Nov 7, 2018

A visualization of multiplicative return generation, terminal wealth and risk over 10 periods

I was doing this exercise for something personal but thought I'd share, assuming I have it right.  The following are frequency distributions (3000 iterations) of terminal wealth after 10 periods under two regimes:

1. Normally distributed returns (sorry) 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 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 red dashed line. Y axis is frequency, X is the terminal wealth bins. The overflow bins on top chart are designed to put the X on the same scale in both (otherwise chart 1 is a log-normalish distribution). Note that there is no consumption and there are no fees, taxes, inflation, etc.  Just running it out. 


Conclusion? Chart 1 looks like an expensive exercise in lottery-like thinking if you happen to have any goals you want to achieve at year 10...despite it's higher mean expected return. Multiplicative, non-ergodic processes can create vast wealth but otherwise look like a killer for an otherwise modest retiree.


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