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SUMMARY:The Statistical Limit of Arbitrage
DTSTART;VALUE=DATE-TIME:20220610T103000
DTEND;VALUE=DATE-TIME:20220610T120000
UID:7dc39682cb64aa7618ef775093154b1e1d788117ce12f92442f64aed
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dacheng Xiu\, Chicago Booth\nIn the context of a linear asset
pricing model\, we document a statistical limit to arbitrage due to the fa
ct that arbitrageurs are incapable of learning a large cross-section of al
phas with sufficient precision given a limited time span of data. Conseque
ntly\, the optimal Sharpe ratio of arbitrage portfolios developed under ra
tional expectation in the classical arbitrage pricing theory (APT) is over
ly exaggerated\, even as the sample size increases and the investment oppo
rtunity set expands. We derive the optimal Sharpe ratio achievable by any
feasible arbitrage strategy\, and illustrate in a simple model how this Sh
arpe ratio varies with the strength and sparsity of alpha signals\, which
characterize the difficulty of arbitrageurs' learning problem. Furthermore
\, we design an ``all-weather'' arbitrage strategy that achieves this opti
mal Sharpe ratio regardless of the conditions of alpha signals. We also sh
ow how arbitrageurs can adopt multiple-testing\, LASSO\, and Ridge methods
to achieve optimality under distinct conditions of alpha signals\, respec
tively. Our empirical analysis of more than 50 years of monthly US individ
ual equity returns shows that all strategies we consider achieve a moderat
ely low Sharpe ratio out of sample\, in spite of a considerably higher yet
infeasible one\, suggesting the empirical relevance of the statistical l
imit of arbitrage and the empirical success of APT.\n\nJointly written wit
h Rui Da and Stefan Nagel
LOCATION:UniL Campus\, Room Extra 126
STATUS:CONFIRMED
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