Portfolio Sorts and Decile Spreads

You have a number for every stock — an accounting ratio, a momentum score, a sentiment reading — and you want to know whether it predicts returns. The portfolio sort is the answer the profession settled on. Rank the universe by the signal, cut it into ten equal-count buckets, hold each bucket for a month, and compare the top decile to the bottom. The difference is the decile spread, and it is the first number anyone will ask you for.

It won out over regression for three reasons. It assumes nothing about returns being linear in the signal, so an effect that lives in the tails still shows up. It uses ranks, not levels, so one stock with a book-to-price of 40 because its equity nearly vanished cannot dominate the result. And it outputs a portfolio you could have held, not a coefficient you must translate into positions.

The recipe, concretely

At the close of each month:

1. Take the universe as it existed at that date — including the companies that later went bankrupt, or you have manufactured Survivorship Bias.
2. Compute the signal using only data publicly available at that date. Accounting data needs a reporting lag; a fiscal-year-end December number is not usable until the following March or later.
3. Rank and cut into 10 buckets. A 3,000-name universe gives 300 stocks per decile.
4. Weight within each bucket — equal or by market cap — hold for one month, then repeat.

Fifty years of monthly data gives 600 observations of the spread, which is what makes the statistics tractable.

A worked sort

Here is what a twelve-month-minus-one momentum sort on US large caps looks like, in mean monthly return by decile.

Decile 1 returns 0.15% a month and decile 10 returns 1.35%, so the spread is $1.35 - 0.15 = 1.20$ percent per month. Annualise it, and annualise the risk. If the monthly spread has a standard deviation of 6.0%:

$12 \times 1.20 = 14.4 \qquad 6.0 \times \sqrt{12} = 20.8$

so 14.4% a year at 20.8% volatility, a Sharpe ratio of $14.4 / 20.8 = 0.69$. And the statistical significance over $T = 600$ months:

$t = \frac{1.20}{6.0 / \sqrt{600}} = \frac{1.20}{0.245} = 4.90$

A t-statistic of 4.9 clears any bar, including the raised one now applied to anomalies found by searching.

Then subtract the costs

A spread portfolio is not free to hold. Momentum deciles turn over roughly 30% of their names each month on each side. That means 30% sold and 30% bought monthly on the long book and the same on the short book. At a 15 basis point round-trip cost in liquid large caps:

$0.30 \times 15 \times 2 = 9 \text{ bp per month} = 1.08\% \text{ per year}$

Against 14.4% of gross spread, that is a rounding error. Now run the identical sort in small caps where the round trip costs 60 basis points:

$0.30 \times 60 \times 2 = 36 \text{ bp per month} = 4.32\% \text{ per year}$

Nearly a third of the gross spread, gone. This is why the same anomaly is "strong" in one paper and "not implementable" in another — they sorted the same signal on different universes.

What quietly inflates the number

• Equal weighting. Equal weights put as much money in the 2,900th largest stock as in Apple. Many published decile spreads roughly halve when re-run value-weighted, because the return lived in names too small to hold.
• The short leg. A large share of many spreads comes from decile 1 underperforming rather than decile 10 outperforming, and decile 1 is disproportionately hard to borrow. Always report both legs against the universe mean, not just the difference.
• Design choices. You picked deciles rather than quintiles, monthly rather than quarterly rebalancing, this universe, this date range. Each was a fork in the road, and the reported spread is the best branch you walked down.

Sorts versus regressions. A Fama-MacBeth cross-sectional regression uses the magnitude of the signal, not just its rank, and lets you add controls, so you can ask whether the signal survives after size and beta. A sort cannot control for a second variable without splitting into a double sort, and a 5-by-5 double sort on 3,000 names leaves 120 stocks a cell. Use sorts to see the shape, regressions to test whether the effect is incremental.

In interviews

Give the recipe in order — point-in-time universe, lagged fundamentals, equal-count buckets, monthly hold — and then the arithmetic: annualised spread, annualised volatility, Sharpe, and the t-statistic $\bar{x}/(s/\sqrt{T})$. Say explicitly that you would check monotonicity across all ten buckets, not just the ends. Then volunteer the criticisms before you are asked: equal weighting, the short leg, turnover cost, and the fact that the sort's design was chosen with the answer already visible.