Another look at the effects of time on terminal wealth in presence of volatility

I did this before a few weeks ago here.  This is the same thing with a different view. Most of the text is the same but with a different, integrated chart.

The following are mass functions from simulated, empirical frequency distributions (3000 iterations) of terminal wealth after 10 periods under two scenarios:

1. Normally distributed returns with mean = .09 and standard dev = .25 (high risk)

2. Normally distributed returns: (50%) r=.08, sd=.18, (50%) r=.035, sd=.04 (diversified)

This is a little apples and oranges, and the "normal" assumption for returns is for ease of analysis, but I wanted to see the breadth of the distributions vs the modes and try to get a general intuitive sense of likelihood related to "positive" outcomes, however that may be defined. The risk free rate of 3% (arbitrary) is the grey area. Y axis is mass, X is the terminal wealth bins. Note that there is no consumption and there are no fees, taxes, inflation, etc.  I'm just running this out for fun.

Conclusion? Multiplicative, non-ergodic, high vol processes can create vast wealth but otherwise looks like a killer if one were to happen to desire to focus on one's specific goals rather than max wealth.  Note that median terminal wealth is a fair representation of expected geometric returns over time. The mode is instructive, too, though. Take a look at where the mode goes under the two regimes. If I am going to take risk and I have a specific goal at or near t=10+, my attitude towards risk will likely be tempered a bit.