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# The Sum of Log Normal Distributions

The Skinny On Options Math

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options before deciding to invest in options.

If underlyings evolve as geometric Brownian motions, and so have log-normally distributed future values, what is the distribution for a portfolio consisting of various underlyings? While this is something that we could compute, the sum of long-normally distributed random variables remains an area of active research.

Today, Tom Sosnoff and Tony Battista are joined by Jacob Perlman as Jacob explains the math behind these calculations. Jacob also explains that instead of the lengthy calculations, you could use the Central Limit Theorem but this is based on approximately normal distribution. The problem here is that this ignores tail risk.

After all is said and done, Jacob explains how you can use all of these mathematical models together. Stay small and define your risk. By sticking to these two tenets, you are able to use the Central Limit Theorem to approximate your returns and avoid tail risks by keeping your size in check!