In a six-hour data task, a feature predicts next-day returns across 400 stocks with an average daily information coefficient of 0.02 and a standard deviation of 0.08 over 750 days. Is it real, what information ratio should you expect, and what do you check before presenting?

The IC is statistically real, with a t-statistic of about 6.8, and implies an information ratio of about 4.0 a year before costs. The daily IC is noisy, but 750 days pin its mean between 0.014 and 0.026. Dividing the mean by its spread and scaling by the square root of 252 gives the IR; the naive 400-stock breadth figure of 6.3 overstates it. Before presenting, check timing, overlap, universe and costs.

Picture a coin that lands heads 51 times in 100. One afternoon of flips proves nothing; a year of flipping settles it. The daily IC of 0.02 is invisible on any single day, but the average of 750 days has a standard error of only 0.0029, so the t-statistic is 6.85. The 95% interval for the mean runs from 0.014 to 0.026, nowhere near zero. Because the label is a one-day return and features are computed before it, the daily ICs do not overlap, so the plain t-test is fair here. Split the sample into three years as a first check: the yearly means are 0.017, 0.025, 0.018, all positive.

Grinold's fundamental law says the information ratio is roughly the IC times the square root of breadth, the number of independent bets a year. Counting 400 stocks on 252 days as independent gives 6.35, but the IC's own spread says the bets are far from independent. If 400 stocks were independent, the daily IC would wobble with a standard deviation of about 1 over the square root of 400, 0.05. It wobbles at 0.08, which implies only 1 / 0.08 squared, about 156, independent bets a day: stocks move together through sectors and factors. Using the IC's own variability, the IR is 0.02 / 0.08 = 0.25 a day, times the square root of 252, about 3.97 a year.

A number this good on a one-day horizon deserves suspicion first. Check timing before anything else: the feature must be computable from data available before the return window opens, or the IC is leakage. Then run the rest in order of how often each kills a signal. Is the IC carried by the smallest, least liquid stocks, where you cannot trade? Does it survive neutralising sector and market exposure, or is it a disguised factor? Is the universe as it was each day, including stocks later delisted? How fast does the IC decay at two, five and ten days, because a one-day signal turns the book over daily and costs will eat much of it? Finally, estimate costs explicitly: at full daily turnover, even 10 basis points a trade is a large fraction of a 0.02 IC's edge.

State the finding and its limit together. The feature has a small, stable and highly significant IC; its gross information ratio is about 4.0, and whether it survives depends on costs and on the leakage checks. Give the three yearly ICs, the decay profile and a cost-adjusted estimate even if rough. A take-home is judged on whether you found the ways it could be false, not on the size of the number you report.