A model predicts the sign of the next-day return with 55% accuracy and loses money. Another predicts the return magnitude with an information coefficient of 0.03 and makes money. Explain how both are possible and state what the sign model is missing.

A model predicts the sign of the next-day return with 55% accuracy and loses money. Another predicts the return magnitude with an information coefficient of 0.03 and makes money. Explain how both are possible and state what the sign model is missing.

Approach: Write the profit as the sum of signed returns and note that accuracy weights every observation equally while profit weights each by its magnitude.

Sign accuracy weights every day equally while profit weights each day by the size of the move, so a model can be right on 55% of days and wrong on the days that carry the largest magnitudes, and a continuous forecast with an information coefficient of 0.03 makes money because it sizes positions in proportion to the expected return and is therefore largest when it matters. Profit is sum_t position_t * r_t, which depends on the joint distribution of the forecast and the return magnitude, and nothing in a sign accuracy figure constrains that. A model that is right on many small quiet days and wrong on a handful of large ones is a common outcome, since the large moves are driven by news the features do not contain. The sign model also discards the information needed for sizing: a binary output takes the same position on a day with a 0.2% expected move and a day with a 2% one, so it cannot concentrate risk where the edge is. Costs make this worse, because a fixed cost per trade is paid on every position regardless of size and eats the small-move days that make up most of the wins. The correct target is the expected return itself, evaluated with the information coefficient and then by a profit and loss simulation with realistic costs, and the correct action is a position proportional to the forecast divided by the forecast variance, capped by risk limits.

Follow-up: With an information coefficient of 0.03 across 500 names rebalanced daily, what Sharpe does the fundamental law of active management predict, and what assumption of it fails in practice?

Key concepts: sign accuracy, information coefficient, position sizing, expected profit.