I have programmed my own MC analysis in Excel and the results do not generally agree well with what I get from FC, which I am trying to use as a check on my methodology. One odd thing I notice about FC is that the MC results are serially correlated with one another. If you look at the right graph, showing how the portfolio would have ended up in each of the 205 runs, you can see clearly that successive results are highly correlated. In a true Monte Carlo simulation, this should not be the case.

What is going on here ?

That's because the methofology isn't changed when you substitute random data for historical data.

The monte carlo process in FIRECalc generates random numbers within the bounds you set and assigns them to each year being tested. Then FIRECalc uses the same methodology for survival testing as it uses on historical data. So result 1 is a sequence of year 1 - year 30, and result 2 is a sequence of year 2 - year 31, etc.

If you are looking for a true brute force monte carlo analysis, FIRECalc ain't it. The monte carlo option is just to let people substitute different rates of return and volatility while retaining the methodology, so they can investigate different investment classes.

(When FIRECalc was being developed, it was tested against a then-available web tool for monte carlo analysis. That tool ran 10,000 iterations using a given rate of return and volatility. Not surprisingly, the results approximated what FIRECalc was showing, when historical returns and volatility were entered.)

Sorry to say, that tool disappeared years ago. The remnants can be seen at http://web.archive.org/web/200302030...drawalSim.html. I haven't seen a tool as easy to use.

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Thanks for the reply Dory, I can now stop wondering why it doesn't agree with my "brute-force" excel method, in which I run 8000 iterations per year. I did find that Firecalc results were significantly worse than my method and it had me quite concerned.

I still don't understand what FC is doing though, can you give me a little more detail on how it generates its series ?

I also think that I have found a problem with the MC calculator.

If you put in a $1mm starting portfolio and take out 25000 per year for 40 years , with a 3.1% return and 3.1% inflation, with zero volatility, then you should end up with 0 in the portfolio at the end, this being a zero real return. In this case, FC returns -63,361, which I think is a significant difference from the expected 0.

See How about describing FIRECalc step by step? at http://firecalc.com/intro.php.

The effect you are seeing is because the money you withdrew on Jan 1, enough to get you through the year with enough to cover inflation for the year as well, does not contribute to the growth of the portfolio for that year. It is cash under your mattress.

If you were to pay all your expenses using a zero-interest credit card that you then paid off at the end of each year AFTER the portfolio growth had occurred, then your numbers would match up.

__________________
Often uninformed, seldom undecided.

Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. Mark Twain

I must disagree with you here Dory, in a zero real return environment with investment certainty (zero vol), then your annual wd's are simply principal divided by years.

In a world with no inflation and no return, it seems quite clear that we should be entitled 40 separate payments of 25000 per year in the example I gave you.

Thank you for your prompt replies and I will read the link you gave me.

I also found a pretty good Monte Carlo tool here :

http://www.effisols.com/

Unfortunately, the trial version is fairly worthless and the one that works costs $29, but I think it's worth it, it's a very nice tool.

macnjus, you might want to use the search button to take a look at some of the threads discussing how FIRECalc differs from traditional Monte Carlo tools. Note that Monte Carlo calculations largely ignore the correlation between asset classes, something many of us think is important. Here is one sample thread:

http://early-retirement.org/forums/i...6395#msg166395

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Thanks Wahoo. When I run my MC, I first put together a variance/covariance matrix to take correlations and volatilities of the various assets into account, using this, I generate an overall portfolio expected return and volatility and run the MC using these overall numbers. I agree that the correlations between asset classes are crucial and you shouldnt use MC without taking them into account.

How do you model correlations that change over the decades and volatility that rises/falls in magnitude?

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That obviously gets a lot more complicated, I simply assume constant correlation and vol, which certainly will not be the case. But we also know for certain that the future will not be like the past, so I think it helps a lot to look at both.

When you get to 100% success on the historicals, then I think it helps to look at some MC's to model situations where the returns are not like the past. For example, My "conservative" assumption right now is that stocks are priced to return in the 6.5% zone, which is well under historicals. I think historicals are overstating the likelihood of portfolio survival.

Why?

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Many many reasons why. For example, the existence of this board is one indication that many more people are aware of the power of investing in the stock market; I believe that the demand for stocks has gone up relative to the supply. Any time you increase demand in a market without increaing supply, the price goes up, and all else equal, when the price goes up the expected return goes down. John Hussman runs an interesting mutual fund and has posted some very good research on this topic on his web-site at this address :

www.hussman.net

You missed my point.

In the FIRECalc methodology, you take the withdrawal on Jan 1, and calculate returns on 12/31. The withdrawal you take has the inflation in it.

So year 1 has growth based on 975000, not 1 million.

The withdrawal includes the inflation for the year though, as described in the link I gave you.

So in a 40 year model in FIRECalc, you have inflation on 40 withdrawals, but the growth is based on a starting point of 39/40 of your starting amount.

__________________
Often uninformed, seldom undecided.

Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. Mark Twain

That makes sense, it's a timing issue. For example, a contiinuous withdrawal of the inflated amount each day over the course of the year would balance out.

Dory'll be glad to know that...

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Co-author (with my daughter) of “Raising Your Money-Savvy Family For Next Generation Financial Independence.”
Author of the book written on E-R.org: "The Military Guide to Financial Independence and Retirement."
I don't spend much time here— please send a PM.