CAGR, log of negative numbers

Question

I am trying to calculate the Compound Annual Growth Rate (CAGR) of a number of companies using the Geometric mean of the annual growth of their EPS.
Some of the EPS values are negative(loss making) and therefore the growth is negative and I cant get a log value for them.
Is there a way to calculate the Geometric mean when some of the values(in this case the growth values) are negative?
I am using natural log and exp functions in a MS Access database with a shaky understanding of the math behind it. Any assistance is appreciated

Answer 1

Why would you take the geometric (as opposed to e.g. arithmetic) mean in the first place? Because growth is multiplication with a factor, not adding an amount! However, if the growth is $+5\%$ then you actually multiply with $1.05$ and if the growth is $-5\%$ (i.e. in fact loss) then you actually multiply with $0.95$. You should try to take the geometric mean of these numbers $1+\frac p{100}$ in place of $p\%$. Is this a realistic suggestion? Yes! Assume agrowth of $20\%$ in one year and of $-10\%$ in the second year. That is, the development is $1000\$\to1200\$\to 1080\$ $. The geometric mean of $1.2$ and $0.9$ is $\approx 1.03923$, corresponding to $3.923\%$. And indeed, two years in sequence with a growth of $3.923\%$ would mean $1000\$\to 1039.23\$\to1080\$$ (within rounding error).