Perfect Withdrawal Rates with normal and fat-tailed return distributions

Point of the Post

In this post I am taking a non-rigorous, non-exhaustive peek at what  happens to a perfect withdrawal rate (PWR) distribution when generated with either a normal or a fat-tailed return distribution where I have coerced the first and second moments to match.  The goal is mostly just to do it as a placeholder for something I want to try later...but also to see what happens visually to the PWR distribution as well as to get a first pass look at the scale of the effect on the 5th or 10th percentile PWR for quasi-reasonable but fake assumptions.


Background

I won't go into detail here. See these links for background:

• Revisiting Perfect Withdrawal Rates But with Variable Duration
• Putting an adaptive PWR up against changing longevity estimates
• Some PWR acknowledgements and comments
• Prelim. study of PWRs and stochastic longevity
• Perfect withdrawal rates, trend following, and stochastic longevity
• PWR v Kolmogorov v MC simulator
• Trend Following Can Enhance Withdrawal Rates - Part 4
• Trend Following Can Enhance Withdrawal Rates - Part 3
• Trend Following Can Enhance Withdrawal Rates - Part 2
• Trend Following Can Enhance Withdrawal Rates
• Perfect Withdrawal Rates and Asset Allocation

Assumptions 

PWR Iterations:  10,000

PWR Periods: 30

Mean and standard deviation for both normal and fat tailed distribution

  - r:    .0792

  - sd: .1411

Gaussian Mix Parameters

   - r1       .10   

   - sd1     .10

   - r2       -.03

   - sd2     .25

   - % r1   .83

Process

Returns - First, a fat tailed return distribution is created using a Gaussian mix process and the assumptions above. Then a normal distribution is generated through an R function using the mean and sd from the last sentence.  The two distributions match in the first two moments but obviously that's about it. I'll chart it out later.

PWRs - A PWR algorithm is run once with a normal return generating process and then again with a fat tailed generating process.  At the end the returns and PWRs are plotted and some summary stats are run on the two PWRs.

The Output

Returns

PWRs

Conclusions

Not only do the output data speak for themselves but we knew going in what was likely: spending might need to be more conservative in the presence of the possibility for fat tailed returns.  The 5th and 10th percentiles under these fake but not outrageous assumptions -- percentiles that can be viewed, with squinted eyes, as akin to fail rates i.e., where 5 or 10% of simulations had needed to have lower PWRs in order to end the 30 periods with zero capital -- are impinged by the presence of a fat tail, similar mean and standard deviation notwithstanding.  Since this is not a survey or a comprehensive review that is about all we can say.  As a retiree, I have to say that if these assumptions were to be realistic, a 5th percentile PWR move from a 4% to 3.6% is non-trivial to me. It can perhaps be viewed as something like one less trip a year with them when I already take too few as it is.  That's not just an academic "lifestyle" thing in a math-heavy paper, that's a real, hard cut into how I raise my kids and live with my family in real life.