
Statistical arbitrage risk premium
Any asset can use a portfolio of similar assets to hedge against its factor exposure. The factor residual risk of the hedged position is called statistical arbitrage risk. Consequently, the statistical arbitrage risk premium is the expected return of such a hedged position. A recent paper shows that both theoretically and empirically this premium rises in the stock’s statistical arbitrage risk. ‘Unique’ stocks have higher excess returns than ‘ubiquitous’ stocks. The estimated premium is therefore a valid basis for investment strategies. Statistical arbitrage risk can be estimated by using ‘elastic net’ estimation and related machine learning. This method selects a relatively small hedge portfolio from a large array of candidate stocks.