Understanding Monte Carlo Simulation

[Onward]

This is an interesting, seven-part introduction to Monte Carlo simulation and the effect of variable returns on portfolio performance and survival.

He's written only the first five parts. The last two are still to come.

He occasionally mentions Weathcare, which seems to be a money-mgt service he offers. It doesn't intrude much on the content of the articles, though.

Atlanta, GA Fee Only Wealth Management Investments and Financial Planning - Blog - Understanding Monte Carlo Simulation - Part 1 of*7

 

[ronocnikral]

thanks for sharing. i perused and plan to read in depth later.

i was hoping for more of a detailed technical discussion about how to run stochastic models for personal finance. as someone who uses stochastic modeling in their joe j*b (geostatistics), I would be highly skeptical of someone being capable to properly to do this modeling. it's more complex than many lead to believe...

 

[NW-Bound]

I just gave this article a quick glance. It may be an OK introduction to the topic of financial modeling, but I think there are better ones out there.

Look at Table 5. I suppose the author is trying to demonstrate that a portfolio with a lower standard deviation may be a worse choice than one with a higher standard deviation if their returns are poorly distributed (and different from each other!), and if one is unlucky to start out with a bad year. This is somewhat along the "Black Swan" theme, but the made-up strings of year-to-year returns are so contrived they look terrible.

Is the author trying to tell the reader that his service would prevent his clients from such a terrible "Black Swan"? If so, I do not see how one can construct Portfolio A and B such that they are so much out-of-synch with each other, meaning in Year 30 one would have a return of -35% while the other one is at +25%?

In order to convince ourselves that starting one's retirement right at the beginning of a string of bad years is really SOL, we do not need to use contrived numbers, but to use real past market histories. FIRECalc and the e-book by Otar that was mentioned in a concurrent thread demonstrate that a lot better and more convincingly.

The e-book by Otar also discusses how Monte Carlo simulations that assume a Gaussian distribution of market return does not portray the tendency of the market to give a string of several bad market yearly returns in series, something that statisticians call a "fat tail". Otar's e-book is highly recommended.

 

[Onward]

I haven't read Otar's book, but it's in my queue. I still have a lot of questions about Monte Carlo, particularly about how the data is created and combined.

 

[ronocnikral]

I haven't read Otar's book, but it's in my queue. I still have a lot of questions about Monte Carlo, particularly about how the data is created and combined.

combining the data is rather straightforward. the formulas are the formulas, and people rarely argue about the algorithms you are putting the "data" through.

as nw pointed out, the issue is in "creating" the data (or as I say, defining the assumptions). defining the ranges of the assumptions and the distributions are what people will argue about. then you start to run into issues with the central limit theorem depending on if you are multiplying or adding...

imo opinion, it's very difficult to be accurate with stochastic modeling. my company, which employs many people to exclusively run stochastic modeling, and pays them very well, have only hit their 80% confidence interval less than 50% of the time over the last decade. not sure how the finance industry is in running this modeling...

 

[haha]

not sure how the finance industry is in running this modeling...

Sales tool. Like the oldtime flip chart.

Ha

 

[cho oyu]

The e-book by Otar also discusses how Monte Carlo simulations that assume a Gaussian distribution of market return does not portray the tendency of the market to give a string of several bad market yearly returns in series, something that statisticians call a "fat tail". Otar's e-book is highly recommended.

I'm not sure how well Otar or the first link cover terminology, but it sounds like they might be mixing things up?

A gaussian distribution looks somewhat like a hill - the center of the distribution is the arithmetic mean of the expectation function and both sides of the hill taper off symmetrically and relatively quickly. This means that results very far away from the mean aren't too likely to happen (e.g. for investing, 50% gains or losses in a year). A fat (or heavy) tailed distribution indicates that events far from the mean will be more common; it doesn't say anything about whether they will be correlated, however. A heavy-tailed distribution is a better model for real financial systems.

A string of several good or bad years in a row, or temporal autocorrelation, is independent of the expectation distribution function. Monte Carlo simulations, in their pure form, look at every new cycle (e.g. every year) as being independent. Last year has no effect on this year which has no effect on the next year; all of the results are random. However, it's pretty clear in real life that what happened last year does affect this year to some extent. So adding in a weighting function that simulates this correlation also can help improve results.

 

[NW-Bound]

Yes, you are correct! It is actually my careless posting that mixes up the non-Gaussian distribution with the temporal correlation of the sequential yearly returns.

So, let me rephrase that. It is well known that the market return distribution has a fat-tail and cannot be simply modeled as a Gaussian distribution. Otar discusses how other people can tweak the distribution to make it look more like "real life", but his point was that one can just play back past histories, like FIRECalc does.

Regarding the temporal correlation, I have not seen anyone address that in a Monte Carlo simulation.

PS. If anyone has seen a plot of the autocorrelation curve of the historical market return, please provide a link. It is likely someone has done it, but I myself have not seen it.

 

[Nords]

So, let me rephrase that. It is well known that the market return distribution has a fat-tail and cannot be simply modeled as a Gaussian distribution.

Eh, now it's well known after the last few years! Before then I think an entire generation of financial advisers made many boat payments by using vocabulary like "positively skewed kurtosis"...

Monte Carlo simulations, in their pure form, look at every new cycle (e.g. every year) as being independent. Last year has no effect on this year which has no effect on the next year; all of the results are random. However, it's pretty clear in real life that what happened last year does affect this year to some extent. So adding in a weighting function that simulates this correlation also can help improve results.

Regarding the temporal correlation, I have not seen anyone address that in a Monte Carlo simulation.
PS. If anyone has seen a plot of the autocorrelation curve of the historical market return, please provide a link. It is likely someone has done it, but I myself have not seen it.

Raddr's board is kinda tough to search for threads & posts, but IIRC a few years back there was a discussion of attempting a Monte Carlo simulator that included "persistence" between one year's returns and the next.

Enhanced Monte Carlo Simulation

Raddr's Early Retirement and Financial Strategy Board :: View topic - Shortfall risk in retirement- rates and allocation (I think it's safe to just skip over Rodmail's contributions to the thread)

The consensus seems to be that there's not many 50-year conclusions which can be beaten out of only 130 years of data.

 

[Archman]

This is an interesting, seven-part introduction to Monte Carlo simulation and the effect of variable returns on portfolio performance and survival.

He's written only the first five parts. The last two are still to come.

Understanding Monte Carlo Simulation - Part 1 of*7

Parts 5 and 6 are available.

 

[Nords]

And... the conclusion (part 7) is up.

Atlanta, GA Fee Only Wealth Management Investments and Financial Planning - Blog - Understanding Monte Carlo Simulation - Part 7 of*7