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I am having difficulty deciding whether a company's earnings should be modelled normally or lognormally.

If we consider two arguments:

(i) The earnings of a company are the returns on the assets of the company, therefore we could model them as normally distributed.

(ii) However, in some industries, say if the company is a commodity producer, one could argue the earnings should be lognormally distributed (because the commodities are modelled this way)

What is the most correct way to model this? Say for a commodity producer but also for a non commodity producer (say retail)?

Edit: I fully understand that earnings can be negative therefore one would naturally assume a normal distribution. However, for a commodity producer the revenue will be dependent on a commodity. In a lognormal simulation there will be paths where revenue less costs is negative (there will be both fixed and variable operating costs). In other words there could be negative earnings paths if revenue is modelled lognormally.

Edit 2: Strictly speaking, I am modelling the revenue of a company with the costs being largely fixed.

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    $\begingroup$ you should ask yourself "can earnings be negative?" $\endgroup$ – AFK Jul 12 '15 at 11:10
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Well, log-normality does not allow you to have negative earnings and companies do have negative earnings. I suggest you to download the earnings data and perform a Jarque-Bera test for normality.

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    $\begingroup$ Just to add more information, strictly I am modelling the revenue of a commodity producer, the revenue will be dependent on a lognormal distribution (commodity price). In some simulated paths, the revenue less costs will still be negative if revenue (dependent on commodity prices) is modelled lognormally. In other words, it is possible to get negative earnings in both normal and lognormal cases in this situation $\endgroup$ – Zakoff Jul 12 '15 at 12:36
  • $\begingroup$ Well, then is not clear to me. If you are modelling prices already why do you need to model earnings? Shouldn't you model costs and from that get earnings? $\endgroup$ – phdstudent Jul 12 '15 at 13:00

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