A dataset of one-minute order-flow imbalance against next-minute futures returns gives a slope of 0.8 bps per unit, a t-statistic of 12 and an R-squared of 1.5%, with a 3 bp spread. Is the signal tradeable?

The signal is real and untradeable as a taker. A t of 12 over roughly 9,458 minutes says the slope is not zero, but a one-sigma imbalance predicts only 0.8 bps against 1.5 bps to cross one way and 3 bps to get out again. Trading every minute loses about 2.4 bps a trade. Its value is as an input: skewing a market maker's quotes or timing other orders.

Start with the sample size, because it explains both numbers. The t-statistic and R-squared are linked by the number of observations, and solving that link gives about 9,458 minutes, roughly 25 trading days of 375 minutes. With that many rows, a slope that explains 1.5% of the variance is detected with overwhelming confidence, and the t-statistic only confirms that the slope is not zero. Think of weighing yourself a thousand times on a slightly biased scale: you can be certain the scale reads 200 grams heavy, and that certainty says nothing about whether 200 grams matters to you.

The R-squared also tells you how noisy each minute is. The slope of 0.8 over an R-squared of 1.5% implies next-minute returns have a standard deviation of about 6.5 bps. The signal shifts the centre of that spread by less than one basis point. That is normal for high-frequency data and is not a sign of overfitting; it is the reason costs decide everything.

Put the prediction and the cost in the same units. A taker buys at the offer, 1.5 bps above the mid, and sells a minute later at the bid, 1.5 bps below it, so each round trip costs 3 bps. The fitted line only reaches 3 bps at an imbalance of 3.75 standard deviations, which happens in about 0.02% of minutes. Even covering the one-way half-spread needs 1.88 standard deviations, about 6% of minutes, and then you still pay to exit. The average absolute prediction across all minutes is 0.64 bps.

Change who pays the spread. A market makerA trader who posts bids and offers and earns the spread when others trade against them, rather than crossing the spread to trade. earns 1.5 bps each time a resting order fills, and loses when it fills just before the price moves through it. The imbalance signal tells the maker which side is about to be run over: at +2 standard deviations the predicted move is +1.6 bps, larger than the 1.5 bps the offer earns, so the maker should pull or widen the offer and lean on the bid. Used this way the signal does not need to beat the spread; it only needs to avoid the worst fills.

Two other uses are worth naming. An execution desk that must buy anyway can wait a minute when imbalance points down and buy now when it points up, saving part of the spread on flow it was going to trade regardless. And the signal can be one input among several: two weak, independent signals that each predict 0.8 bps combine into something larger, and only the combined forecast has to clear the cost.

Close with what you would check before believing any of it. Is the imbalance known at the moment you would act, or computed with the minute's final print? Does the slope hold in each week separately, or is it one volatile day? Does it survive a fee of even 0.5 bps a side? A take-home is marked on whether you separate statistical significance from economic significance, and then say what you would test next.