Monte Carlo Simulation

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HappyJack
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Monte Carlo Simulation

Post by HappyJack » Sat Jun 08, 2019 3:14 pm

I recognize that a Monte Carlo simulation looks backward, and that can be no guarantee of future results. However, if I have entered in all the correct information regarding my assets and my intended withdrawals, is this a reasonably accurate tool to use for planning. Any other vehicles that people like. Thank you.

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patrick013
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Re: Monte Carlo Simulation

Post by patrick013 » Sat Jun 08, 2019 5:50 pm

MC does the job of measuring the probability or likelihood of a certain return or event being realized. All of the probabilities used are from prior observations so future results can vary.

Also estimates are based on the current estimates of the program's user.

Portfolio managers can use MC to examine the possibilities of various portfolio strategies and estimates and statistics. The numerous simulations performed are supposed to give evidence of a percentage of future expected combinations of events those results are investment success.
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Re: Monte Carlo Simulation

Post by Tyler Aspect » Tue Jun 11, 2019 2:19 am

"Early Retirement Now" web site hosts a google spread sheet based retirement calculator. It appeared to be quite flexible.
Past result does not predict future performance. Mentioned investments may lose money. Contents are presented "AS IS" and any implied suitability for a particular purpose are disclaimed.

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Re: Monte Carlo Simulation

Post by gd » Tue Jun 11, 2019 6:12 am

As I understand the term, Monte Carlo simulations use statistics of past behavior to provide estimates of future ranges. Given that financial markets are unlikely to be well-behaved statistical processes, I find MC unconvincing. I've no hard reason to think firecalc-style application of past market patterns will be any more accurate, but given sufficient patterns I find that approach the more appealing choice of the coin flip.

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Re: Monte Carlo Simulation

Post by Seasonal » Tue Jun 11, 2019 6:26 am

HappyJack wrote:
Sat Jun 08, 2019 3:14 pm
I recognize that a Monte Carlo simulation looks backward, and that can be no guarantee of future results. However, if I have entered in all the correct information regarding my assets and my intended withdrawals, is this a reasonably accurate tool to use for planning. Any other vehicles that people like. Thank you.
Unfortunately, there is no way to tell if predictions of future portfolio performance are going to be reasonably accurate. We don't have enough data and we don't know if the underlying conditions that generated the data we have will continue unchanged in the future.

MC simulations are highly dependent on the data you use for them. Garbage in, garbage out, as the saying goes.

It's probably better than nothing. Just don't get too attached to the results and realize that there's a huge amount of uncertainty.

There's also uncertainty on the withdrawal side - your spending patterns may change, you may be hit with a massive unexpected expense, etc.

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Re: Monte Carlo Simulation

Post by JoeRetire » Tue Jun 11, 2019 7:06 am

HappyJack wrote:
Sat Jun 08, 2019 3:14 pm
I recognize that a Monte Carlo simulation looks backward, and that can be no guarantee of future results. However, if I have entered in all the correct information regarding my assets and my intended withdrawals, is this a reasonably accurate tool to use for planning.
The correctness of any simulation can only be determined after the fact.

It is a widely used tool.

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Re: Monte Carlo Simulation

Post by JoeRetire » Tue Jun 11, 2019 7:13 am

gd wrote:
Tue Jun 11, 2019 6:12 am
Given that financial markets are unlikely to be well-behaved statistical processes, I find MC unconvincing.
The value of a Monte Carlo simulation is not dependent on having a "well-behaved statistical process" as the target.

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Re: Monte Carlo Simulation

Post by Shallowpockets » Tue Jun 11, 2019 7:56 am

i understand the premise behind skepticism regarding MC simulators. What I don't understand is what other means one might use to try and plan for the future. Since we cannot input future data, we only have the past. How else to manage things?
People say, garbage in, garbage out, but that is simplistic and could be wrong. Maybe it's not garbage in. People say not enough data. In this day and age of mega data and analysis, if we don't have enough data now, when will we?
I see MC as a tool that is the only tool to really be useful for our planning. When I run my numbers I set the paremeters to poor market performance and I upscale my expenses so that when the results spit out and it looks good, I am satisfied.
Barring any black swans I have to believe in the MC results. I have nothing else that would help me fill in the future blanks.
So, to those who do not put any credence in an MC scenario, what do you use to help you down the path that you feel is more concrete?

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Re: Monte Carlo Simulation

Post by Barsoom » Tue Jun 11, 2019 8:50 am

Monte Carlo analysis is essentially about understanding risk.

In its simplest use (like forecasting cash flows under uncertain market conditions), it just shows you the range of outcomes and the associated probabilities. You would have to supply the various risk ranges for stock growth, bond growth, inflation growth, portfolio ratios, etc. It's then up to you to pick the risk level you're comfortable with and plan accordingly (such as planning to the 25% probability (P25), meaning 25% of the time the results will be at or below that amount). What is the SWR at the P25, or the P50 (the median)? The P25 SWR means that 25% of the time, the safe withdrawal rate was lower.

In its more complex use, Monte Carlo is used to make decisions with uncertainty. You would combine your risk assumptions with decisions to be made, such as what stock/bond ratio to use, or what funds to include. Combined with decision trees, you can now get insights into which uncertain conditions would cause your decision to change, or how "wrong" do you have to be about various growth assumptions before you would choose a different decision. You might model a 65/35 portfolio, a 50/50 portfolio, and a 40/60 portfolio, and then see which portfolio returns the highest probabilistic NPV, or if probability curves cross given different conditions? You then interrogate the model to see how much, say, stock growth/decline has to happen to cause the preferred portfolio to change. You would then have to decide how likely that outcome would be to decide if you're comfortable with your decision.

At this point, you would probably need custom tools to deep dive into decision trees.

-B

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Re: Monte Carlo Simulation

Post by HappyJack » Tue Jun 11, 2019 7:36 pm

Thanks to everyone for taking the time and effort to post these comprehensive replies. Any further thoughts - please keep them coming.

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Re: Monte Carlo Simulation

Post by Raybo » Tue Jun 11, 2019 8:32 pm

I have written several financial MCS programs. The main problem that I have seen is how to model future stock, bond, and inflation. What distributions to use? Past returns? Normal Distribution? Some customized random values? Using the wrong distribution just generates wrong estimates.

Also, what time frame should the MCS use? Years, Months, Weeks?

These issues have stopped me from writing my next financial MCS....
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Re: Monte Carlo Simulation

Post by willthrill81 » Tue Jun 11, 2019 9:06 pm

Anyone interested in Monte Carlo simulations would be well served to read Derek Tharp's post on Michael Kitces' website. Basically, he shows that MC simulations tend to produce tails that are too 'fat' on both ends of the spectrum (i.e. statistically significantly worse results than the worst in history, etc.). MC simulations that incorporate mean reversion can overcome this limitation and can manipulate how much mean reversion occurs (e.g. rather than only examining single year returns, examine 3 or 5 year blocks).
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Re: Monte Carlo Simulation

Post by abc132 » Tue Jun 11, 2019 9:29 pm

Like some others here, I have written my own Monte Carlo code so that I can make adjustments, and also so that I make sure I understand the assumptions of the model, and the various alternatives.

Some comments on Monte Carlo models:

They usually depend on some combination of historical performance, whether that is starting at a random year of the market and progressing forward, grabbing individual years randomly, or starting at a random year and having some chance of grabbing sequential years. Historically in the USA, 2/3 of years are up years and 1/3 of years are down years. Using historical data, a Monte Carlo model would be producing results based on a similar ratio of good-to-bad years. They always grab data from the same year, so that stock performance, bond performance, cash, interest rates, etc happen from the same year. This means that if high interest rates are likely to produce a particular trend, that trend may be captured through coordinating the yearly data.

A Monte Carlo model that randomly grabs a year is likely going to produce too many really good combinations of years, and too many really bad combinations of years. I would be very careful of using such a model to try and produce very low failure rates (less than 5%).

I prefer a Monte Carlo that uses a historical year, but has a high chance of grabbing the next year (80-90%). Such a model captures the length of years in a recession, and that bad years are often followed by good years, while still allowing both better and worse sequence of events than the past data on which it was modeled.

What I learned:

Having too many bonds at a young age really decreased my portfolio's chances of meeting my goals, and without any obvious benefit.

Using mostly stocks and increasing bonds around 6-8 years before retirement removed most of the sequence of returns risk, while giving the best chance of meeting my goals.

High quality bonds (treasuries) were superior for my situation during that 6-8 years before retirement.

How my portfolio performed using historical performance (put 100% chance of grabbing next year for each run).


So while not being able to predict the future as being anything like the past, the Monte Carlo model allowed me to determine how my financial portfolio/additions/withdrawals would have done historically, and what actions might have a good chance of meeting my desire for risk vs reward, if the future looks something like the past. The results are still more conservative than historical when looking for high success rates, because there are more worst case scenarios of combining several bad years in a row.

It's also possible to run some cases based on future scenarios, such as muted gains for the next 10 years, by taking a fraction of the gains from any positive year.

All in all it's a pretty good tool, but having a good perspective of what the model can and cannot do is very important.
Last edited by abc132 on Tue Jun 11, 2019 10:18 pm, edited 2 times in total.

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Re: Monte Carlo Simulation

Post by abc132 » Tue Jun 11, 2019 9:33 pm

willthrill81 wrote:
Tue Jun 11, 2019 9:06 pm
Anyone interested in Monte Carlo simulations would be well served to read Derek Tharp's post on Michael Kitces' website. Basically, he shows that MC simulations tend to produce tails that are too 'fat' on both ends of the spectrum (i.e. statistically significantly worse results than the worst in history, etc.). MC simulations that incorporate mean reversion can overcome this limitation and can manipulate how much mean reversion occurs (e.g. rather than only examining single year returns, examine 3 or 5 year blocks).
Probability of next year is the way to go.

There is really no need for the things you mentioned to be a problem if the Monte Carlo model allows sufficient choices.

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Re: Monte Carlo Simulation

Post by abc132 » Tue Jun 11, 2019 10:25 pm

Raybo wrote:
Tue Jun 11, 2019 8:32 pm
I have written several financial MCS programs. The main problem that I have seen is how to model future stock, bond, and inflation. What distributions to use? Past returns? Normal Distribution? Some customized random values? Using the wrong distribution just generates wrong estimates.

Also, what time frame should the MCS use? Years, Months, Weeks?

These issues have stopped me from writing my next financial MCS....
Years would be most appropriate.

Grabbing a random month or week's data is going to compound the issue of really good and really bad sequences that have almost no probability of ever happening, and someone investing/planning for the long term shouldn't really care about weekly or monthly differences.

A sequence of years is the best answer, and using probability rather than a fixed number of years, we can say that a model that captures several years of decline is likely to capture several years of recovery that follow.

3-5 years is a good average sequence of years in order to capture a full recession or recovery, which would correspond to 79% - 87% correlation, respectively.

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Re: Monte Carlo Simulation

Post by protagonist » Tue Jun 11, 2019 10:43 pm

HappyJack wrote:
Sat Jun 08, 2019 3:14 pm
I recognize that a Monte Carlo simulation looks backward, and that can be no guarantee of future results. However, if I have entered in all the correct information regarding my assets and my intended withdrawals, is this a reasonably accurate tool to use for planning. Any other vehicles that people like. Thank you.
Short answer....no. Because future returns are unknown, and even if you believe that past performance is relevant (a moot point), there is not nearly enough past data to make extrapolation on the order of decades statistically relevant. Using 90 years of data to estimate performance for the next 30 years is the statistical equivalent of using Monday through Wednesday's stock performance to estimate what the stock market will do on Thursday. It is no more or less accurate than that.

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Re: Monte Carlo Simulation

Post by LeftCoastIV » Tue Jun 11, 2019 10:58 pm

abc132 wrote:
Tue Jun 11, 2019 9:29 pm
Like some others here, I have written my own Monte Carlo code so that I can make adjustments, and also so that I make sure I understand the assumptions of the model, and the various alternatives.

Some comments on Monte Carlo models:

They usually depend on some combination of historical performance, whether that is starting at a random year of the market and progressing forward, grabbing individual years randomly, or starting at a random year and having some chance of grabbing sequential years. Historically in the USA, 2/3 of years are up years and 1/3 of years are down years. Using historical data, a Monte Carlo model would be producing results based on a similar ratio of good-to-bad years. They always grab data from the same year, so that stock performance, bond performance, cash, interest rates, etc happen from the same year. This means that if high interest rates are likely to produce a particular trend, that trend may be captured through coordinating the yearly data.

A Monte Carlo model that randomly grabs a year is likely going to produce too many really good combinations of years, and too many really bad combinations of years. I would be very careful of using such a model to try and produce very low failure rates (less than 5%).

I prefer a Monte Carlo that uses a historical year, but has a high chance of grabbing the next year (80-90%). Such a model captures the length of years in a recession, and that bad years are often followed by good years, while still allowing both better and worse sequence of events than the past data on which it was modeled.

What I learned:

Having too many bonds at a young age really decreased my portfolio's chances of meeting my goals, and without any obvious benefit.

Using mostly stocks and increasing bonds around 6-8 years before retirement removed most of the sequence of returns risk, while giving the best chance of meeting my goals.

High quality bonds (treasuries) were superior for my situation during that 6-8 years before retirement.

How my portfolio performed using historical performance (put 100% chance of grabbing next year for each run).


So while not being able to predict the future as being anything like the past, the Monte Carlo model allowed me to determine how my financial portfolio/additions/withdrawals would have done historically, and what actions might have a good chance of meeting my desire for risk vs reward, if the future looks something like the past. The results are still more conservative than historical when looking for high success rates, because there are more worst case scenarios of combining several bad years in a row.

It's also possible to run some cases based on future scenarios, such as muted gains for the next 10 years, by taking a fraction of the gains from any positive year.

All in all it's a pretty good tool, but having a good perspective of what the model can and cannot do is very important.
Thank you abc123. Insightful and helpful. Is there a public tool (website) that allows for this level of customization?

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Re: Monte Carlo Simulation

Post by abc132 » Tue Jun 11, 2019 11:29 pm

LeftCoastIV wrote:
Tue Jun 11, 2019 10:58 pm
Thank you abc123. Insightful and helpful. Is there a public tool (website) that allows for this level of customization?
Here is a thread that might help you with various options:

viewtopic.php?t=272332

Since I write my own code, I have no idea which are the best simulators.

I was a Boglehead before I knew about Bogleheads, so it's really interesting to have formulated much of my own thought process, and then come here and see what is recommended and how other people think. I am always looking to learn.

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Re: Monte Carlo Simulation

Post by abc132 » Tue Jun 11, 2019 11:41 pm

protagonist wrote:
Tue Jun 11, 2019 10:43 pm
HappyJack wrote:
Sat Jun 08, 2019 3:14 pm
I recognize that a Monte Carlo simulation looks backward, and that can be no guarantee of future results. However, if I have entered in all the correct information regarding my assets and my intended withdrawals, is this a reasonably accurate tool to use for planning. Any other vehicles that people like. Thank you.
Short answer....no. Because future returns are unknown, and even if you believe that past performance is relevant (a moot point), there is not nearly enough past data to make extrapolation on the order of decades statistically relevant. Using 90 years of data to estimate performance for the next 30 years is the statistical equivalent of using Monday through Wednesday's stock performance to estimate what the stock market will do on Thursday. It is no more or less accurate than that.
Monte Carlo simply means using a bunch of random numbers to model something. You could pick a mean and standard deviation for each asset class, use a normal or non-normal distribution, etc. None of it has to be historical.

Monte Carlo models are limited by the people creating the model, and/or the options they make available to users. If you understand the assumptions of the model you are using, you can use it appropriately. I agree that most models should not be a one-stop solution --> they should be used along with other tools.

Comparing historical and non historical results is probably the best way to use this tool. I do this by comparing what would have happened historically (correlation from year to year = 100%) to various other scenarios that I devise.

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Re: Monte Carlo Simulation

Post by Aptenodytes » Wed Jun 12, 2019 4:35 am

You can tune your simulation to any probability distributions you want - you can shift the expected return of any asset you want, and you can shift the shape of the distribution, you can shift the correlations across after asset classes. Likewise you can shift the probability distributions of future spending needs or contribution rates.

E.g., I never run a simulation with historic returns without also running a simulation with half those values.

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Re: Monte Carlo Simulation

Post by patrick013 » Wed Jun 12, 2019 11:03 am

To resolve the uncertainty which controls the outcome of a long term plan, a thousand different simulations have to be taken into account, some samples important and some slight, all varying in their effect, and with the probability of new combinations appearing which would be temporarily positive or negative and also contributing to success or failure long term, always included randomly.

So the probability table provides for the simulation until the thousand simulations are tabulated. Kind of like picking numbers out of a hat for a pure random effect.

Very few finance grads have taken a course in MC so the exact details are unknown but basic probability assumptions are no doubt in use. The main problem would be estimating annual returns too high. It's one of several methods to use.
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Re: Monte Carlo Simulation

Post by vineviz » Wed Jun 12, 2019 12:35 pm

willthrill81 wrote:
Tue Jun 11, 2019 9:06 pm
Anyone interested in Monte Carlo simulations would be well served to read Derek Tharp's post on Michael Kitces' website. Basically, he shows that MC simulations tend to produce tails that are too 'fat' on both ends of the spectrum (i.e. statistically significantly worse results than the worst in history, etc.). MC simulations that incorporate mean reversion can overcome this limitation and can manipulate how much mean reversion occurs (e.g. rather than only examining single year returns, examine 3 or 5 year blocks).
Just to expand on this, controlling for mean reversion and/or serial correlation in this way is generally called "block bootstrapping", and any competent MC simulation algorithm should allow for it.

PortfolioVisualizer, for instance, sets the default boostrap at one year but the user to adjust the range of bootstrapping. Even modest increases in the length of the bootstrap can generate tails in the simulation output that are much less extreme than the results from single year bootstraps.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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Re: Monte Carlo Simulation

Post by protagonist » Thu Jun 13, 2019 8:57 am

abc132 wrote:
Tue Jun 11, 2019 11:41 pm
If you understand the assumptions of the model you are using, you can use it appropriately. I agree that most models should not be a one-stop solution --> they should be used along with other tools.
I think the crux of the issue is that most people DON''T understand the assumptions....or rather they believe the assumptions have validity because they don't understand statistics (sadly this is very commonplace). If you realize that the predictions are based on a house of cards, then I agree with you.

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Re: Monte Carlo Simulation

Post by vineviz » Thu Jun 13, 2019 9:00 am

protagonist wrote:
Thu Jun 13, 2019 8:57 am
If you realize that the predictions are based on a house of cards, then I agree with you.
Wait. Are you saying that if someone thinks that Monte Carlo simulations are inherently built on a house of cards that they don't understand statistics?

If so, I agree with you.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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Re: Monte Carlo Simulation

Post by protagonist » Thu Jun 13, 2019 9:15 am

vineviz wrote:
Thu Jun 13, 2019 9:00 am
protagonist wrote:
Thu Jun 13, 2019 8:57 am
If you realize that the predictions are based on a house of cards, then I agree with you.
Wait. Are you saying that if someone thinks that Monte Carlo simulations are inherently built on a house of cards that they don't understand statistics?

If so, I agree with you.

No, not ALL Monte Carlo simulations are based on a house of cards. It is a very useful tool with several valid applications, where there is enough prior data available and where there is enough theoretical basis to render future predictions meaningful. It is an invaluable tool when applied properly, and is used as such in physics, climatology, mathematics, astronomy, engineering, etc.
But using less than a century of data to predict things 30 or 50 years into the future with no solid theoretical basis for why the available data is what it is, or is meaningful or predictive (e.g.: the stock market) , is a house of cards.

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Re: Monte Carlo Simulation

Post by abc132 » Thu Jun 13, 2019 10:39 am

protagonist wrote:
Thu Jun 13, 2019 9:15 am
No, not ALL Monte Carlo simulations are based on a house of cards. It is a very useful tool with several valid applications, where there is enough prior data available and where there is enough theoretical basis to render future predictions meaningful. It is an invaluable tool when applied properly, and is used as such in physics, climatology, mathematics, astronomy, engineering, etc.
But using less than a century of data to predict things 30 or 50 years into the future with no solid theoretical basis for why the available data is what it is, or is meaningful or predictive (e.g.: the stock market) , is a house of cards.
None of these are necessary to use a model to explore and learn. The baseline is past performance, but the model can be used to go anywhere from there. Computers are used specifically because they can run hundreds, thousands, millions, billions of cases.

Case In Point: Using historical data (100% correlation from year to year), and looking at my situation late in life, I see two peaks in likely outcomes, one based on a good sequence of returns and one based a a poor sequence of returns. Something in-between those two cases is less likely to happen. If the future is exactly like the past, I can make sure I am prepared for a future similar to the past.

From there, I can run some scenarios:
1) Historical performance but 3% worse annual performance than the past performance
2) Historical but 3% better annual performance than the past.
3) Use historical data with 85% correlation (85% chance of grabbing the next years data)
4) Run Japan scenario or any other scenario I care to think of

Result:

I can test to see how my financial plan will react to literally any scenario that I can think of. Trying to make the same decisions without this information is much more of a house of cards than doing so with this information.

The limitation is really behind the person running the model, and has nothing to do with some of the requirements you laid out.

Modern science theory crafts our best guess of how the universe might work, and then looks for confirmation. It does not wait for perfect understanding to try and predict things. The fact that the exact future is unknown does not prevent us from exploring what it might look like.

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Re: Monte Carlo Simulation

Post by carolinaman » Thu Jun 13, 2019 10:54 am

MC is a good planning tool as long as you recognize its limitations. It is best if the tool you use allows you to input different estimates for inflation, performance, etc. so you can gauge results from different scenarios, ranging from expected to conservative.

You should redo your MC analysis every year or two to see what the latest estimates are.

A lot of people on the forum seem negative on MC. I wonder what kind of planning tool they use in its place.

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Re: Monte Carlo Simulation

Post by ohai » Thu Jun 13, 2019 11:58 am

1) Monte Carlo is not backward looking. The parameterization is usually based on historical data, but by definition, the simulation is not historical analysis. You can always backtest a strategy based on historical data if your intention is to study historical periods. In fact, this is arguably a better tool than MC simulation for testing investment strategies.

2) Simulations are highly sensitive to their probability distributions. Most of the off the shelf models that you might find will use very simple, unrealistic distributions. A lognormal or normal distribution might not have modeled a 2008 scenario, or even a December 2018 scenario. Fitting a good market data path is the most difficult part of designing a simulation.

3) Simulation seems to be abused a lot. Why do you need a simulation to produce percentile results for some investment with known (assumed) drift and volatility? This has a close form solution. Just because a calculation is complicated, doesn't mean it's better.

Simulation is used a lot for a variety of useful financial purposes. However, don't be fooled by thinking it's some special magic tool. What do you mean by "simulation" is the important question.

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Re: Monte Carlo Simulation

Post by Barsoom » Thu Jun 13, 2019 12:07 pm

protagonist wrote:
Thu Jun 13, 2019 9:15 am
But using less than a century of data to predict things 30 or 50 years into the future with no solid theoretical basis for why the available data is what it is, or is meaningful or predictive (e.g.: the stock market) , is a house of cards.
"House of cards" = Bayesian Probabilities.

-B

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Re: Monte Carlo Simulation

Post by patrick013 » Thu Jun 13, 2019 12:21 pm

Barsoom wrote:
Thu Jun 13, 2019 12:07 pm
protagonist wrote:
Thu Jun 13, 2019 9:15 am
But using less than a century of data to predict things 30 or 50 years into the future with no solid theoretical basis for why the available data is what it is, or is meaningful or predictive (e.g.: the stock market) , is a house of cards.
"House of cards" = Bayesian Probabilities.

-B
I usually think of the modern market being 1950 or 1960 forward. That excludes the great
depression of the 1930's but maybe it should.

Some posters obviously have some book learning about MC. My nagging question is having limited MC knowledge except it's the work off a probability scheme and data table is this. My MC config may have 2 choices. Do the sampling without replacement or do the sampling with replacement. There's enough data to cover the sampling either way, but which is the wisest choice.

THX.
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Re: Monte Carlo Simulation

Post by protagonist » Thu Jun 13, 2019 12:25 pm

abc132 wrote:
Thu Jun 13, 2019 10:39 am
protagonist wrote:
Thu Jun 13, 2019 9:15 am
No, not ALL Monte Carlo simulations are based on a house of cards. It is a very useful tool with several valid applications, where there is enough prior data available and where there is enough theoretical basis to render future predictions meaningful. It is an invaluable tool when applied properly, and is used as such in physics, climatology, mathematics, astronomy, engineering, etc.
But using less than a century of data to predict things 30 or 50 years into the future with no solid theoretical basis for why the available data is what it is, or is meaningful or predictive (e.g.: the stock market) , is a house of cards.
None of these are necessary to use a model to explore and learn. The baseline is past performance, but the model can be used to go anywhere from there. Computers are used specifically because they can run hundreds, thousands, millions, billions of cases.

Case In Point: Using historical data (100% correlation from year to year), and looking at my situation late in life, I see two peaks in likely outcomes, one based on a good sequence of returns and one based a a poor sequence of returns. Something in-between those two cases is less likely to happen. If the future is exactly like the past, I can make sure I am prepared for a future similar to the past.

From there, I can run some scenarios:
1) Historical performance but 3% worse annual performance than the past performance
2) Historical but 3% better annual performance than the past.
3) Use historical data with 85% correlation (85% chance of grabbing the next years data)
4) Run Japan scenario or any other scenario I care to think of

Result:

I can test to see how my financial plan will react to literally any scenario that I can think of. Trying to make the same decisions without this information is much more of a house of cards than doing so with this information.

The limitation is really behind the person running the model, and has nothing to do with some of the requirements you laid out.

Modern science theory crafts our best guess of how the universe might work, and then looks for confirmation. It does not wait for perfect understanding to try and predict things. The fact that the exact future is unknown does not prevent us from exploring what it might look like.
I don't disagree with this, abc. However, you also wrote,
If you understand the assumptions of the model you are using, you can use it appropriately.
As I previously stated, I think the crux of the issue is that most people DON''T understand the assumptions....or rather they believe the assumptions have validity because they don't understand statistics (sadly this is very commonplace). If you realize that the predictions are based on a house of cards, then I agree with you.

For instance, you mention assumptions 3% better or worse than past performance. What about 20%, or 50%, or 90% better or worse than the past performance? You and I have no clue what the probability is of that happening within the next 30 or 50 years. Without having some gauge to analyze the relative probabilities of one scenario vs all others, the tool is limited in usefulness because you can generate outcomes but not relative likelihood of them happening. Maybe the past 50 or 100 years was an outlier....after all, it was very possibly the century of greatest economic growth in the entire history of civilization. And if you are going to run that wide a gamut of possible scenarios, then it boils down to an admission that it is impossible to predict the relative probability of outcomes that far into the future with any reliability given the relatively small amount of data (information) available today. You can generate accurate results, but the results have little real-life meaning.

When Monte Carlo techniques become very useful is when you have enough of a theoretical basis and/or (preferably and) enough data to be able to estimate probabilities of future scenarios with at least some accuracy, and can thus extrapolate relative probabilities of outcomes. That last phrase is the critical missing link in financial planning. It is often not missing in scientific fields of inquiry, where the technique is very valuable.

Also note ohai's post above. He makes additional valid points regarding how the technique is being used incorrectly.
Last edited by protagonist on Thu Jun 13, 2019 1:24 pm, edited 18 times in total.

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Re: Monte Carlo Simulation

Post by HomerJ » Thu Jun 13, 2019 12:25 pm

abc132 wrote:
Tue Jun 11, 2019 9:29 pm
A Monte Carlo model that randomly grabs a year is likely going to produce too many really good combinations of years, and too many really bad combinations of years. I would be very careful of using such a model to try and produce very low failure rates (less than 5%).

I prefer a Monte Carlo that uses a historical year, but has a high chance of grabbing the next year (80-90%). Such a model captures the length of years in a recession, and that bad years are often followed by good years, while still allowing both better and worse sequence of events than the past data on which it was modeled.
This is a great post.

Any Monte Carlo method that randomly grabs historical years is almost certainly garbage. Stock market returns year-to-year are not independent events.

I do like the above revision where it has a high chance of grabbing the next year. That would be more interesting to me.

How can we tell what type of model a website or an author uses, when all they usually say is "Using Monte Carlo simulation...."
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Re: Monte Carlo Simulation

Post by patrick013 » Thu Jun 13, 2019 12:33 pm

carolinaman wrote:
Thu Jun 13, 2019 10:54 am

A lot of people on the forum seem negative on MC. I wonder what kind of planning tool they use in its place.
Expected returns and a pro-forma cash flow worksheet. For example I did a long term CD accumulation and withdrawal worksheet. Well the expected interest rate used was 4%. Recently redid that for a expected interest rate of 3%. More inline with the current market.

Same with stocks. Expected return of 6% long term. That's the controlling number. MC probably does a better job as the worksheet is all the same every year. But it does a give a ball park estimate of very average annual cash flow accumulations and withdrawals thru many years. Oh well.
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Re: Monte Carlo Simulation

Post by abc132 » Thu Jun 13, 2019 2:16 pm

protagonist wrote:
Thu Jun 13, 2019 12:25 pm
As I previously stated, I think the crux of the issue is that most people DON''T understand the assumptions....or rather they believe the assumptions have validity because they don't understand statistics (sadly this is very commonplace). If you realize that the predictions are based on a house of cards, then I agree with you.
I think we can agree that there are probably many poor models out there, and that even with a good model, the user may not understand how important the inputs are to the results.
protagonist wrote:
Thu Jun 13, 2019 12:25 pm
For instance, you mention assumptions 3% better or worse than past performance. What about 20%, or 50%, or 90% better or worse than the past performance? You and I have no clue what the probability is of that happening within the next 30 or 50 years. Without having some gauge to analyze the relative probabilities of one scenario vs all others, the tool is limited in usefulness because you can generate outcomes but not relative likelihood of them happening. Maybe the past 50 or 100 years was an outlier....after all, it was very possibly the century of greatest economic growth in the entire history of civilization. And if you are going to run that wide a gamut of possible scenarios, then it boils down to an admission that it is impossible to predict the relative probability of outcomes that far into the future with any reliability given the relatively small amount of data (information) available today. You can generate accurate results, but the results have little real-life meaning.
I was running 3% worse - per year - using historical values minus 3%, which is bigger than 20% or 50% over a long term horizon. The model already includes 50%+ drops from historical data.
protagonist wrote:
Thu Jun 13, 2019 12:25 pm
When Monte Carlo techniques become very useful is when you have enough of a theoretical basis and/or (preferably and) enough data to be able to estimate probabilities of future scenarios with at least some accuracy, and can thus extrapolate relative probabilities of outcomes. That last phrase is the critical missing link in financial planning. It is often not missing in scientific fields of inquiry, where the technique is very valuable.
Here is where we disagree. If I can model some worst case scenarios, and get through them, I can view my portfolio in that light without ever knowing the probability of that scenario happening. Using a tool to investigate the things you are concerned about is just one use of MC.
protagonist wrote:
Thu Jun 13, 2019 12:25 pm
Also note ohai's post above. He makes additional valid points regarding how the technique is being used incorrectly.
All investing techniques and tools are being used incorrectly. You can guarantee it.

MC simulation can do some unique things.

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Re: Monte Carlo Simulation

Post by abc132 » Thu Jun 13, 2019 2:20 pm

patrick013 wrote:
Thu Jun 13, 2019 12:33 pm
carolinaman wrote:
Thu Jun 13, 2019 10:54 am

A lot of people on the forum seem negative on MC. I wonder what kind of planning tool they use in its place.
Expected returns and a pro-forma cash flow worksheet. For example I did a long term CD accumulation and withdrawal worksheet. Well the expected interest rate used was 4%. Recently redid that for a expected interest rate of 3%. More inline with the current market.

Same with stocks. Expected return of 6% long term. That's the controlling number. MC probably does a better job as the worksheet is all the same every year. But it does a give a ball park estimate of very average annual cash flow accumulations and withdrawals thru many years. Oh well.
MC is most useful for what happens through the withdrawal phase, but it also can give you a chance of something happening (retire by 60, etc), not just one expected value. In the risk assessment world, tools that give one answer are not accepted - they are entirely inappropriate. Volatility is the big risk during withdrawal, and your model doesn't appear to incorporate this. You can correct me if I am misunderstanding your tool.

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Re: Monte Carlo Simulation

Post by protagonist » Thu Jun 13, 2019 5:15 pm

abc132 wrote:
Thu Jun 13, 2019 2:16 pm

Here is where we disagree. If I can model some worst case scenarios, and get through them, I can view my portfolio in that light without ever knowing the probability of that scenario happening.
The worst case scenario needs no modeling. It is that you lose all your money- the value of your investments drop to zero. It could theoretically happen to all of us....possible but improbable (though the probability increases with passing time).

(Actually the worst case scenario is dying tomorrow, regardless of how much you have saved....the actuarial tables may be more useful than financial modeling....)

I do agree with you that, used judiciously, the techniques can have some value. For instance, if they indicate that, at your current spending levels, unless your investments yield over 10%/year you will run out of money in a decade, it might convince you to work longer or spend a lot less. On the other hand, if they indicate that the market can lose 5%/year over the next decade and you will still have more than enough money to maintain your lifestyle, that can be comforting and reduce your level of worry or tendency to respond with panic to a bear market.

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Re: Monte Carlo Simulation

Post by patrick013 » Thu Jun 13, 2019 5:38 pm

abc132 wrote:
Thu Jun 13, 2019 2:20 pm
patrick013 wrote:
Thu Jun 13, 2019 12:33 pm
carolinaman wrote:
Thu Jun 13, 2019 10:54 am

A lot of people on the forum seem negative on MC. I wonder what kind of planning tool they use in its place.
Expected returns and a pro-forma cash flow worksheet. For example I did a long term CD accumulation and withdrawal worksheet. Well the expected interest rate used was 4%. Recently redid that for a expected interest rate of 3%. More inline with the current market.

Same with stocks. Expected return of 6% long term. That's the controlling number. MC probably does a better job as the worksheet is all the same every year. But it does a give a ball park estimate of very average annual cash flow accumulations and withdrawals thru many years. Oh well.
MC is most useful for what happens through the withdrawal phase, but it also can give you a chance of something happening (retire by 60, etc), not just one expected value. In the risk assessment world, tools that give one answer are not accepted - they are entirely inappropriate. Volatility is the big risk during withdrawal, and your model doesn't appear to incorporate this. You can correct me if I am misunderstanding your tool.
No correction needed. But if I use a 50-50 AA the plot thickens. Stocks are not bonds of course.

My simple 6% stock charting could end up being 4% or 10%, the danger is on the down side.

But with a 50-50 AA I have the option of withdrawing from stocks or bonds accordingly as the market provides advantage.

So MC or my average charting has it's bad points. That's why I like age-in-bonds to capture those stock gains when they occur for future "living with means". The past provides data the future does not. But the future can provide "your screwed" declines which prevent "average" withdrawals in my average'd out model. Need those darn bonds for portfolio stability in any case when computing portfolio overall return long term. Using bonds to weather stock AA downturns. Of course.
age in bonds, buy-and-hold, 10 year business cycle

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Re: Monte Carlo Simulation

Post by abc132 » Fri Jun 14, 2019 8:43 am

patrick013 wrote:
Thu Jun 13, 2019 5:38 pm
So MC or my average charting has it's bad points.
This is why people should be clear about how to use a method, instead of just trashing it. Equating these two things is entirely inappropriate.

In the field of risk management, you need probability distribution to make the best decisions. When Mad Cow Disease broke out, they didn't try different expected values to make decisions, they came up with complex probability models to determine what action to best take.

Any model that can give you a probability distribution of meeting your goals, or making changes, is going to be vastly superior to one that simply calculates a single mean, or expected value. Probability is key to risk management.

Monte Carlo can tell you the probability of having $1 million at age 80, the probability of retiring by age 60, etc. The output is only as good as the input, but the quality of the input is based on the intelligence and thoughtfulness of the user. Monte Carlo may not be the best casual tool, but it can be quite powerful for those who understand how to use it.

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Re: Monte Carlo Simulation

Post by Seasonal » Fri Jun 14, 2019 12:13 pm

abc132 wrote:
Fri Jun 14, 2019 8:43 am
Monte Carlo can tell you the probability of having $1 million at age 80, the probability of retiring by age 60, etc. The output is only as good as the input, but the quality of the input is based on the intelligence and thoughtfulness of the user. Monte Carlo may not be the best casual tool, but it can be quite powerful for those who understand how to use it.
Please explain what you mean by the emphasized language. An example of intelligent and thoughtful input for financial planning would be helpful.

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Re: Monte Carlo Simulation

Post by abc132 » Fri Jun 14, 2019 8:15 pm

Seasonal wrote:
Fri Jun 14, 2019 12:13 pm
Please explain what you mean by the emphasized language. An example of intelligent and thoughtful input for financial planning would be helpful.
Sure. I would recommend looking at the range of outcomes for the the things that are driving your decisions.

One of my goals is early retirement.

I had a portfolio with 99% low fee index funds for international, emerging, and US stocks. The reason for this portfolio is that Monte Carlo (MC) simulations showed that taking on the risk of stocks with a large time horizon was more likely to get me to early retirement, and more likely to get me to non-early retirement goals. MC simulations showed that volatility was going to start becoming a problem 6-8 years before my early retirement date. As I approached 8 years before early retirement, I started altering my portfolio to better handle volatility.

Note that volatility was not a problem early on during investing, and it started to become a problem before retirement.

You won't have to look too far to find people focusing exclusively on volatility reduction when volatility reduction doesn't really matter (early years of accumulation), or those that ignore volatility risk around retirement because their stocks paid off nicely despite that past volatility.

Monte Carlo helps to show what risks you are really taking from various investment options, and the results can be specific to your exact situation. This can include inflation risk, diversification risk, volatility risk, or whatever parameter you are interested in investigating. Probability of success is critical to making an informed decision about risk vs reward - and to determine changes you can make to a portfolio to have the best chance of meeting your desired goals.

With a healthy dose of both historical and non historical simulations, you can better understand your risks and decisions.

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Re: Monte Carlo Simulation

Post by jmk » Sat Jun 15, 2019 12:13 pm

It's easy to attack monte carlo if one assumes it means more than it does. I don't know many people who use any monte carlo simulation as a hard fact of probability of success. All monte carlo and other simulations are meant to do is explore the implications of certain assumptions. One data point among others to be used to make your decision. Everyone makes some kind of assumptions in planning; all monte carlo does is extend the implications of that assumption.

There are different types of monte carlo and they answer different questions and are based on different set of founding assumptions. First is a parametric monte carlo, in which you define the parameters of a statistical distribution. Your parameters might be based on history or they might be based on your own predictions. Common distributions are the normal distribution (for returns) and lognormal (for prices), though sophisticated versions make these more accurate by incorporating fat-tails, kurtosis, etc and autoregression to account for return-to-mean. A common use of all of these is to calculate upper and lower bounds for planning purposes.

To give a typical example, suppose you are assuming 3.4% real return on TSM (1/CAPE). You've run your standard spreadsheet with 3.4% returns every year using RPM; but you want a better sense of the range of what might happen over 20 years if the SD remains about its historical 18%-19%. So you run a monte carlo using a normal distribution and find the "volatility drag" cuts the 3.4% median down to 2%. So you adjust your spreadsheet to see what that does and how much more you're going to need to save. Although you'd see a maximum drawdown of 71%, if you held through you'd see the 10th percentile of distribution over 20 years is -3% and even the 25th percentile is close to zero! So, say, as an investor who's very risk-averse, you conclude that even over 20 years you can't count on a positive return (even rebalancing through an expected 71% drop!) with your current 3.4% return assumptions, and you might rely more on guaranteed bonds and CDs to fund your most vital liabilities "just in case".

You also know this result is to be taken lightly, since a normal distribution doesn't reflect return-to-mean and equities haven't exactly followed a normal curve and we're talking 25th percentile. But it does give you a nice rough outer limit of the range, and more information than you simply from your 3.4% original assumption. (So it's unlikely stocks will end up, say, 20% lower over 20 years but it could quite easily be close to 0 to -3% if luck is awful or valuations are high.)

You'd most likely at this point also want a sensitivity analysis, where you re-run the monte carlo but change some variables from your original assumption, to see what would happen if sd or inflation was higher or lower. You might see which factors affect outcomes the most, so you could focus on those in your static-return planning sheets. You might discover for instance that asset allocation doesn't matter much in calculating your SWR, but inflation protection does.

Most of us also want to look at history. One always start with actual historical returns in different time periods, to give you a sense of what would have happened historically (e.g 1927, 1967, 2008, 1980s). This is invaluable, as it shows how things would have turns out in different historical (macroeconomic) situations. (I won't give example here.) But then you might want to also run a bootstrapping monte carlo to flesh this out. Bootstrapping simply takes the historical record and gives it back to you in a different order. So in-so-far as history acts within the constraints of the paste but in different order (depressions, wars, inflations, political pendulums, etc), we might what is the 10th percentile then? One main reason for this is to account for sequence of return risk: what happens if history repeats itself but you get bad returns at the worst time? You can explore "with replacement" (draws from original sample but can repeat entries) and "without replacement" (only varies the order but keeps the whole sample) depending on what you want to explore.

Running this bootstrap we see historically a 6.67% median; but we note the 5th percentile of the bootstrap is -1% over 20 years-- which is roughly what we saw from the simple normal curve. So this second data point reinforces the first: over 20 years it's within ordinary possibility to end up with 0% or even a negative equity return. Historically, we'd expect a 74% drawdown within the 20 years, slightly more than the normal curve. So as we contemplate things, we think "over 20 years likely we'll get drawdown in the 70s at some point."

Now, realizing that a completely random re-ordering of historical returns doesn't reflect the auto-regression we find in actual returns, we might decide to re-run the bootstrapping monte carlo using "chunks" of, say, 5 years, to help reflect the return-to-mean. Indeed this gives a higher safe-withdrawal rate (4.1% vs 3.8%)--but you'd be counting on bad returns "bouncing back" within five years like they have in the past. In other words: If one agrees this trend will continue, go with 4.1, if one disagrees or is more cautious go with 3.8%. Now you also might want to reflect longer macro-economic secular trends, which tend to last 7-15 years. Re-running the bootstrap with 7-15 year chunks gives you a lower draw-down (80%!), but roughly the same 5th percentile (0.39% cagr) overall returns for the 20y. The SWR jumps to 4.57% though. Interesting. So you add into your thinking "if history not only reflects the statistical range of the past, but has long secular trends of the past, I could squeeze out more SWR of almost 1%. But do I have any reason to think these long trends will continue in the next 20 years? No, the world is changing too much.... So I'll stick with the lower SWR."

The above examples are for an ultra-conservative investor focusing on the "low end"; but many of us would also be interested in the median and "high" expectations in order to have high and low bounds to our planning. Just as you could plug the lower bound (e.g. 10th percentile) monte carlo or bootstrapped results into your standard spreadsheet, you could plug the median and upper bound 80th percentile too. That would give you a range of outcomes and you could have different plans for each depending on how history developed.

So in short, you run a simple year-by-year analysis, you run historical to show how things would have looked in different macro-economic situations, you run bootstrapping and statistical monte carlo to extend out current history. As user ABC132 notes, the results can be specific to your exact situation, and can include inflation risk, diversification risk, volatility risk, or whatever parameter you are interested in investigating. All of this gives you more info for your simple spreadsheets than you have with a simple constant assumption: here's my "median" assumption, but here's what happens if things go high or low within bounds of history. You'd run sensitivity analyses to figure out what factors matter and what don't. All of this helps temper one's over-confidence: no matter what you predict or what history shows, things will likely get a bit more extreme than you can imagine. So let's plan for it.

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Re: Monte Carlo Simulation

Post by Seasonal » Sat Jun 15, 2019 2:21 pm

abc132 wrote:
Fri Jun 14, 2019 8:15 pm
Seasonal wrote:
Fri Jun 14, 2019 12:13 pm
Please explain what you mean by the emphasized language. An example of intelligent and thoughtful input for financial planning would be helpful.
Sure. I would recommend looking at the range of outcomes for the the things that are driving your decisions.

One of my goals is early retirement.

I had a portfolio with 99% low fee index funds for international, emerging, and US stocks. The reason for this portfolio is that Monte Carlo (MC) simulations showed that taking on the risk of stocks with a large time horizon was more likely to get me to early retirement, and more likely to get me to non-early retirement goals. MC simulations showed that volatility was going to start becoming a problem 6-8 years before my early retirement date. As I approached 8 years before early retirement, I started altering my portfolio to better handle volatility.

Note that volatility was not a problem early on during investing, and it started to become a problem before retirement.

You won't have to look too far to find people focusing exclusively on volatility reduction when volatility reduction doesn't really matter (early years of accumulation), or those that ignore volatility risk around retirement because their stocks paid off nicely despite that past volatility.

Monte Carlo helps to show what risks you are really taking from various investment options, and the results can be specific to your exact situation. This can include inflation risk, diversification risk, volatility risk, or whatever parameter you are interested in investigating. Probability of success is critical to making an informed decision about risk vs reward - and to determine changes you can make to a portfolio to have the best chance of meeting your desired goals.

With a healthy dose of both historical and non historical simulations, you can better understand your risks and decisions.
Perhaps I'm missing it, but you do not appear to have provided examples of inputs.

"The reason for this portfolio is that Monte Carlo (MC) simulations showed that taking on the risk of stocks with a large time horizon was more likely to get me to early retirement"

A MC simulation can not show this unconditionally. All it can show is a possible set of outcomes that are dependent on your inputs and your modeling. As jmk wrote above, "All monte carlo and other simulations are meant to do is explore the implications of certain assumptions.".

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Re: Monte Carlo Simulation

Post by abc132 » Sat Jun 15, 2019 4:05 pm

Seasonal wrote:
Sat Jun 15, 2019 2:21 pm

Perhaps I'm missing it, but you do not appear to have provided examples of inputs.

"The reason for this portfolio is that Monte Carlo (MC) simulations showed that taking on the risk of stocks with a large time horizon was more likely to get me to early retirement"

A MC simulation can not show this unconditionally. All it can show is a possible set of outcomes that are dependent on your inputs and your modeling. As jmk wrote above, "All monte carlo and other simulations are meant to do is explore the implications of certain assumptions.".
The input was my financial situation (rate of deposit, time to expected retire date, current asset allocation, expected future investment, etc).

I made a conclusion from the implication of certain assumptions, which was best portfolio distribution to have the highest chance to meet my goals. I learned some things about volatility along the way (where it was important and where it was not important).


A probability model can certainly show you are more likely to meet an outcome with some change to your portfolio. That's the basis of probability. Reaching 100% probability, or your word "unconditionally", really doesn't exist in the type of risk management we typically use/compare, and if you need 100% certainty about the future to take any action in the present, you won't be able to take any action in the present.

I'm confused why you would use any financial tool if you need unconditional answers about the future.

Most of us seek for either good enough, and/or better than existing.

Maybe you need to provide some examples of tools that provide your word "unconditional".

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Re: Monte Carlo Simulation

Post by Teague » Sat Jun 15, 2019 6:03 pm

jmk wrote:
Sat Jun 15, 2019 12:13 pm
It's easy to attack monte carlo if one assumes it means more than it does. I don't know many people who use any monte carlo simulation as a hard fact of probability of success. All monte carlo and other simulations are meant to do is explore the implications of certain assumptions. One data point among others to be used to make your decision. Everyone makes some kind of assumptions in planning; all monte carlo does is extend the implications of that assumption.

[... poster jmk then continued with a remarkably nice and thorough detailing of monte carlo simulations.]
Thank you for that! I know that took some time to write and it is very much appreciated.
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Re: Monte Carlo Simulation

Post by patrick013 » Sat Jun 15, 2019 6:24 pm

Teague wrote:
Sat Jun 15, 2019 6:03 pm
jmk wrote:
Sat Jun 15, 2019 12:13 pm
It's easy to attack monte carlo if one assumes it means more than it does. I don't know many people who use any monte carlo simulation as a hard fact of probability of success. All monte carlo and other simulations are meant to do is explore the implications of certain assumptions. One data point among others to be used to make your decision. Everyone makes some kind of assumptions in planning; all monte carlo does is extend the implications of that assumption.

[... poster jmk then continued with a remarkably nice and thorough detailing of monte carlo simulations.]
Thank you for that! I know that took some time to write and it is very much appreciated.
The Advisor's manual mentions MC as a possible tool. Thanks for your explanatory remarks also.
age in bonds, buy-and-hold, 10 year business cycle

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