Berkeley professors Richard Grinold (pictured on the right) and Ronald Kahn state in their book, which was well read among quantitative hedge fund managers, that the information ratio (explanation here) of a manager is equal to their investment skill times the square root of the number of independently correlated investment opportunities available. They called it the "fundamental law of active management." Here's the formula, for those interested.
Information Ratio = Information Coefficient (Skill) * Number of Bets ^1/2
In plain English, this means that if you want to get higher returns, you