Overbetting to Twice Kelly

Under the small-edge approximation $G(f)\approx \mu f-\tfrac12\sigma^2 f^2$ for the expected log-growth of a repeated bet, the growth-optimal fraction is $f^*=\mu/\sigma^2$. At what (nonzero) betting fraction does the expected log-growth fall back to zero, and what does this say about the symmetry of growth around $f^*$?