In Finance, and in option pricing in particular, compounding arithmetic average rates of return gives us the wrong result for holding$-$period$-$return $($HPR$)$ over time.

Assume you have calculated monthly average returns for Google over the past $60$ months and the simple arithmetic average monthly return was $1\mathrm{.}120\%.$ The monthly standard deviation around this mean return of $1\mathrm{.}120\%$ was $10\mathrm{.}80\%/$month $($hint: no need to annualize $-$ keep everything monthly$).$

Using the formula learned in class $($ch$.14$ slides$),$ what is the monthly rate of return, also know as the geometric average rate of return?