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CATEGORIES:Cambridge Finance Workshop Series
SUMMARY:Portfolio Choice with Model Misspecification: A Fo
undation for Alpha and Beta Portfolios - UPPAL Ram
an\, PhD Professor - Speciality: Finance\, EDHEC
Business School
DTSTART;TZID=Europe/London:20151029T130000
DTEND;TZID=Europe/London:20151029T140000
UID:TALK61137AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61137
DESCRIPTION:Hedge funds such as Bridgewater Associates o↵er tw
o kinds of portfolios: “alpha”portfolios (a strate
gy with both long and short positions with overall
zero market risk)and “beta” portfolios (a long-on
ly strategy with exposure to market risk)\; simila
rly\,sovereign wealth funds such as Norges Bank se
parate the management of their alpha and beta fund
s. Moreover\, hedge funds and sovereign funds hold
a large number of assets in their portfolios\, ra
nging from several hundred to thousands (the portf
olio of Norges Bank has over 9\,000 assets). In th
is paper\, we provide a rigorous foundation for “a
lpha” and “beta” portfolio strategies and characte
rize their properties when the\nnumber of assets i
s asymptotically large and returns are given by th
e Arbitrage Pricing Theory (APT). The APT is ideal
for this analysis because it allows for alphas\,
while still imposing no arbitrage. Our first contr
ibution is to extend the interpretation of the APT
to show that it can capture not just small pricin
g errors that are independent of factors but also
large pricing errors that arise from mismeasured o
r missing factors. Our second contribution is to s
how that under the APT\, the optimal mean-variance
portfolio in the presence of a risk-free asset ca
n be decomposed into two components: an “alpha”\np
ortfolio that depends only on pricing errors and a
“beta” portfolio that depends only on factor risk
premia and their loadings. We then demonstrate th
at the alpha portfolio is the minimum-variance por
tfolio that is orthogonal to the beta portfolio\,
and vice versa\, `a l a Roll (1980). This optimali
ty property implies that the alpha and beta portfo
lios satisfy properties similar to those of the op
timal mean-variance portfolio in terms of the rela
tion between portfolio mean and variance. Moreover
\, their optimality implies that the squares of th
eir Sharpe ratios sum to the square of the Sharpe
ratio of the optimal mean-variance portfolio. Our
third contribution is to characterize alpha and\nb
eta portfolios when the number of assets is asympt
otically large: in this setting\, we show that the
portfolio weights of the alpha portfolio typicall
y dominate the weights of the beta portfolio. We o
btain similar decompositions and asymptotic result
s for the tangency portfolio\, the global-minimum-
variance portfolio\, and the portfolios that compr
ise the Markowitz efficient frontier. Our fourth c
ontribution is to show how these results about the
decomposition of various portfolio weights\, toge
ther with the restriction arising from the extende
d APT\, can and should be used to improve the esti
mation of portfolio weights in the presence of mod
el misspecification.
LOCATION:Room W4.03 Judge Business School
CONTACT:Cerf Admin
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