Sina Seyfi

This paper tackles a simple but difficult question: with so many predictors for stock returns, how do we know which ones truly matter?

Traditionally, the way to test a signal is straightforward: sort stocks into portfolios based on that signal and see how average returns differ. Sort on momentum? Momentum looks important. Sort on size? Size matters. Whatever you sort on ends up looking powerful.

This is where my paper flips the exercise on its head.

Instead of asking:
“What is the return difference between small vs. big firms, or value vs. growth?”
I ask:
“What is the characteristic difference between low-return vs. high-return firms?”

Reverse-engineering returns

Here’s the idea:

• Step 1 (in-sample): I sort stocks directly by their realized returns—no signals involved. This gives me “return-sorted portfolios” that capture, as closely as possible, the true but unobservable drivers of expected returns.
• Step 2 (out-of-sample): Using a large set of firm characteristics, I then construct new portfolios that mimic those return-sorted portfolios. Each stock is assigned to whichever return-sorted portfolio its characteristics most resemble.

The beauty of this approach is that realized returns contain information from all signals—observed and unobserved. By starting from returns themselves, we avoid the bias of choosing one characteristic at a time. Also, my out-of-sample portfolios by construction are the closest sorting to the return-sorted portfolios (in terms of a large set of characteristics).

How well does this work?

Very well. A long-short portfolio built from this strategy generates an out-of-sample monthly alpha of about 2.4% (with a t-stat of 14.5) and an annualized Sharpe ratio above 2 (equally-weighted? SR above 3.5). This performance not only survives transaction costs, but also beats leading machine learning methods and is robust to various specifications.

What really drives the cross section?

Finally, once we have these return-sorted portfolios, we can ask: which characteristics separate the losers from the winners?

The answer is clear:

• Price-based characteristics dominate. Momentum, reversals, announcement returns, volatility, and industry returns carry the most weight.
• Fundamental (accounting-based) signals still matter, but far less.
• Losers and winners share surprising similarities. Both groups tend to be small, illiquid, young firms with high volatility and wide bid–ask spreads. What sets them apart is not everything about them, but a handful of key price-related signals.
• Interactions and non-linearities add further predictive power.

The essence

So, the “essence of the cross section” is this: instead of chasing one predictor at a time, reverse-engineer from realized returns. Doing so reveals which characteristics consistently line up with low vs. high expected returns. And the winners are, overwhelmingly, price-based signals—though interestingly, losers and winners are more alike than we might think.

That, in short, is the essence of the Essence of the Cross Section.