Investment Allocation Complexity

It gets complicated fast

For about three weeks now, we have looked at the implications of investing in stocks, bitcoin, and gold. Those are three interesting investments but there are a lot of other investments out there we can still add to a portfolio. However, there is one particular challenge that is worth mentioning - computational complexity.

For example, when you are looking at potential combinations of stocks and bitcoin, you are looking at 101 potential portfolio allocations if you round your percentages to whole values (e.g. 73% and 27% not 73.452% and 26.548%). If you want to analyze every 1% interval after adding a third investment to the analysis, the number of possible portfolios suddenly increases to 5,151!

It gets worse the more investments you add:

This allocation problem spirals out of control pretty quickly. By the time you get to eight investments you have about four times as many options as their are people on Earth. Imagine trying to pick out the best option from a population like that?

Jumping up to over 200 investments, you are looking at more portfolio allocations than the estimated number of atoms in the universe. Now, I don’t know exactly how a bunch of scientists made an estimate for atoms in the universe. I’m going to venture a guess that there is some imprecision in that number. But, the point is that you can’t readily analyze all those investment options one-by-one in Excel (no matter how many summer interns you have to give busy work to).

Fortunately, many mathematicians are pretty lazy, so as soon as they have to start crunching a big routine calculation they usually start looking for alternative solutions to a problem. Believe it or not, there are some really good ways around these big messy portfolio allocation numbers. But, first, we need to talk about some more investments out there besides stocks, bitcoin, and gold.