Choosing Normal or Lognormal Models for Company Earnings

Summary

The document considers whether company earnings should be modeled with a normal or lognormal distribution, contrasting firms with potentially commodity-linked revenues against non-commodity businesses such as retailers. It notes that earnings can be negative, which is incompatible with a lognormal distribution if earnings themselves are modeled directly. The question also distinguishes revenue from earnings: commodity prices may be modeled as lognormal while largely fixed costs can still make profit negative on some paths.

The reply recommends examining earnings data and applying a Jarque–Bera normality test. This is a proposed diagnostic, not a reported analysis: no company data, test result, or comparison of alternative models is provided. The document therefore raises relevant distributional constraints but does not establish a universally suitable model. Its brief answer focuses on testing normality and does not explain how to model revenue, costs, or negative outcomes in a fuller simulation.

Key ideas

• A lognormal distribution cannot represent negative values when applied directly to earnings.
• Lognormal commodity revenue can still yield negative earnings when costs exceed revenue.
• The question distinguishes revenue modeling from earnings modeling, especially when costs are largely fixed.
• The reply suggests testing earnings data for normality with the Jarque–Bera test but reports no results.

Tags

# Should earnings be modelled normally or lognormally?


# Should earnings be modelled normally or lognormally?












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.

## Answer by phdstudent (score 1, accepted)

https://quant.stackexchange.com/a/18839

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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