# CAGR, log of negative numbers

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

• Compute the logarithm of their absolute value, and then put a minus in front of it. Theoretically, logarithms of negative quantities do exist, but I highly doubt that's what you're supposed to do in such cases. Commented Feb 9, 2014 at 18:38
• No, it doesn't make sense. Commented Feb 9, 2014 at 18:42
• This seems to indicate that the geometric mean is not the adequate tool in the first place. Commented Feb 9, 2014 at 18:47
• As an aside, even if the EPS were positive, computing a mean without regard to the underlying share price might be misleading. Commented Feb 9, 2014 at 18:50

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).