Alpha in Statistical Arbitrage

To build off the last post, let’s examine the expected return of a skillfully constructed market neutral portfolio:

\(E[r_p]=E[\alpha_1]-E[\alpha_2]\)

Looking at this, it’s straightforward to see that if we can expect the second alpha to be negative, and the first alpha to be positive, we’ll have a very positive expected portfolio return.

But in what case would this happen, you might ask. Well if the alphas are realizations of a specific quantification of a single factor, and you run this quantification across a pair of stocks, then it’s like seeing the manifestation of a single factor across your cross section of 2 stocks.

So pricing inefficiencies across a cross section would arise from the buy/sell pressure imbalance that is captured by different scores on the quantification of this factor.

One might think of it as the cross section having a buy/sell imbalance spread around a factor.

Now when we think of stat arb beyond pairs trades through this lens, we can frame the endeavor as probabilistic betting on momentum or reversion based on factor quantification.