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Mathematica, What Is The Area For Circle Of Competence?

|Includes: Vanguard Mid Cap ETF (VO)

One of our core corporate enterprise business value ethics here at Joe Springer is to have an immeasurable circle of competence - not infinite, but always expanding.

So when erudite commenter JasonC suggested Mathematica to check our retirement strategy we said - "let's learn this thing."

Is that really what happened?

No, we actually sent out a tweet hoping someone would do it for us.

Alas, that has not worked, so we looked up Mathematica, saw that it is free to download a trial of the software, which you can do here, and we are off and running.

Mathematica is installed, and after Googling some free info and diving in we have run our first ever function:

We will use the comments here to track our progress...install and learn with us (and get ahead of us and teach us!)!


First got to figure out what we're trying to model. What we need is sort of out there, this gets close but annoyingly does not give full control of all the variables. No matter, we were able to model 3.5% real return with annual $60,000 payouts:

As you can see, there is about a 20% chance that retirees will either fall short of their 95th birthday by more than a decade, or become richer than when they retired.

This is helpful, some commenters suggested rebalancing which we initially resisted, but it seems that we can trade some upside for an initial extra year or two position in liquid CDs. If the market goes up in the beginning, great, lock some in, we are not trying to get rich, just not die poor. If it sinks then the cash can be put to use...


We are proud of ourselves - Jason C said:

The right way to test the proposed system is the following.

Use the past 10 years of daily total returns from the VO fund to create a distribution. Randomly draw 252 returns from that distribution and multiply them together to get an annual return. Do this over and over to create a distribution of annual returns to expect from VO. Basically we are creating a larger bootstrap sample using the assumption that the returns are not serially correlated (plus or minus), which is close enough for government work - we are not using any assumption that they are lognormally distributed etc...

We (think we) have accomplished compiling "the past 10 years of daily total returns from the VO fund":

Now to "Randomly draw 252 returns from that distribution and multiply them together to get an annual return," hmmmm...


Random drawing, we are starting to like this:

Update: We have been having the darndest time pulling just the daily change data out and leaving the dates in, but we had a small victory in plotting all the data, and we needed it, there is not sufficiently foul enough language for coding frustrations:

Update: We are flustered, but we have a plan:



You may question my methods, but look at this:

"Sorority Simulator" got 8 views in 16 minutes, "S&P 500 Historical Data" got 1 view in 42 minutes. Clockwork.


Ask and ye shall receive! We got a brilliant answer to our forum question, and JasonC posted help as well, love the internet!