  How to hedge factor risks without knowing the identities of the factors? We
first prove a general theoretical result: even if the exact set of factors
cannot be identified, any risky asset can use some portfolio of similar peer
assets to hedge against its own factor exposures. A long position of a risky
asset and a short position of a "replicate portfolio" of its peers represent
that asset's factor residual risk. We coin the expected return of an asset's
factor residual risk as its Statistical Arbitrage Risk Premium (SARP). The
challenge in empirically estimating SARP is finding the peers for each asset
and constructing the replicate portfolios. We use the elastic-net, a machine
learning method, to project each stock's past returns onto that of every other
stock. The resulting high-dimensional but sparse projection vector serves as
investment weights in constructing the stocks' replicate portfolios. We say a
stock has high (low) Statistical Arbitrage Risk (SAR) if it has low (high)
R-squared with its peers. The key finding is that "unique" stocks have both a
higher SARP and higher excess returns than "ubiquitous" stocks: in the
cross-section, high SAR stocks have a monthly SARP (monthly excess returns)
that is 1.101% (0.710%) greater than low SAR stocks. The average SAR across all
stocks is countercyclical. Our results are robust to controlling for various
known priced factors and characteristics.
