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June 18, 2009


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The problem is that MCS is based on a risk model where the future market returns are projected to be “normal.” Where in reality, market returns are far from normal because they are “uncertain.”

I think you are halfway there but do not yet have it quite right.

Yes, models that assume normal returns are dangerous.

No, returns are not all that uncertain. Long-term returns are predictable enough for effective retirement planning purposes.

I've done extensive research into the historical stock-return data re this question. What the data shows is that normal returns apply only at times of normal valuations. At low valuations, long-term return are far higher than normal. At high valuations, long-term returns are far lower than normal.

There has been academic research showing that valuations affect long-term return for 28 years now. I think it is a scandal that millions of middle-class investors are going to suffer busted retirements in days to come because of the demonstrably false claims made in the conventional retirement studies and calculators.


I don't think that's an accurate description of a properly designed Monte Carlo simulation. Most MCS programs assume that returns will follow a normal distribution, but that doesn't mean that returns will be "normal". On the contrary, it's the simulation of varying returns that allows MCS to say that an investor is 98% likely to reach his/her goals; if you just assume a certain return, then you will or will not reach your goal. A similar, though not quite MCS approach is used by FIREcalc, which uses historical returns (rather than random values) by asset class to make projections.

Oh god. This is so wrong. The author obviously has zero grasp of numerical techniques. His characterization of Monte Carlo techniques is so primitive its like watching a caveman urinating on a car battery.

I apply non-Gaussian Monte Carlo techniques all day long to finance problems. I can assure you we don't keep billions of dollars in play without more accurate techniques.

If you want to play at home then get, at the very least, something like @risk which is an excel plugin that does decent albeit basic Monte Carlo. And rest assured it offers non-normal probability distributions so that you can escape the curse of normality.

These simulation technologies work in the market until they don't. Just ask the Wall Street risk managers who used all types of probability distributions when evaluating mortgage related investments. They were thunderstruck and stunned.


Monty, you are off base. To someone who works in the business what you are saying sounds like "That long division stuff. Never did anyone no good. Them folks are using fancy talk.".

Many securities these days cannot be accurately priced without the use of techniques like Monte Carlo. We don't have closed form solutions for the vast majority of interesting options for example. No one really uses an untweaked Black Scholes as anything more than a convenient lowest common denominator for discussion these days.

One of the many things that went wrong with the mortgage backed securities, and more particularly the CDO and CDS instruments, was that essentially some fairly straightforward math was used to pull the wool over unsophisticated investors eyes. It was a bubble very much like the housing bubble itself. Everyone was buying and selling these things because everyone knew things just go up in price, right?

People were writing bonds with amazing sensitivity to housing price appreciation. Then using copula based models to claim they were triple-A bonds - the copula models were using CDS to calculate correlation. CDS data was available for about a decade, and was over a decade when housing prices were zooming up which meant the models spat out that default correlations were tiny. So the CDOs were worth a lot. There were plenty of people who knew this was dangerous, but, shockingly enough, there are lots of short-sighted greedy people playing in the markets. Heads of banks among them. And you'd be surprised at the lack of mathematical sophistication which lead people to actually believe some of the triple A nonsense.

The simulation techniques work just fine. They are simple and reliable. But, like long division, you put garbage in then you get garbage out. (And in fact, looking at your description, our in-house MC and MHMC based software would have no problems churning out simulations that match what you are talking about if we wanted to tweak parameters to match yours). If you don't want to use the techniques, then don't, but what you are claiming about them is just incorrect.

It seems to me that a widespread miscalculation of risk among sophisticated buyers is a more accurate description of what occurred. After all, the players who contributed to the buying frenzy were not only the Wall Street risk managers, but also academics (including Nobel Laureates), financial journalists, foreign governments, highly-regulated foreign banks, Freddie and Fannie, and so on. This long list of participants, with very few dissenters, tells me that the many sophisticated parties who do their due diligence were just wrong.

But going back to retirement planning and online calculators, I refer people to Dr. David Nawrocki’s white paper in the Journal of Financial Planning:

Also, a great book is Dr. Nassim Taleb’s NY Times best-seller “The Black Swan.”



You are confusing 2 things. Use of the Monte Carlo technique, and the creation of bad models which are evaluated using Monte Carlo techniques. As I pointed out in my previous reply, there were absolutely some bad models being used to 1) get a false sense of security and 2) pull the wool over people's eyes when it came to the soundness of certain investments. For example, the CDO/CDS fiasco was mathematical charlatanism to use enough greek letters to make people think the levels of risk were low. Monte Carlo simulation techniques were used as part of building the models but this was a case of feeding the techniques unrealistic data and not a problem with using such techniques. Monte Carlo is simply a mathematical technique that recalculates many different possible scenarios – but only within boundaries set by the user. I completely agree people mispriced the risk but that was an MC problem.

So for example, you can perfectly well use fat tail distributions to model extreme events - I know Nassim Taleb and have listned to many of his rants against the Gaussians - and I take objection to painting Monte Carlo techniques as bad just because some people use them with normal distributions and low correlations. I pointed to the @risk tool which uses MC. It lets you use a wide variety of distributions besides normal. Nawrocki is off base.

Do people build bad MC based models? Absolutely - I make my living taking their money. Can we build good MC based models? Yes - I make my living with them taking people's money. BTW, mostly we use pseudo-MC using low-discrepnecy sequences to speed convergence in fast trading models rather than pure MC but that's simply a runtime optimization to a first approximation.

A colleague pointed out to me that I should mention a couple of the books we have our college grads read to get them up to speed

Peter Jaekel's "monte carlo methods in finance" and Paul Glasserman's "monte carlo methods in financial engineering". Flipping thru the latter I see a chapter where he uses non-normal distrbutions.


My number one concern is the tens of millions of baby boomers using online retirement calculators for long-range financial planning. After completing a questionnaire that takes 5 or 10 minutes of their time and having the calculator run scenarios using MCS, they receive a sunny sky or cloudy sky picture with a number that reflects their likelihood of success. This method could wreak havoc on their retirement years and our economy.

People flock to these tools because they're quick and easy to use. And these people are sold on MCS being a panacea (e.g., they don't not worry about projecting things like their health-care premiums if they retire early because MCS shows that they are 98% likely to retire successfully). This is the way average Americans use this technology to plan for their future.

Thanks for your feedback and the book recommendations. I'll check them out.


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