Validating the T-distribution for use in my retirement blog

In the last post I mentioned that I saw in a Sanjiv Das paper that he used the T-distribution to model returns. This had intuitive appeal because it forces fat tails and is easy to code. This is easier than trying to figure out how to parameterize a gaussian mix or a chaos hit on net wealth. For those I need to figure out how to do them every time I fire up my R-console..again.  (t) has the disadvantage of being too symmetrical in the tails where the S&P, say, has mostly a fat left tail and it's fatter in monthly series than annual.  But I liked the hassle free nature of using a simple random t function. The only question was "does it matter enough?"

To answer than I turned to a "perfect withdrawal rate" analysis first offered by Suarez and Suarez to test it. PWR is the constant spend that with perfect foresight (and in this case no bequest) will spend a portfolio to zero at the end of the horizon. That PWR thing is run a bunch of times and then the distribution of spend rates that might fall out of all the alternative futures is examined to see what we can find out about spending given the other assumptions.

For this post:

• 50,000 iterations
• 50 years, fixed horizon (long but we are early retirees)
• 4% real return
• 12% standard dev (kinda like a balanced portfolio)
• degrees of freedom = 5 for T-dist like in the Das paper

The output from this for: 1) standard normal, and 2) t-dist looks like this

The asterisk is because the t-dist kicks out some negative spend rates, something I don't quite get so I forced it to zero. The n/a is because the fat right tail kicks out some absurd and extreme values, something else I don't quite get. The other stats are what they are and are relatively arbitrary in terms of how we see the underlying distribution.  

Thoughts

• Meh. 
• The fat right tail I think is a little weird. 
• The negative spend rates are weird but maybe I don't really know what I'm doing.
• The mean and median are a little higher for something where we are trying to force bad outcomes like we see in real markets
• The 5th and 20th percentiles are a little lower which I guess are the right outcomes but if I knew how to do something like confidence intervals the differences would probably end up being meaningless
• The different placements of a 3% spend in the distributions, a reasonable rate I think for a 50 year horizon, is too trivial to even mention 

In sum, I don't think this moves the needle enough for me and adds some weirdness to the extent that a normal distribution is probably fine if we caveat its use sufficiently. Alternatively, I would go back to using a gaussian mix for returns (but one has to figure out the mix) or using some kind of chaos on a net wealth process -- which at least has the grace of assuming the hit can be from spending as well as returns which means I like it the best.  It's just that it takes a bunch of time to remember what to do where a random normal var in R takes about a millisecond. So,

T-distribution? Out. 

References