As you can read below, we're not a big fan of Monte Carlo simulations. But people kept asking for it, so we implemented it into the Integrated Financial Planner, all versions of our retirement software, and both college planners.

They all use a superior methodology of simulating Monte Carlo compared to other financial plan software vendors. The reasons why we're not a big fan are detailed below, and some of these shortcomings are negated by the way ours is programmed.

The vast majority of other retirement planning software uses Monte Carlo to just randomly fiddle with the rate of return on the inputted investments, to give you a bottom-line probability of success number. Ours also fiddles with inflation and taxes at the same time (except for RP, SRP, and the free retirement calculator, which doesn't do taxes).

Why We're Not a Fan

Monte Carlo simulators, and/or software, DOES NOT DO ANYTHING to overcome financial market volatility. It will NOT help you when it comes to losing money you invested. It will also NOT help you retire earlier, nor will it keep you from outliving your retirement investments.

What will it do that is actually useful to your life - not much of anything!

What Monte Carlo Is

Monte Carlo is a city in Monaco that's famous for gambling, more specifically, roulette wheels. The ball rolls around and it lands on a number on the wheel at random. That's how this kind of software got its name - the investment rate of return used in each iteration of the simulation is random. Mystery solved.

The first Monte Carlo simulations took place designing the first atomic bombs at Los Alamos Labs, NM, in the 40's. They needed to simulate thousands of different random outcomes of the detonation, so they used random inputs into a complex computer algorithm as a way of doing this. It worked very well.

Monte Carlo in computers (sometimes) use random input numbers to form models for assessing risk (the probability of a bad financial outcome). But in the context of financial plan software, Monte Carlo refers to the randomness of the input data from the simulator's point of view.

It's good for use in modeling portfolio losses and unexpected losses when pricing options and other complex derivative securities.

For example, say a stock analyst wants to forecast earnings for a company. Analysts will input many criteria into the modeling software program, and give it a target EPS (earnings per share) number - say $1.00 per share. The computer will then come up with an EPS number based on that input.

Since there can be dozens of inputs to get the EPS number, and all of these inputs can vary within a range of what's reasonably expected to happen, it would take a person an eternity to input all of the variations within the range of possibilities. Now computers can do it in milliseconds. So Monte Carlo was adapted for business applications like this (mostly by Hertz in 1964).

You've just started to hear about it in the 21^st century because computers have just recently become powerful enough to do the jobs. A simulation on a 486 computer would literally take days to calculate all of the outcomes, then another day to plot the probabilities from these outcomes.

Since it's practical enough to market now because of fast computers, what you have is Monte Carlo added to everything under the sun to make more money selling financial software. Then you got the usual self-reinforcing academic articles to let people know programs are on the market (how to buy now). So a new mini-academic-fad was born.

What you need to do is realize what Monte Carlo is, what's it's good for, and what it's not good for. Just because it sounds cool, spends a lot of time computing, is being heavily advertised, and used by other fields of finance doesn't mean it will do anything of value for you or your financial planning and/or investment management clients. Like the old saying goes, "Just because you can doesn't mean you should, or you have to."

It's basically a gimmick used to raise a vendor's flat / falling financial planning software sales. You're hearing about it because it's relatively new, and there's really no other news to report in the world of boring investment software.

Let's go back to our example. Say the stock analyst is using real Monte Carlo software and wants to calculate the probabilities of EPS being at least $1.00.

If one run (one computer iteration based on one set of Free Cash Flow input) comes up with $0.99 of EPS, that would be a false outcome (because it needs to be at least $1.00 to be a true outcome). This one iteration would create one statistical data point with a 0% probability.

Now let's say that the next FCF input is set to $1,100,000 and another run is made, EPS is computed to be $1.01, and a true outcome is logged. Adding these two iterations together, the probability is now 50% of getting EPS of $1.00.

Instead of incrementing FCF up a notch each iteration, and re-running the simulation, each iteration is input as an input number selected at random by the simulator.

This is all Monte Carlo does. The program allows the user to set iterations and ranges for each input (some just use random numbers within the specified range, but there's so many iterations that essentially all variables within that range are simulated, and duplicated many times too).

For example, the user may tell it to make 100 iterations on the FCF input field - starting at $950,000 and increasing $1,000 until it gets to $1,050,000. So the program runs the first one at $950,000, and logs a true or false answer. Then it runs the next one at $951,000, and logs a true or false answer. It does this 100 times up to the last value of $1,050,000. The results make a log of true and false answers, and all that's needed to construct a probability distribution curve. This will then give you a bottom-line answer like, "You have a 73% chance of getting EPS of $1.00 given these ranges of FCF input parameters." All this means is 73% of the outcomes were true, and 27% were false.

This is what it is. There's no magic, no crystal ball, no more mystery. It just saves the user from having to manually input thousands of different combinations of data, by doing it automatically.

True Monte Carlo programs allow you to set iterations and ranges for dozens of input values. As you can see, the computer could run the same simulation millions of times with one set of input. This is why it's so slow, and why only newer computers can do it.

Now let's get back to personal financial planning software. Most vendors that use Monte Carlo use it in their retirement planning software. The most-common use is to see if a fund of money will last until some assumed age given an assumed rate of return.

It just runs numerous iterations with various random investment rates of return. This then gives you a bottom-line probability based on all of the true and false outcomes.

The problem is that it doesn't let you set the number of iterations, nor the range of assumed values. It just makes all of this up for you based on what the vendor wants (which has little-to-nothing to do with what will happen in the Real World).

Another enormous problem is when it's married to a database of historical returns, which allows you to select a prior time frame's rolling ten-year return data (like NaviPlan). When you can go way way way back in time like this, To a period so foreign to our current reality that it's like being on another planet, this increases the end probability number by 5% to 10%. So you're telling people their plan has X% probability of success, when in reality, it's up to less than half as much. This is because if you just let it use Ibbotson stock market return data going back to 1926, it's going to be using rates of return that are twice as high as you'll actually see these days. So if you do that, then it will be iterating annual average annual rates of around 9% to 12%, when you know the probable band of 10-year average rolling returns nowadays have been permanently lowered to around 5% to 8%.

So this is an example of a Monte Carlo simulator being allowed to run amok like a wild animal, just like a portfolio optimizer. You think you're doing the "right thing" for people by using the very longest averages possible, but it turns out that this is moving your plan from reality into fantasy land, and this is not serving anyone well. Just the opposite - you're setting people up for a major life failure.

When a very simple sample financial plan was input in the IFP, and the same data input into NaviPlan - the IFP's Monte Carlo number was 17% and NaviPlan's was 31%. So let's say that their number is 5% too high just because of using dangerously optimistic returns, then 2% of the difference is from NaviPlan not iterating inflation, and 2% from not iterating taxes, 2% is from the egregious errors in the way their assets accounts for cash flows, then the rest is just from the combination of all of these rosy scenarios compounding upon each other.

So that's why NaviPlan's bottom line Monte Carlos probability numbers are so rosy sky high. So it tells people their chances of plan success are twice as high as they really are, on top of it projecting their plan will last two years more than it probably will (because of the egregious errors in the way their assets account for cash flows). And this is NaviPlan, the "industry leader" with the "best calculation engine." Then when you get to the MoneyWhatevers, they don't even care nor even try to be accurate, as their software is mostly so "fake" that they should just be banned by FINRA altogether.

This makes it all virtually useless, because you're relying on a probability number based on only one factor (the average rate of return on investments).

In order to properly use Monte Carlo in retirement planning, dozens of inputs need to change to reach a Real World probability - age, age of retirement, investment payouts, investment returns, inflation, income goals, Social Security, taxes, pension payouts, duplicate all of that for every investment individually, then for the spouse, and the list goes on and on.

No personal financial planning program on the market today is true Monte Carlo because none give the user the ability to control the input ranges and/or set the number of iterations for even the few most critical input fields. This is because vendors don't feel customers have the required attention span to do this kind of tedious work, they won't spend that kind of money on the simulator, then won't wait literally days for the results to compile. Advisors don't have that kind of time to spend on generating retirement plans - they whine now when Dual RWR takes half an hour.

This is the bottom-line people should keep in mind - it's not near as cool as one is being led to believe (because its application is limited to as few as only one variable, when it should be applied to several at the same time). Only our financial plan software uses more than two of these variables at once.

When Monte Carlo is used in asset allocation (or anything having to do with predicting investment returns), the proper name for it is "portfolio optimization." So if you're reading that some new slick asset allocation / investment program has Monte Carlo, it's really just someone slapping the Monte Carlo name onto on old-hat portfolio optimizer to increase sales.

Empirical Criticism of Monte Carlo by People In-the-Know

Registered Rep article about the drawbacks of Monte Carlo

Mark Kriztman, CFA, well known author in the financial planning and investment management field, found a major flaw in most all vendors using Monte Carlo in their software. He wrote about the fact that at the end of each year, their software reverted to the base number instead of "continuing from the trunk of the same tree," which is what happens in the Real World.

For example, let's say that you input a 10% base annual rate of return, and you tell Monte Carlo to use a range of ±20%. Its worst-case iteration is going to be a -10% rate of return (+10% + -20% = -10%). So it uses -10% in its last iteration path.

But instead of continuing the next compounding period at -10% where it left off, it reverts back to original base truck rate of +10% in the next iteration. For example, if the next iteration is +2%, then the correct rate of return applied should be -8%. But it resets itself, using +12% instead. This is not correct.

You're totally neglecting the fact that you can have more than one year in a row with huge negative investment returns. So in the Real World, you can easily lose 85% more money than the worst case iteration shows. This also dramatically understates actual volatility. Just this flaw alone makes results from retirement software with Monte Carlo meaningless.

So the bottom-line is that Monte Carlo usually does not do the main function that it's hyped up to do - which is to create an end result probability number based on all of the best and worst case scenarios. It compounds all of the positive returns just fine, but ignores compounding of negative returns. This is bad and useless in the Real World when it comes to retirement software.

This is also why our simulation results show a much lower probability number than you may be used to seeing.

No other vendor has yet to overcome the tree-trunk problem, nor allows the user to control or vary the inputs enough to make Monte Carlo worth much, yet. Some day, when computers are about 100 times faster, this may happen.

Now why the huge number of iteration runs a program simulates doesn't matter:

Let's say, for example, that a Monte Carlo run generates a simulated ten-year list of returns like this:

8%
-2%
6%
10%
-3%
-1%
5%
11%
-8%
-1%

The average annual compound rate of return over this ten-year horizon would be 2.32%. The program used up ten iterations to do this. This could have been done in one iteration of 2.32%. So even if the tree trunk problem was solved, the average over the long haul still can be summarized in just one iteration.

So don't be impressed when a vendor claims its Monte Carlo is superior because it can have 10,000+ runs. All this is going to do is make it take an eternity to run (hours). Over 80% of them are just randomly generated duplicates. This is why generating an enormous array of random numbers is not needed. It is in scientific work, but not in financial planning.

Also don't be impressed when a financial planning software vendor says that their Monte Carlo simulator uses historical standard deviation of an asset, or portfolio, when determining the ranges of returns used. Historical performance (returns, standard deviations, or covariances) has little-to-no predictive ability. The only guarantee is that what happened in the past will not happen in the future. This is opposite of what these simulations project. The long-winded version of why historical performance isn't a good predictor of future performance is at the end of the portfolio optimization page.

The bottom-line is that not one of these things (sigma, beta, Jenson, Treynor, Sharpe, etc.) has any predictive value whatsoever. It's interesting to see what these stats have been in the past on whole portfolios, and/or on individual assets, but NONE of them have any consistency at all. If they "flop around wildly all the time at random," then they are TOTALLY USELESS in making any future predictions. If they did have any predictive value, even just a little bit, then we'd have been using them over a decade ago.

As one should know, all of this "backtesting" has little-to-no predictive value because financial assets respond randomly to complex sets of financial variables, which are traded by humans that have diverse reasons for trading, none of which can be predicted by anyone nor any computer software program.

So the best way to run simulations is to just make a range of most likely outcomes, then just iterate down the list in reasonable increments. This eradicates the duplicates, and greatly decreases the wait times.

There also is little-to-no difference in 2.32% and 2.3% when it comes to successes or failures in retirement software. So rounding things down to one decimal place will also eliminate a significant number of useless iterations.

This is what we did. We eliminated most all of the duplicate iterations so it will run a lot faster (it's still very slow) and give results that are more meaningful in the Real World at the same time.

For example, we use a worst case -15% annual rate of return. This is similar to what would have happened if you bought the DJIA at the top in 1929, saw 89% of your money disappear at the beginning of 1933, then got 11% from 1933 to 1939. Also from 1/1/1926 to 12/29/1950, the DJIA was only up 2% annually.

So as you can see, losing 15% annually for ten years, or getting returns less than inflation for 25 years, is a reasonable worst-case scenario. So this is how our Monte Carlo simulations work. We feel this is a much better methodology than other vendors that use things like iterating from -100% to 100%, using historic standard deviations, and other scenarios that will have an extremely low probability of ever happening again.

So the range of returns are iterated from -15% to +15% in 0.1% increments, with one set of tax and inflation rates. Then this is repeated using two other tax and inflation rates.

So don't get all excited about Monte Carlo programs being added to personal investment software - it's just marketing at this point.

This is great stuff for corporate finance people, or stock analysts, because they need it and will pay software vendors the big bucks to make real Monte Carlo software. But this is just not so for financial planning for Real World people, yet.

Here's why our financial software even without Monte Carlo does one better than even the most expensive retirement software with it: You can change what you think the investment's rate of return will be in every year - before and after retirement. So you can illustrate any kind of market environment you want, solve the tree-trunk problem by just inputting back-to-back years of negative returns, AND have control over all of the other details of someone's life at the same time. In addition to that, it has a better Monte Carlo capability then everyone else. So you can compare these two ways of doing things.

This is something that no other program can do - especially including any retirement software with Monte Carlo. The only thing you get with Monte Carlo is a mostly useless probability number. Ours does that too,

Then by using Excel's built-in Goal Seek function, you can also easily solve for the minimum rate of rate of return on all investments to reach the retirement goal. This is even more valuable than simulation results.

The reason it's mostly useless, is because none of these programs account for all of the important details of someone's Real World situation.

Because it takes so much calculating power, everything is stripped down just to get the mostly useless probability number. What's useful (in retirement planning) is knowing how well off you'll be off in terms of comparing how much money you'll want to spend with how much money you can get, and/or how long it will last, compared to how long one expects to live.

Knowing what will most likely happen with these factors over time (given the assumed fluctuations in the markets - which you can control every year by using different rates of return on every investment for every year - including negative rates of return, and being able to change your income goal every year) is much more important to show than a probability number to a real person's life.

So don't be taken in by Monte Carlo because some big-shot financial guru (e.g., William Sharpe) is touting it (by spending small fortunes on advertising). They're just trying to get investors to buy more of their software.

Some more points and limitations about Monte Carlo simulations:

• It assumes the generated statistical distributions are normal, and they're not.

• It assumes correlation coefficients are zero (or one), and they're not.

• The results are still dependent on assumed input ranges and iterations (which cannot be defined by the user).

• Return inputs are not linear. They go up and down at random over the input time frames.

• Inflation, asset class returns, taxes, and most everything to do with money (sigma, beta, Jenson, Treynor, Sharpe, etc.) cannot be predicted from historical data. Then iterating standard deviations has no value whatsoever.

So even though it's interesting, and has promise someday, it's not Real World, and is virtually useless in today's financial planning and investment management businesses. Even ours is semi-useless, but it's what customers want, and "they're always right"!

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