Feb 18, 2018

Probability distribution of a net wealth process over 20 periods

A RH recurring theme: I wanna see what "it" looks like.

Today's look-see: probability distribution of a net wealth process over N periods

In this case I am doing a very abstracted or stylized process where wealth is in wealth units (e.g., $1M/$40k = 25 units, which in fact are the units we start with here) and the spend is a constant spend of 1 unit  so

Wt =  mWt-1 - 1.  

Return m in this case was an arbitrary 2% real net return with a 10% standard deviation (I call two percent "arbitrary" but I just read a paper where some semi-reputable ret-fin guy made a case that an expectation greater than 2% real over forthcoming years starting in 2018 might be more unreasonable than not. The 10% std dev I just made up. We'll go with these assumptions for now because it makes an interesting illustration[1]).  Start age is irrelevant because we are looking at the net wealth process which is independent of longevity.  Given the process for Wt ,  I simulated it over 20 periods (actually more than that but 20 makes the charting easier) 4000 times. Off of that sim I created an empirical density from the frequency distribution of wealth in any period t. The chart looks, without comment, like this:





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[1] Note that I am ignoring any discussion of or interpretation of or adjustments for the concept of negative wealth. That's because I am either lazy or confused or both.  In the past I have described it as proxy for fail magnitude or a proxy for claims made on family or society or maybe it is some type of factor related to the opportunity cost of foregone wealth from too much spending.   That's a grab bag of ideas...tbd.


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