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

  • 1
    $\begingroup$ 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. $\endgroup$
    – Lucian
    Commented Feb 9, 2014 at 18:38
  • $\begingroup$ No, it doesn't make sense. $\endgroup$
    – copper.hat
    Commented Feb 9, 2014 at 18:42
  • $\begingroup$ This seems to indicate that the geometric mean is not the adequate tool in the first place. $\endgroup$ Commented Feb 9, 2014 at 18:47
  • $\begingroup$ As an aside, even if the EPS were positive, computing a mean without regard to the underlying share price might be misleading. $\endgroup$
    – copper.hat
    Commented Feb 9, 2014 at 18:50

1 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).

  • $\begingroup$ I am guessing the OP is referring not to growth, but to actual losses instead, which may be negative. $\endgroup$
    – copper.hat
    Commented Feb 9, 2014 at 18:53
  • $\begingroup$ @copper.hat Thats exactly why I am trying to get the Geo mean, it would be a uniform comparison for the companies, how has the company been performing over time. $\endgroup$
    – Avagut
    Commented Feb 9, 2014 at 19:14
  • $\begingroup$ Take for instance a company has the following annual eps values: 2009: -8.85 2010: 4.41 2011: 7.66 What is the Geometric mean of the 3 values? $\endgroup$
    – Avagut
    Commented Feb 9, 2014 at 19:15
  • $\begingroup$ Hagen von Eitzen got it exactly right. -8.85% loss is multiplication by (100-8.85)/100, or 0.9115. $\endgroup$
    – philwalk
    Commented Sep 8, 2019 at 21:22

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