# Mathematical proof of $g = \mu - \frac{\sigma^2}{2}$ relationship between CAGR and average returns

I found in a paper the relation between the CAGR and the arithmetic average of returns to be

$$g \sim \mu - \frac{\sigma^2}{2}$$

where g is the geometric average, $$\mu$$ the arithmetic average and $$\sigma^2$$ the variance of the returns. I cannot find any formal derivation of this relationship.