# CAGR VS Geometric Mean in real world

Dear all,

Analyzing the 2019 annual statements from a company I found that they have calculated their own ROE as well their average last 5 years ROE, which I find very useful. However, having a closer look to their figures I found that something didn’t quite match.

This is what they have in their statement:

Year: Return on Equity (ROE)
2015: 6.3%
2016: 7.3%
2017: 7.8%
2018: 8.4%
2019: 9.2%
Annual average 2015-19 (%): 9.8%

If you calculate the Geometric mean of these 5 values, you end up with an average rate of 7.8%. Quite different to the 9.8% that they say.

I wrote them to understand how they calculate this figure, and it looks like the use the CAGR between 2019 and 2015 and 4 periods to do it. So (9.2/6.3)^(1/4) = 9.9%

Which confused me a lot. After some researches I saw that the CAGR is usually used to compute the compound annual growth rate when you have a set of values, not percentages.

Shouldn’t the company use a geometric mean considering the 5 periods instead of CAGR with 4 periods? Or at least use the CAGR considering the 5 periods? Am I understanding it wrong?