Labelling: Deciding What You Are Actually Predicting

In most supervised learning the label arrives with the data. This image is a cat. This review is negative. Nobody chooses.

In finance nothing is labelled. You have a price series, and turning it into a supervised problem requires you to decide what question you are asking. That decision is made before any modelling, is rarely revisited, and determines more about your results than the model does.

Key idea: A label encodes a trade. It says what position was taken, when it was closed, and under what conditions. If that implied trade is one no desk would ever place, then a model that predicts it perfectly is worth nothing, and no amount of validation rigour will reveal the problem, because the model is answering the question you asked.

The near-universal starting point is the sign of the return over a fixed horizon:

$y_t = \mathrm{sign}\!\left(\frac{p_{t+h}}{p_t} - 1\right)$

Written as an instruction to a trader, that reads: open a position now, hold it for exactly $h$ periods whatever happens, use no stop-loss, take no profit, and close at the end regardless of where the price went in between.

Three things are wrong with it, and they compound.

• No stop. The label calls a trade a winner even if it was deeply underwater on the way.
• A fixed holding period. Real positions close when a target or a stop is reached, not when a calendar says so, so the horizon is an arbitrary parameter with a large effect on the labels.
• No risk scaling. A 1 percent move is a large event in a quiet regime and noise in a volatile one, but the label treats both identically.

These are the labels the model is being asked to learn. It will faithfully learn to predict outcomes that a real position, with a real stop, would not have collected.

Gotcha: This error does not show up as noise. It is systematic, it correlates with volatility and with drawdown depth, and it biases the model toward exactly the trades that look best on paper and behave worst in execution.

López de Prado's answer, in Advances in Financial Machine Learning (2018), is to label by whichever of three barriers the price touches first.

1. Upper barrier, a profit target, set above the entry price.
2. Lower barrier, a stop-loss, set below it.
3. Vertical barrier, a maximum holding period, in time rather than price.

The label is which one is hit first: 1 for the target, -1 for the stop, and either 0 or the sign of the realised return for a timeout.

Definition: The horizontal barriers are set as multiples of a volatility estimate at the time of entry, not as fixed percentages. A 2 percent target is ambitious in a calm week and trivial in a crisis, so the barrier has to scale with the prevailing risk or the label means something different on every date.

What this buys is that the label now describes a trade with a defined risk, a defined reward and a defined exit, which is to say a trade someone could actually place.

The barrier multiple is a real parameter with a real trade-off, and the label distribution shows it directly. Simulated on driftless returns with a 10-day vertical barrier:

Narrow barriers produce a nearly balanced two-class problem and label mostly noise, since at half a sigma the price touches something almost immediately. Wide barriers produce meaningful events and 80 percent timeouts, leaving few examples of what you care about.

In practice: The upper and lower shares are equal here because the simulation has no drift, which is a useful sanity check on any labelling implementation. If your barriers are symmetric and your labels are not roughly balanced on driftless synthetic data, the bug is in the labeller rather than in the market.

The mechanics are a search for the first touch, and the only subtle part is that the vertical barrier must be resolved together with the other two rather than after them.

import numpy as np

def triple_barrier(prices, t0, sigma, pt=1.0, sl=1.0, max_hold=10):
    """Return (label, exit_index) for an entry at index t0."""
    entry = prices[t0]
    upper = entry * (1 + pt * sigma)      # sigma is the vol estimate AT ENTRY
    lower = entry * (1 - sl * sigma)
    end = min(t0 + max_hold, len(prices) - 1)

    for t in range(t0 + 1, end + 1):
        if prices[t] >= upper:
            return 1, t
        if prices[t] <= lower:
            return -1, t
    return 0, end                          # vertical barrier: timed out

Two details decide whether this is correct. sigma must be estimated using data available at t0 and nothing after it, or you have inserted the future into the barrier itself. And the returned exit_index is not optional bookkeeping: it defines the label's time span, and the next two lessons need it to compute sample weights and to purge the validation folds.

Gotcha: On intraday or gapping data, checking only closing prices misses barriers that were touched and crossed within a bar. The label then records a timeout for a trade that was stopped out hours earlier, which reintroduces the exact error the method was designed to remove.

A primary model predicts direction. Meta-labelling adds a second model that predicts whether the primary model is right this time, and it turns out to be an easier and more useful question.

The procedure has three steps. Run the primary model to get a side, long or short. Apply the triple barrier to the trade that side implies, giving a binary outcome: did it work. Train a second model on that binary label, using features that may include the primary model's own confidence.

Key idea: The split maps onto precision and recall. A primary model can be tuned for recall, catching most opportunities and accepting false positives, while the meta model supplies precision by filtering them. Optimising both at once in a single model forces a compromise; separating them lets each be tuned for what it is good at, and gives you a natural sizing signal as a by-product.

The technique is most valuable when you already have a signal you cannot or will not replace.

• A discretionary or rules-based strategy. A portfolio manager's calls, or a moving-average crossover, produce sides. Meta-labelling learns when to back them without touching the underlying logic, which matters when that logic is a person or a system nobody wants rewritten.
• A model you must keep interpretable. Regulators or risk committees may require an explainable primary model. The filter can be more complex, because it only ever reduces activity.
• Anywhere you need position sizing. The meta model's predicted probability is a natural size, and this is often the largest practical gain: same trades, better allocation across them.

Gotcha: Meta-labelling cannot create an edge. If the primary model is at chance, then filtering its calls filters noise, and any apparent improvement is selection on the validation set. It improves an edge that already exists by allocating to it better, and treating it as a way to rescue a strategy that does not work is the standard misuse.

There is a decision before labelling that most pipelines never make consciously: which rows are samples at all.

Daily bars are the default and they are an odd choice. Markets do not deliver information at a constant rate; a quiet August day and a central bank announcement day are one row each. Sampling by clock time therefore oversamples quiet periods and undersamples exactly the events that carry information.

The alternatives sample on activity rather than on time.

In practice: A second approach is event-based sampling: label only bars where something happened, such as a volatility breakout or a structural break. It shrinks the dataset and raises the share of samples that carry a decision, which is usually the better trade when the base rate of interesting events is low.

Before any feature engineering, the labelling decision should survive these questions.

1. Write the label as a trade instruction. Entry, exit condition, stop, target, maximum hold. If it is not a trade you would place, stop here.
2. Are the barriers scaled by volatility at entry? Fixed percentage barriers mean something different in every regime, and the volatility estimate must use only past data.
3. Do you know each label's time span? The exit index is required for sample weighting and for purging, and a pipeline that discards it cannot be validated honestly later.
4. What is the class balance, and is it an artefact? Heavy timeout classes usually mean the barriers are too wide for the horizon.
5. Does the sampling scheme match where information arrives? Time bars are a default, not a decision.
6. Sanity-check on synthetic driftless data. Symmetric barriers should give symmetric labels. If they do not, the labeller has a bug.

Key idea: Everything downstream inherits this choice. A leak introduced in the labels cannot be detected by a model, corrected by a better architecture, or caught by the validation scheme in lesson 4, because from every one of their perspectives the label simply is the truth.