\, we show that the portfol
 io weights of the alpha portfolio typically dominate the weights of the be
 ta portfolio. We obtain similar decompositions and asymptotic results for 
 the tangency portfolio\, the global-minimum-variance portfolio\, and the p
 ortfolios that comprise the Markowitz efficient frontier. Our fourth contr
 ibution is to show how these results about the decomposition of various po
 rtfolio weights\, together with the restriction arising from the extended 
 APT\, can and should be used to improve the estimation of portfolio weight
 s in the presence of model misspecification.
LOCATION:Room W4.03 Judge Business School
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