Simulating Ending Wealth from Mean and Volatility Assumptions

Summary

The document asks how to model the distribution of ending wealth from a starting investment when an asset’s arithmetic mean return and standard deviation are known. It suggests running repeated simulations in a spreadsheet and plotting their cumulative distribution, with separate runs for different holding periods.

The response points to an external example and says a formula can generate simulations, but the formula and screenshots are absent from the supplied text. It therefore does not specify the return model, how to translate arithmetic return parameters into a wealth distribution, or whether returns are independent and identically distributed. The question’s assumption that wealth is lognormally distributed is not examined. The exchange gives a general simulation workflow, but not enough detail to reproduce it or assess the resulting distributions.

Key ideas

• Repeated simulations can be used to estimate a distribution of ending wealth.
• The simulated outcomes can be plotted as a cumulative distribution.
• The supplied text omits the formula and does not explain the return assumptions needed to build the simulation.

Tags

# Generating wealth distribution from return parameters (mean, SD)


# Generating wealth distribution from return parameters (mean, SD)












Super basic question here!

Suppose I start with $100 and invest in an asset with known mean (arithmetic) return and standard deviation of returns.

I'm interested in plotting the distribution of my ending wealth over varying time frames in Excel. My understanding is that the distribution will be lognormal. For example, I'd get one distribution for a 1-year holding period and another distribution for a 20-year holding period.

What would be the right way to set this up in Excel?

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/77308

Very easily. See screenshots below:

This is the only formula you need:

You can do as many simulations you want and then just plot the cumulative distribution.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.