Let’s represent a strategy’s return stream using a random variable *X* with mean μ,
variance σ^{2}, and risk-free rate *r*. The growth rate over *n* time steps (approximated by the 2nd order taylor expansion) is:

Allow *n* to go to infinity:

This function is maximized at the optimal kelly-betting fraction / leverage level:

Let *r*=0 and apply f^{*}:

Refactor:

Now recall the definition of the Information Ratio:

Substitute in the definition of the information ratio:

Refactor:

Indeed, an optimally levered strategy’s growth rate is proportional to it’s Information Ratio (equivalent to a Sharpe Ratio with a zero risk-free-rate). Put differently, a high information ratio strategy not only has a high return per unit of risk, but can also be safely operated at a higher risk-level using leverage. High risk-return strategies deserve to be run hot.