Think
about it: 'Past
investment performance is not an indicator of future investment results' is a
required, responsible, and absolutely true investing footnote, an
investing fact that anyone who has spent more than a nanosecond in the financial
markets would or should know, and an investing law designed to protect the investing
naive, innocent, and unsuspecting. Then
why would one blindly place his/her trust in the present and his/her hope for
the future in a mythical investing science — Modern Portfolio Theory and
all of its illegitimate relatives
such as Monte Carlo Analysis, Efficient Frontier Analysis, Beta, Brinson's
Asset Allocation, Pie Charts, and a distant relative, Technical Analysis (worth
a glance) —
that relies solely on past performance investment data to feed hypothetical and
contrived investing algorithms in a misguided effort to predict future investment
results? All
are just other ways to record and to illustrate investment history without valid
analytical, interpretive, deductive, predictive, or directional investment value.
If
this nonsense were valid, there would be no need for investing analytics, forecasting,
or guidance of any kind — research, analysis, opinion, advisors — and
one would simply select investments based on past performance without regard to
suitability, quality, structure, or risk. Explained
another way, a thermometer measures temperatures in degrees as the weather changes.
A thermometer is a recording device not a forecasting one and, therefore,
it cannot be used to predict future temperature levels. Standard
Deviation, Efficient Frontier, Beta, VaR, and Sharpe Ratio are much
like a thermometer; merely means to measure past (contrived) relative investment
performances between investment variables and neither the cause of nor the predictor
of either. Furthermore,
if a thermometer also happened to store prior temperature readings on a daily
basis, you certainly would not retrieve that information and use it to predict
tomorrow's or next week's temperature readings. As
one would have to analyze the weather-changing causal variables that affect weather,
such as humidity and barometric pressure, to predict future temperature levels. The
same holds true for historical Standard Deviation,
Efficient Frontier, Beta, VaR, and Sharpe Ratio readings
as a basis for predicting the investing future. Future
investment values and associated investment/investing risks can only be meaningfully
understood and predicted based on one’s correct understanding and interpretation
of the fundamental performance changing, causal investment performance variables
that actually affect an equity’s behavior. Keep
in mind, there
is no theory — modern or otherwise — that can be ordained, no computer
that can be programmed, no software that can be designed, no investing tool that
can be 'imagineered,'
no technical analysis voodoo methodology that can be contrived, and no equation
that can be divined to quantify, evaluate, and predict the primary forces that
drive the sublime chaos of the financial markets and investment prices; human
consensus, mood, and behavior; intelligent and not, knowledgeable and not, reasoned
and not, rational and not, and logical and not. |
Monte
Carlo Analysis 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 below 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.
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 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.
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."
- 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. |