macrocephalopod

Well, you're clearly making some assumptions on the (1+R) noise multiplier with geomean=1. If it's highly volatile noise, you could get rich as as fast as Rentech did with Medallion. And it's just random noise!

Yes I'm assuming it's similar to real-world stocks. If you took Bitcoin with 100% annualized vol you would only have a Sharpe of 0.5 so you need to compound for 16 years to be 95% sure of profit. For a stock with 50% vol you need to compound for 64 years to be 95% sure.

Shannon's original example used 50% vol for each period -- if we assume that a period is one day, the asset in his example would be 8x more volatile than Bitcoin (!)

More volatility is easy to find. It just requires leverage.

I see, so you will increase leverage to get the desired volatility, and then decrease leverage to get the desired returns?

why would you decrease leverage to get the desired returns?

The whole point of “volatility pumping” is that an asset with zero geometric return can be made to have positive geometric return if you reduce the leverage. My claim is that you can’t find assets with high enough volatility for that to be interesting in practice.

That is a very simplistic view of what vol pumping is. Vol pumping isn't abut an asset with zero geo return, its just the most eye catching type. There are plenty of articles on vol pumping where cash isn't involved, and the "pumping" is just between a bunch of risky assets.