Prediction Without Explanation: How Much to Trust a Model That Is Right for Reasons No One Can State

A model that predicts returns and cannot say why is not a hypothetical case. It is the ordinary output of a modern research pipeline. Fit a gradient-boosted tree or a neural network to a few hundred features and a decade of cross-sectional returns, hold out the most recent years, and the machine will often rank securities better out of sample than any single relationship a researcher could write down. Ask what it has found and the honest answer is a list of inputs with weights attached, which is a description of the model rather than an explanation of the market. The uncomfortable question follows at once: if the forecasts keep being right, how much does the missing explanation matter?

There are two easy answers and both are wrong. The first is that prediction is all that matters, that markets pay for forecasts and not for stories, and that a demand for explanation is a form of nostalgia. The second is that an unexplained signal is a curve fit waiting to fail and should not be traded at all. This piece treats the question as a quantitative one. We ask what an explanation actually buys, why the data alone cannot replace it within a useful horizon, and how a research organization can turn the admission that it does not know why something works into a specific, smaller, and more closely watched allocation rather than a verdict.

The Trade-Off Is Real, and Smaller Than It Looks

Begin with the trade-off everyone assumes exists. Simple models are easy to explain and, the folk wisdom goes, less accurate; flexible models are more accurate and opaque. Both halves are partly true, and the relationship between them is not a straight line. Figure 1 places a set of stylized model classes on two axes. The horizontal axis is a rough interpretability score, running from a linear regression whose coefficients can be read directly, through tree ensembles whose partial dependences can be inspected one input at a time, to deep networks and sequence models in which the mapping from input to forecast has no compact description. The vertical axis is an out-of-sample information coefficient, the rank correlation between forecast and realized return, generated from the simple concave curve stated in the note.^[1]

Two features of the picture matter. The frontier rises as interpretability falls, but it flattens: in the stylized construction, most of the gain from flexibility arrives in the move from a single linear model to a well-regularized ensemble of shallow learners, whose behavior can still be interrogated. The move from there to fully opaque architectures adds less than the folk wisdom promises, and at the far end the additional flexibility begins to buy noise about as often as it buys signal. The cost of explanation, in other words, is real but modest, and it is paid mostly at one step of the ladder rather than spread evenly along it.

That changes what the question is about. If the price of an explanation were a large fraction of the available predictive power, a firm would have to choose between understanding and returns. If it is a modest fraction, the choice is between a slightly weaker model that can be reasoned about and a slightly stronger one that cannot, and the right answer depends on what reasoning is worth. The rest of this piece is an attempt to price it.

What an Explanation Is For

An explanation of a predictive relationship is not a courtesy to the reader. It is a statement of the conditions under which the relationship should hold: who is on the other side of the trade, what they are paid for or constrained by, and what would have to change for them to stop. A signal that works because index rebalancing produces price-insensitive flows on known dates arrives with its expiry conditions written in. A signal that works for reasons no one can state arrives with none, and the difference is invisible until the world changes.^[2]

Figure 2 stylizes what happens at that point. Two signals with the same information coefficient are drawn through a regime shift at month zero: a change in market structure, a shift in the behavior of the participants who were supplying the return, a rule change. The explained signal's IC decays toward a floor with a long half-life, because the mechanism it depends on has been weakened rather than removed, and the researchers who own it know which part of the mechanism to watch. The unexplained signal decays with a short half-life toward a lower floor, because whatever it was exploiting is gone and nothing about the model says so. The parameters are chosen for exposition, but the shape follows from the argument: the explained signal degrades in a way its owners can anticipate, and the unexplained one degrades in a way they can only observe.

The obvious objection is that the decay will show up in live performance, and the model can be retrained or retired when it does. That is true, eventually. The question is how long eventually is, and here the arithmetic is unforgiving.

Why the Data Cannot Tell You in Time

A monthly information coefficient is a noisy quantity. Across a broad cross-section, the realized IC of a signal whose true value is a few hundredths swings by something like a tenth from month to month, and the standard error of its average over N months is that dispersion divided by the square root of N.^[3] To conclude with ordinary statistical confidence that a signal's IC has fallen by half, one needs enough months for the expected drop to stand two standard errors clear of the noise. Figure 3 plots that requirement across a range of starting IC levels using the formula in the note. For a signal with an IC of 0.03, the kind of modest, broadly diversified relationship a machine-learned model typically produces, the requirement is measured in years, not quarters.

This is the crux of the case for explanation, and it is quantitative rather than aesthetic. An unexplained signal cannot be retired on evidence within any horizon a portfolio can afford, because the evidence accumulates far more slowly than the losses do. It can only be retired on a rule set in advance, or on an argument. An explained signal supplies the argument: its owners can look at the mechanism directly, observe that the flow has stopped or the constraint has been lifted, and act long before the performance data could have told them anything. The explanation is a monitoring instrument with a much shorter lag than the returns themselves. That is what it is worth, and in a regime shift it is worth a great deal.

Five Questions in Place of an Explanation

None of this means an unexplained signal should be discarded. It means the missing explanation has to be replaced with something, and the something has to be more than a good backtest. Over time we have settled on five questions a signal must answer before it is trusted. Each can be asked of a model that cannot explain itself, and each recovers part of what an explanation would have provided. Figure 4 lays them out.

Stability and monotonicity are the cheapest to check and the most often skipped. A relationship that holds in one decade and reverses in the next, or that holds among large-capitalization stocks and vanishes below them, is not a relationship but a coincidence with a long run. A model whose forecast rises with an input up to a point and then falls, for no reason anyone can supply, is usually fitting an artifact of the sample. Ablation asks whether the model's own account of what matters survives an intervention: remove the inputs it claims to depend on, refit, and see whether the loss in accuracy is what the claimed dependence implies.^[4] Economic plausibility is the closest of the five to an explanation and the hardest to satisfy honestly; it asks not for a story but for a counterparty, someone whose constraints or incentives would lead them to take the other side of the trade at a loss. Capacity asks whether the signal survives the trading it would require, because a forecast that is only correct at a size too small to matter is a curiosity rather than a source of return.

A signal that passes all five is, for practical purposes, explained, even if the explanation was assembled from the outside rather than derived from the inside. A signal that passes stability and ablation but not plausibility is the genuinely hard case: it is real, it is not an artifact of the model, and no one knows why it works. That is the case the governance question is about.

Trust as a Budget, Not a Verdict

The mistake in both easy answers is to treat trust as binary. A model is deployed or it is not; an explanation is present or it is absent. In practice trust is a quantity, and the natural way to express it is as a risk budget and a review cadence that depend on how much of the explanatory gap remains open. Figure 5 sketches a stylized version of such a policy. Signals that pass all five questions receive the full budget their forecast strength would justify and are reviewed on the ordinary cycle. Signals with a conjectured but unverified mechanism receive a fraction of that and a faster review. Signals with no mechanism at all receive a smaller fraction still, a review cadence short enough to catch the decay in Figure 2 before it matters, and an automatic retirement rule keyed to a drawdown or a stability failure rather than to anyone's judgment. Signals that fail stability are not deployed, however good the backtest.

The multipliers in the figure are illustrative and the tiers could be drawn differently. The principle is not. An unexplained signal is not worthless, but it is worth less than an explained signal of the same strength, by an amount that reflects how much longer it will take to learn that it has stopped working. Sizing it accordingly is not caution for its own sake. It is the expected-value calculation that the missing explanation forces, done in advance rather than after the fact.

What This Means for How We Work

Three practices follow. The first is to treat explanation as a research output in its own right, with time budgeted for it after a model is built rather than only before: ablations, stability maps across periods and universes, and a written statement of the conjectured counterparty, even when the conjecture is weak. The second is to design the monitoring of an unexplained signal around the arithmetic of Figure 3, which means watching the inputs and the market structure it depends on rather than its returns, because the returns will be the last thing to tell you. The third is to keep the question open. Some of the relationships a model finds without explanation acquire one later, when someone notices which flow or constraint they were tracking, and the work of finding out is often where the next explained signal comes from.

The uncomfortable question at the start has a plain answer. A model that predicts and cannot explain should be trusted in proportion to how much of the explanation can be reconstructed from the outside, and for no longer than it takes the market to change. That is less trust than a good backtest invites and more than a purist would allow. It is also, as far as we can tell, the amount the arithmetic supports.