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Log-normal Distributions for Returns

Hi Folks,

Log-normal distributions are very common in quant finance. They're used as many believe they more closely model stock behavior than other distributions. Some folks have asked how to take log prices and I realized we didn't have any materials on that. I decided to write a quick example notebook showing how to take log returns, and threw in some log-normality testing while we're in there.

The notebook includes a computation to check what percentage of your universe is log-normally distributed at any point in time.

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1 response

It may be obvious maths, but worth pointing out that log returns are just the difference in consecutive log prices.

At an intuitive level, log returns make sense. Prices represent a NPV of a future dividend stream, so changes to the growth rate or the discount rate in the NPV calculation will have an exponential effect on price. However, changes to the near term prospects of the company, such as reduced profitablility due to margin pressure from competition, have only a linear effect on the NPV calculation, which is a sub-exponential effect, clearly. I believe this causes the pronounced peak in the observed distribution of log returns.