From Idea to Signal

The story

Every signal needs a counterparty

Before you touch any data, answer one question: who is on the other side of this trade, and why do they keep losing?

Start with the other side

Every trade has a counterparty. If your signal earns money month after month, someone is giving it up month after month.

If you can't say who, a strong backtest is more likely luck than discovery. Three answers hold up.

They're paying you to take a risk

Some investors pay to get rid of a risk, the way people pay for insurance. You collect the premium and you take the crash when it comes.

This kind of signal rarely dies, because it's compensation, not a mistake.

They're making a mistake

Some investors misread information in a repeatable way. They underreact to news, overreact to stories, or anchor on old prices.

You earn their error until enough capital crowds in to correct it.

They're forced to trade

Index funds have to buy at the rebalance. Some mandates have to sell a bond the day it's downgraded. Rules move prices whatever the value.

This edge lasts exactly as long as the rule does.

Residual momentum's story

The story is behavioral. Investors underreact to firm-specific news, so it reaches prices slowly. Stripping out factor moves leaves that news on its own.

A good story also makes predictions. If underreaction drives the signal, it should be stronger where news travels slowly, in small and thinly covered stocks. Page 4 tests that.

Rule of thumbThe story tells you how the signal will die. Write it down before you see the backtest.

Why does the signal pay?

Risk premium

Other side: Investors paying to shed a risk
Behaves: Pays on average, crashes in bad times
Dies when: Rarely. It's compensation.
Examples: Value, carry, illiquidity

Behavioral error

Other side: Investors misreading information
Behaves: Steady while the mistake persists
Dies when: Arbitrage capital crowds in
Examples: Momentum, post-earnings drift

Structural flow

Other side: Investors forced by a rule
Behaves: Tied to dates and events
Dies when: The rule changes
Examples: Index inclusion, month-end rebalancing

The transform

From raw value to score

A raw value is just a number. A score is something you can compare across 60 stocks and turn into position sizes.

Raw values hide a trap

Here are this month's raw residual momentum values for 60 stocks. Most sit between −2 and +2.

One utility, PWRX, sits near +9. Its residuals barely move, so dividing by a tiny volatility blew up its score. Size positions by raw value and that one name owns a big slice of the long book.

A z-score doesn't fix it

Subtract the mean and divide by the standard deviation. The scale changes, but the shape doesn't.

PWRX still dominates. It also inflates the standard deviation, which squashes every other stock toward zero.

Clip, then standardize

Winsorize: clip each value at ±3 standard deviations, then standardize again.

PWRX keeps its place at the top, but its share of the long book drops by about half, and the other 59 stocks spread back out.

Or throw the magnitudes away

Ranking keeps only the order. Outliers can't hurt it, because the top stock is simply first.

The cost is information. A stock at +2.9 now scores almost the same as one at +1.5.

Rule of thumbRank when you don't trust the magnitudes. Use a winsorized z-score when the size of the value carries information.

Residual momentum · 60 stocks · raw value

Transform

Long book, by weight

PWRX Next two largest Everyone else

PWRX share

0%

of long weight

Top 3 share

0%

of long weight

Rest's spread

0.0

std dev, others

The neutralization

Make the score bet only on your idea

A score can carry sector and beta bets you never meant to make. Page 1's factor model takes them out.

Your score has passengers

Average the score by sector. Tech sits well above everyone else, and high-beta stocks score higher across the board.

Buy the top and short the bottom, and part of your book is a tech-versus-consumer bet plus a market bet. You never asked for either.

Remove the sector means

Subtract each sector's average score from its stocks. Every sector now averages zero.

The long and short sides now hold similar sector mixes. Some of the beta tilt goes too, because beta clusters by sector, but not all of it.

Then remove beta

Regress the score across stocks on sector dummies and beta, and keep the residual. The fitted line goes flat and the correlation with beta hits zero.

This is page 1's model run on scores instead of returns: score = B · γ + what's left. What's left is the part your idea owns.

It isn't free

Neutralizing deletes whatever part of the signal lived in sectors and beta. Here only about two thirds of the original score survives.

If your idea really is about stocks, that's the point. If it's secretly a sector call, you just threw it away.

Decide by the storyIs the bet about individual stocks? Neutralize. Is it about sectors? Don't neutralize; build a sector signal and test it on its own.

Neutralize

Average score by sector

Score against market beta · one dot per stock

Corr with beta

0.00

Sector spread

0.00

top minus bottom

Original kept

100%

corr² with raw score

The calendar

Signals have calendars

Seasonality shows up in two ways: as a signal of its own, or as a pattern hiding inside yours.

Momentum's bad month

Momentum strategies have historically lost money in January, on average, while earning in most other months.

A common explanation is tax-loss selling. Losers get dumped in December and bounce in January, which hurts a strategy that is short the losers. Residual momentum inherits some of this.

Calendar effects as signals

Turn of the month, January in small caps, "sell in May," the Monday effect. Each one has a published paper behind it.

They're also the textbook data-mining trap. Slice the calendar enough ways and some slices look significant by chance. Page 5 counts how many.

Seasonality as noise

Many inputs swing with the calendar. A retailer's sales spike every December. Feed raw month-over-month changes into a signal and you're scoring Christmas, not the company.

Compare each month with the same month a year earlier instead. In this example, only the year-over-year line shows the business slowing in year 3.

Signal or noise?

Every calendar pattern you find goes down the same two-question tree.

Say it this way"Residual momentum is weak in January, consistent with tax-loss reversal. I'd report results with and without January rather than switch it off."

Momentum long-short · average return by calendar month, illustrative

Shape, not exact values. January losses and a strong December are the pattern the literature reports. The bar heights here are illustrative.

Published calendar effects

January effect

Small caps outperform in January.

Rozeff &
Kinney, 1976

Monday effect

Returns are lower over the weekend.

French,
1980

Turn of the month

Returns cluster in the last and first few days of each month.

Ariel,
1987

Sell in May

November to April beats May to October.

Bouman &
Jacobsen, 2002

The trap12 months, 5 weekdays, 22 trading days, holidays, quarter-ends. Test hundreds of slices at 5% significance and you should expect several to pass by chance alone.

Retailer monthly sales · simulated, 48 months

Month over month Year over year

Found a calendar pattern · what to do with it

Is the calendar pattern your idea?

Yes

It's a signal. It needs a counterparty story, like any other, and a multiple-testing correction on page 5.

No

Is it in your inputs or in your returns?

Inputs

Deseasonalize. Use year-over-year changes, or regress on month dummies and keep the residual.

Returns

Report it, don't trade around it. Show results with and without the weak months. A switch fitted to past months is overfitting.