Monte Carlo Analysis

Four Fools' Tools: #2 The Full Monte Carlo Analysis
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Modern Portfolio Theory | Beta Baloney | Efficient Frontier Analysis

Monte Carlo Analysis.mp3

Mindless Modern Portfolio Theory

First of all, if you are an investment advisor, do you mean to tell me that as bright as you are that you are simply going to open a software program that has some selective historical financial markets' data and a few algorithms, enter a little information, and then that you are actually going to have the nerve to look directly into the eyes of some hard working couple — who took years to accumulate their capital and who are depending on your investment expertise —and tell them, with a straight face and without a hint of a smile, the probability(?) of their reaching their financial objectives 10, 20 years down the road, just because some math professor from somewhere has said it is so?

Are you saying that with all of your financial background and all of your experiences in and knowledge of the knowns and unknowns of the financial markets of today and tomorrow, let alone years hence that you actually are going to participate in and rely on this insanity?

Felony stupid!

Numbers, math, and equations are the discovery, the explaining, the unfolding of apparent chaos, to demonstrate and to prove the order and connection of underlying cause and effect variable relationships in an effort to understand the present and to predict the future.

From very simple mathematical matters to the very complex of landing a man on the moon, numbers of the orderly universe are precise and the outcomes are a certainty, or a near certainty, because they depend on finite, actual variable relationships as found in the universe but seldom experienced in the financial markets.

Modern Portfolio Theory use numbers and equations, based on historical information and perceived/contrived investment relationships, as a means of explaining and predicting the probability of future investment outcomes.

Let's begin at the beginning.

Monte Carlo Simulation refers to its origin in Monte Carlo and the answering of the question of the probabilities of specific outcomes when rolling dice.

When you roll dice, you know with 100% certainty that either a 1, 2, 3, 4, 5, or 6 will come up on each die, but you don't know which combination of numbers will come up on a particular roll of the dice.

The probabilities of different outcomes can be calculated by determining how many different ways the same total number can be rolled with the dice. There are more ways to roll a total of 7 than any other total number when rolling the two dice. Therefore, 7 has the greatest probability of being rolled. As the total number decreases down to the lowest total, 2, there are fewer and fewer ways to roll the total number. Therefore, if you need a seven or six to accomplish your goal the probability of success is greater than if you need a 3 or a 2.

Monte Carloists apply the same concept to the financial markets; selected variables in different combinations and historical and projected ranges to predict the probability of investment outcomes.

After making their own "reasonable" and "rational" assumptions (whatever those terms mean in this context) about the plausibility of historical returns being repeated and projected returns occurring, after choosing all of the investment variables that might be associated with the causes of investment outcomes, after divining possible ranges for each of the investment variables, after excluding "unlikely" investment variable ranges, and after applying different combinations of chosen ranges to each of the investment variables, many iterations of "possible" investment outcomes can be created with the application of Monte Carlo Simulation.

Each of the lines in the illustration above represent Monte Carlo Iterations or Scenarios.

Simply count the number of outcomes out of all of the iterations generated that meet the goal, divide that number by the total iterations generated, and you have the percentage chance, the probability, the certainty that you will achieve your investment goal. Mr. and Mrs. Investor, you have a 65% chance of achieving your investment goal when you retire in sixteen years; bah, humbug!

If designing financial markets' models and simulations were, in fact, as simple as designing dice models and simulations, Monte Carlo Simulation would be very valuable as an investment planning tool.

The issue with regard to Monte Carlo Simulation is, how good is the number?

The answer, in my opinion, rests between not very good and probably a lot closer to not good at all.

The origins of the problems with Monte Carlo Simulation start with the fact that conceptual mathematicians, who like and only understand order and feel that everything is or can be explained and predicted with an equation, have attempted to apply the science and certainty of mathematics to the artistry and mysteries of the financial markets; Modern Portfolio Theorists would have had Van Gogh and Da Vinci paint and sculpt by the numbers.

Unlike the universe where there are underlying relationships and forces that are known, connected, predictable, and can be modeled for simulation, the financial markets infinite, changing variables and sometimes and sometimes not associated ranges in an environment of randomness and chaos without rhythm and pattern and without underlying, mathematically explainable and predictable order make it impossible to accurately, consistently, and reliably model and simulate the behavior of the financial markets.

Structurally, Monte Carlo Simulation depends on a thorough knowledge of the nature and design of the driving variables in order to create a coherent model.

Gambling dice have an absolute number of variables (two dies) and each has a finite range (1-6). There are, absolutely, a finite number of outcomes with different frequencies and therefore a model can easily and accurately be designed and the integrity of the simulation assured.

Monte Carlo Analysis Stock Market dice change with every roll. The number of dies is always changing, the shape of each die is always changing (sometimes six-sided sometimes twenty-sided), the number of numbers changes as the number of sides on each die changes, and the frequency of numbers on each side of each die is always changing.

Therefore, as one moves from predicting the probability of outcomes on the roll of Monte Carlo dice to predicting the probability of outcomes with Monte Carlo Analysis Stock Market dice, the probability of correctly predicting outcomes greatly decreases.

The application of Monte Carlo Simulation to investment outcomes is also empirically absurd because anyone who has spent more than a mini-moment investing and advising knows that projecting investment outcomes in the short term is difficult and for the long term impossible.

To resolve these problems Monte Carlo Simulation must simplify and compromise the outcome prediction process by inputting software programmer selected stock market variables and chosen associated variable ranges in an effort to structure Stock Market dice more like Monte Carlo dice and, therefore, creating possible investment outcomes that may, in fact, never occur again and, worse yet, programming incorrect answers to current investment questions about the future:

Using "reasonable" and "rational" assumptions to filter out improbable Monte Carlo Iterations is a distortion of investment risk, uncertainty, volatility, and probability because it incorrectly presumes that "improbable" will not occur.

It is also impossible to conceive of and program the infinite iterations that can be generated in the financial markets. For this reason it entirely possible and certainly probable that a Monte Carlo Simulation program may not even have today's or tomorrow's actual and potential iterations installed and therefore the probability of success computed by the program may be very different from the probability of success found in current and future market conditions.

The frequency and duration of each iteration is not calculated and may produce misleading results.

Monte Carlo Simulation, when trying to understand the driving variables of the financial markets, is exposed to a dilemma:

Assume there appears to be but one stock market variable, let's say a quarter, and it appears to have but two ranges, heads or tails.

If historical data showed that the quarter had been flipped six times and "tails" had shown up five of the six times in the past, then a Monte Carlo simulation programmer would be faced with concluding that either the initial understanding of the variable was incorrect and that it actually has more ranges, possibly with six sides of five tails and one head, or that the variable, in fact, has but two sides as initially concluded, and that for whatever reason, not understood, in six tosses of the coin, tails came up five times .

The point, unlike an observable variable in an assembly line process, the answer is not known and however the Monte Carlo Simulation is programmed, the answer will be either absolutely wrong because the variable is not understood or distorted with bias to reflect historical occurrences; "The market has done this the most in the past therefore, it is most probable the market will do this the most in the future," or worse yet," It would now appear that past performance is an indicator of future results."

The value of the "The Probability of Success" as predicted in Monte Carlo Simulation is also distorted by not taking into account the different investment risks associated with the underlying investment of the iterations generated by Monte Carlo Simulation:

Assume that because of the amount of capital currently held by an investor and because of the investment goal of an investor, very little growth of capital would be needed in the selected time frame to achieve an investor selected investment goal.

Assume that a Monte Carlo Simulation generates 1,000 iterations.

Each iteration is composed of varying combinations of underlying investments; for example, conservative, aggressive, and speculative.

Because of the investment requirements of the investor, Monte Carlo Simulation would project a high probability of achieving the investment goal.

Some iterations, with underlying aggressive and speculative investments, would meet or exceed the investment goal and some iterations of underlying conservative investments would not meet or exceed the investment goal.

Monte Carlo Simulation fails to distinguish the underlying structural investment risks of the underlying iteration investments; understanding that either can be mismanaged, bonds are generally more conservative than equities or blue chip equities are generally more conservative than speculative equities.

An advisor, knowing that some qualifying iterations are more conservative/risky than others, could, unnecessarily, choose a more risky investment path.

Therefore, the reliability of the predicted probability of success may be further compromised depending on which investment path is actually taken.

Therefore, a high probability of success projection is neither helpful, nor meaningful, nor reliable.

Monte Carloists often explain the concept of Financial Markets Simulation using a weather analogy and concluding that it would be helpful, meaningful, reliable, and comforting for an investor to know the probability of an investment outcome as one would want to know the probability of rain so as to make a decision as to what to do depending on an expected activity:

The problem in making a comparison with the weather and the financial markets is the same as comparing Monte Carlo dice with Stock Market dice. The variables that cause different weather patterns are finite and known while the variables that cause different investment performance outcomes in the financial markets are not finite and are not all known.

Certain combinations of weather variables will cause rain. Therefore, the probability of rain can reasonably be determined.

Furthermore, the same combination of variables, unlike rain causing variables, can be combined exactly the same way many times and the outcomes will often be very different. When rolling Weather dice, a combination of a 2 and a 5 will always mean a 7. When rolling Stock Market dice, a 2 and a 5 can mean a 7 and sometimes a 4, and other times a 6.

Monte Carlo Simulation is further remiss in not pointing out to investors that a greater probability of rolling a 7 does not mean that the 7 will be rolled in a given time frame. In a game of craps or in the game of predicting the probability of outcomes in the financial markets it is entirely possible that a 7 will never be rolled within the game time frame.

Monte Carlo Simulation has further problems in that the same input entered in different programs will give significantly different answers. An article by Bennett Voyles in Registered Rep., July 1, 2002 confirmed my experiences when he entered the same data into three different Monte Carlo Simulation programs to obtain simulation projections: Financialengines.com 29%, mpower.com 43% and financeware.com 62%:

Monte Carloists like to infer that Monte Carlo Simulation can be used as an indicator of the level of comfort an investor should have about achieving an investment goal:

Using probability analysis to measure investor comfort may be appealing, but it is absurd.

The more that is known about a process, the better the simulation and the better the forecast.

The more stable the variables and the more known about their ranges, the better the forecast.

The more there is a connection between cause and effect of the variables and their ranges, the better the forecast.

Monte Carlo Simulation, for the financial markets, fails on all points.

Monte Carlo Simulation merely creates its own virtual, presumed, reality and, therefore, its own conclusions which may or may not be a representation of the process of the financial markets.

Investment comfort can only be responsibly measured based on the types and the mix of the investments held in light of investor goals and current market conditions and not as measured as a number generated by the programmed contrivances of Monte Carlo Simulation.

Monte Carlo Simulation, as it applies to investment projections for retirement analysis, concludes that standard spreadsheet analysis, on the other hand, is "misleading, deterministic, and unreliable" for projecting investment outcomes. Monte Carloists would say that spreadsheet analysis:

"Typically uses single or a few interest rates, inflation rates, and growth rates to generate a limited number of possible investment outcomes when applied to capital and time."

Historical data and information is the fools gold of investing.

Actual and projected interest, inflation, and growth rates based on knowledge and experience versus many historical interest, inflation, and growth rates programmed in a simulation? Seems to make sense to me.

Will only reveal a single outcome, generally the most likely or average scenario."

"The most likely or average scenario?" What could be better?

"Incorporates only a few average variables and the use of only a few ranges associated with each variable and, therefore, may not properly assess investment risk, uncertainty, volatility, and probability."

Incorporates only a few average variables and associated ranges? Yes, those that the advisor would deem to be most likely.

Rather than create one or a few iterations (scenarios; strings of events creating different outcomes) to rely on, there are in fact many possible iterations of investment outcomes that need to be considered with the intent of finding investment danger where it did not seem to exist before."

"Investment danger" is for the investment decision maker to fail to distinguish between unlikely, possible, and probable iterations of investment outcomes, therefore diluting the quality of an investment outcome projection and misleading the investor as to the probability of achieving the investment goal.

"Does not indicate the probability of an outcome."

The probability of an outcome will be directly related to the quality of the investment selection and portfolio building and managing process.

"Does not properly account for "average return."

The Implied weakness of spreadsheet analysis, of not clarifying the potential and the probability of having a wide range of total returns depending on the variance and sequence of period returns that comprise an average rate of return, is a semantics sidetrack that has nothing to do with determining the investment goal.

The problem is not over failing to properly account for the variances in total returns that different period returns can cause, but in failing to distinguish between the uses of the terms "average rate" and "constant rate" of return.

Whatever the term and whatever the definition, "average rate of return" (actually constant rate of return) is the industry standard for investment performance comparisons in presentations and illustrations.

Obviously capital growth with a constant rate of return and therefore with the same average return will be different than capital growth with a variable return that has the same average return as the constant rate of return.

Confusion can only result from the users misunderstanding of its' mathematical calculation versus its' conversational application.

Single iterations used in spreadsheet analysis properly assumes a constant rate of return rather than an average rate of return simply to communicate with the client in an effort to establish the investment goal in terms of future dollars; "In order to achieve your investment objective of $1,000,000.00, $500,000.00 starting capital would have to grow at 10% (constant rate of return) over the next seven years."

Use of a constant rate of return to determine the investment goal does not imply that the actual growth of capital in the financial markets will be constant.

Making that statement does not imply ignorance of the variance of returns or the impact that variance can have on total return.

All anyone wants to know is: "What do we have to do and what do you (advisor) have to do in an effort to achieve the investment goal?"

Monte Carloists say that simulation will give the odds of achieving an investment outcome.

Spreadsheetists will use what would seem to be today's single best iteration and will say that each day's market will reveal the odds of achieving an investment outcome.

"The full spectrum of possible investment outcomes may not be fully disclosed with static spreadsheet analysis. The investor may be misled as to the probability of investment success and the possibility of investment failure."

The number of possible investment outcomes is not known by anyone.

Furthermore, Monte Carlo Simulation limits the number of possible investment outcomes as set by the assumptions installed in the Monte Carlo Simulation program.

Which method is best?

Monte Carlo Simulation generates a million guesses of possible investment outcomes based on the past and projected behavior of investment variables to make investment decisions today for the investment future.

Spreadsheet analysis generates a few, simple, straightforward iterations with a few variable and range assumptions based on current and expected market conditions.

Regardless of which technique is preferred both analyses are merely "what if" investment planning starting points comprised of many user created assumptions and guesses.

Assumptions and guesses for both analyses are further diluted the farther out in time the analyses projects outcomes.

Neither one should be relied on as a means of projecting the future but rather as a method for defining the investment task at hand to achieve a future investment objective. Is that a bump in the road or Mount Everest in front of us?

Keep in mind that neither one of the analyses gives you the actual investment trail.

The moment will still come when a very specific investment course must be plotted and a very specific investment iteration must be chosen.

Investment probabilities and investment outcomes cannot be found in or divined from the investment past. Actual vs. projected capital contributions of the investor, the investment task at hand, bump in the road or climb Mt. Everest, the types of investments required, more treasury bills than equities or more equities than treasury bills, the investment time frame, months, a few years or many years, the behavior of the financial markets, good or bad and for how long, and the investment skills of the investment decision maker determine the probability of achieving an investment goal:

The best guide is easy to pick out. He or she will be using binoculars not a rear view mirror to find the way.

Use a guide that will give the most precise and most direct investment directions.

The best chance of getting the best results is to rely on a specifically selected and defined single best investment target iteration.

This single best investment target iteration, as defined by the defenders of Monte Carlo, would be the "most likely scenario."

Secondary iterations may be considered and would include best and worst scenarios above and below the target iteration that would seem to be responsible possibilities defining the extremes of possible investment outcomes for the current time.

All iterations should be based on an educated guess as to which and to what extent investment outcome variables will play a role in the investment future.

With the passing of time, and to remove the possible misleading impact of using averages, periodic adjustments must be made to the single best investment iteration to reflect differences in projected verses actual investment results and changes in variable ranges based on current and anticipated market conditions.

Adjustments must be made for additions and withdrawals of capital and changes in investment goals with the passing of time.

Think of all financial planning analysis as much like a race; the Indianapolis 500 for example.

At the start of the race, take all the current variable information available: track, weather, driver, and general race conditions etc. Select probable ranges for each racing variable based on what is presently known and observed. Use this information to tune and set the car up as best as possible with the hope it will perform well in the current, fluctuating conditions. As the race is in progress, take timely pit stops to make adjustments and then proceed as best as is possible. The results will depend to some extent on uncontrollable variables that cannot be anticipated, but the pit stop adjustments will provide the best chance of achieving the goal of winning.