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Probability density function?

Posted: Sun Apr 01, 2018 1:38 pm
by ethan
Dear FRP,

First, YOU ROCK. I have been using FRP over the last couple weeks and just made a donation. This is an awesome tool.

I am interested in your model that predicts returns and how it might be made more accurate. There are well-known weaknesses with using a normal distribution to model stock market returns. I recently discovered this article, and while I am not a finance guy I am a quantitative guy, and it reads sensibly and well: ... ch-laplace

I see from your shared source that you use a normal distribution with the mean and SD I choose. I would love to see (and would be willing to contribute effort to!) a version that supports a choice of probability density functions. I'm not so great a Java but I believe all it would need is a switch on one line in the calc and a little bit of interface tweaking to support the choice. If laplace isn't built into base it's in plenty of good libraries...

Many thanks and many more-


Re: Probability density function?

Posted: Mon Apr 02, 2018 9:03 am
by jimr
When I first was developing the planner, I experimented with some alternatives to the normal distribution and found that the difference in results was trivially small compared to the impact of changing the mean return by just a dozen or two basis points.

I concluded that it wasn't worthwhile to add extra complexity that would likely slow down the simulation's inner most loop. In my opinion, our estimates of future mean and SD (or any other distribution's parameters) are of such low confidence that we can't really add any precision here. It's sort of like trying to take a measurement in micrometers using a yard stick.

That said, if you'd like to experiment with this yourself, there's an early excel version of the planner with full source code (in excel/visual basic) posted here: ... nal-tools/ (look for Portfolio withdrawal simulation)

This isn't as full-featured as the java planner, but if you're comfortable with Visual Basic, it'd give a good foundation for experimenting with alternative distributions.

Re: Probability density function?

Posted: Mon Apr 02, 2018 6:05 pm
by ethan
Thanks Jim!

Fair observation. It would take some serious effort to determine with high confidence the expected impact of changing the function...if the not-so-rare larger events cancel each other out, it might not matter all that much. If it shifts a plan from 95% probability of success to 94, then...... it's just two crystal balls vying for top spot :-)

Thanks for the link to source. I doubt I'm the one to do the modeling, but you never know when I'll be bored...


Re: Probability density function?

Posted: Mon Apr 02, 2018 6:26 pm
by jimr
To model those not so rare larger events, you can bypass the regular portfolio return function and use additional inputs to 'inject' one-time shocks into the simulation.

To do this, create 'Portfolio Return' entries in the upper table of additional inputs with the start age and end age set the same, the standard deviation set to 0, and the return set to a negative value to represent the size of the crash you'd like to inject in that year.

This could be extended to set up a 5-year bad luck sequence of returns that starts in the first year of retirement.

It's actually not a bad way to stress test a plan. As always, be sure take a look at the results in the detailed view table to make sure the simulation did what you expected it to do.