macrocephalopod

Your tweet clearly implied that in order to make money there has to be some predictable behavior like mean reversion (or trend, presumably). But that's not true - a stock that wanders aimlessly with NOISE with a geomean multiplier of 1, so it goes nowhere - could make you rich.

I agree with that!* I have never disagreed with it! I didn't bring up shannon's demon -- I only pointed out that it doesn't work on price series that have zero arithmetic return (which is true of the price series I was using).

The * is there because this only works in theory (in reality transaction and financing costs would eat all your pnl) and only for certain definitions of "very rich" -- in practice you would need to compound for dozens of years to become rich, even if you had no txn costs.

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?