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An R² of 0.0016 that is worth a fortune

Asked at Two Sigma, Point72

Your daily return forecast has a correlation of just 0.040.04 with realized returns (its "information coefficient"). You apply it across 1,0001{,}000 roughly independent bets per year.

What is the R2R^2, and why can such a tiny number still be a world-class signal? Estimate the information ratio.

Show a hint

R2R^2 is the square of that correlation, a minuscule number. But edge compounds across many independent bets. Recall the fundamental law of active management.

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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