In reply to Anon9001.

I am not an expert in the distribution of stock and gold returns. I suggest you ask a financial modeler.

Mathematically, the distribution of returns when you "buy long" is semi-bounded. It is bounded below because the most you can lose is 100%. It is not bounded above because the share price has no upper limit.

If you hope to use the geometric distribution, you cannot use the returns because they can be negative. Convert the returns into proportions, which are always positive. For example, an annual return of -10% means that the new value of your investment is now 0.9 the value from the previous year.