Monte Carlo Predictions ... what returns does one use?
motivated by a discussion on the WebRingForum

Here's how one might use the Monte Carlo ritual:

  1. We put a bunch of annual returns into a hat.
  2. We start with some portfolio, say $1M, and assume an annual withdrawal of, say 5% of this. example: $50K.
  3. We pick an annual return from the hat and apply it to our portfolio.
  4. Each year we increase the withdrawal by some inflation, say 3%, and withdraw from our portfolio.
  5. We repeat steps 3 and 4 for, say 25 years, and see if the portfolio has survived.
  6. We then repeat steps 2, 3, 4 and 5 a jillion times (that's Monte Carlo, eh?) to see what fraction of the portfolios failed to survive.
>Yeah, so?
So we're withdrawing yearly and using annual returns.
Aah, but suppose we put monthly returns into our hat and apply them to our portoflio.
We'll still withdraw every year (that is, after 12 months) and we'll still increase this annual withdrawal by annual inflation.

>Yeah, so?
So, would you expect to get the same survival rates?

>Uh ... I have no idea. Where do you get the stuff in the hat?
We could download annual prices or monthly prices for some stock and stick 'em in the hat. Then we could ...

>You've already done this, right?
Yes, using GE stock prices over the past twenty years. That's 25 annual returns or 300 monthly returns to stick in our hat.
What's interesting is that the failure rates can be quite different!
For our GE example, using a 5% withdrawal rate and 3% annual inflation and 10,000 Monte Carlo iterations, I got failure rates of ...

>Don't tell me! They're almost the same, right?
I got 9.3% and 4.7%.

>Which is which?
Note, however, that if you use annual returns you'd miss the October, 1987 crash.

>Okay, what about a portfolio with 60% stocks and 40% bonds and what about 30 or 40 years, instead of 25, and what about ...?

There's a spreadsheet to play with. It looks like this:

You can see the difference (if any) between using returns by "Years" or by "Months" ... assuming some single-stock portfolio.