# Average of a financial ratio: which average

A financial ratio, like e.g., return on equity (ROE) is a division of two numbers ROE=return/equity.

If I analyse a whole sector then one can compute the ROE for each company in that sector and thus the distribution of ROE for that sector.

If I want to 'summarise' the distribution then I have the choice (ao) to (1) take the average of all ROE or (2) take (sum of all returns) / (sum of all equities).

Which one is preferable?

It depends on what you are interested in. Assume that only two companies are in your sample and the ROE is defined as

$ROE = \frac{Icome}{Equity}$

Company 1 has an ROE of 10 and company 2 has an ROE of 0.0001:

$ROE_1 = \frac{1}{0.1} = 10$

$ROE_2 = \frac{1}{10000} = 0.0001$

Your second suggestion implies that the mean ROE is

$\overline{ROE} = \frac{2}{10000.1} = 0.0002$

This would be the appropriate number if you needed to calculate the return on equity of a whole sector and you want to compare it to another sector. But the statistic would hide the fact that there are very profitable companies in your sector and maybe one badly managed company with huge equity dominates the mean. Or put differently, there would be no variance within a sector. If you have several sectors and each sector contains several companies I would actually use both statistics that you suggested.

@HOSS_JFL, thanks a lot, this makes things clearer to me, do I get it right if I say that $\overline{ROE}$ as you defined it above is more like a ratio at an aggregated (sectoral) level ?

If this is the case than could I not have 'trouble' with some ratios like e.g. profit margin = $\frac{profit}{turnover}$, because in that case, summing all the turnovers of the companies in one sector may have ''double countings'': if a company sells to another company in the same sector, then the sales of the first one are counted in the turnover of the first company, but also in the turnover of the second company ?

• You are right on my definition of $\overline{ROE}$. You are also making a good point on the profit margin. It makes the calculation very complex. I think that a goldmine does not sell to other goldmines and Amazon does not sell to other retailers. So in these sectors the turnovers are "disjoint". If there are many overlappings you would need to find the sector-based origin of the turnovers in the sense of an adjacency matrix or a transition matrix. Jul 27, 2015 at 10:34
• @HOSS_JFL, thanks again. I was even thinking about another thing that might happen; it has to do with Simpson's paradox. If I compute the 'aggregated' ratio for two sectors s1 and s2, and then I do the same but separating both sectors into 'small' and 'large companies', then it might be that the ratio $\overline{ROE}$ in s1 is smaller than the one in s2 for each of the subgroups (small and large), while without distinguishing 'large' and 'small' the ratio is large in sector s1 than for s2 ?
– user83346
Jul 27, 2015 at 12:35