How Monte Carlo Simulation Gambles with Your Retirement

Kristin Novotny, AIF, CRPS

Darrin Farrow, AIF

2011

Preface

What is Monte Carlo simulation and how is it important to planning your retirement?

Have you ever dreamed of what your retirement would look like? Perhaps you picture yourself

on a European adventure. You sojourn along the Mediterranean, starting in Barcelona, Spain,

enjoying the excitement of its culture and then make your way into France with a stop at the

Eiffel Tower, of course. Your travels finally lead you to Monte Carlo in Monaco. Monte Carlo,

the mecca of casinos and luxury.

So many of us have a dream of retiring and spending our time in relaxation and respite at a

place like Monte Carlo. Unfortunately, using Monte Carlo simulation to help invest for

retirement may not land you in Monte Carlo.

The following white paper will analyze Monte Carlo simulation, the engine that drives almost all

401(k) advice software solutions. In it we will look at how Monte Carlo simulation is currently

being utilized in the retirement industry; we will show you the research being done that depicts

the shortcomings of Monte Carlo simulation; and we will uncover a forward-thinking approach

to retirement that could land you at a Monte Carlo casino while others spend their planned

retirement years working.

History of Monte Carlo Simulation

Monte Carlo simulation was originally developed in 1946 by Stanislaw Ulam as a means to

predict the probability of winning a game of solitaire. The term “Monte Carlo” was coined by

Ulam and his partner, John von Neumann, referring to the Monte Carlo Casino in Monaco.

From solitaire, Monte Carlo simulation became widely utilized in the areas of physics,

chemistry, engineering, biology, statistics, research, and games. The basic principles and

concepts behind Monte Carlo simulation were helpful in the development of the hydrogen

bomb in the 1950s, and the method became heavily supported by the US Air Force. Basically,

these two men created one of the fastest statistical methods to predict the outcome of

occurrence.

For investment purposes, Monte Carlo simulation uses historical data to predict future

outcomes. Based on the past performance and variations of asset classes, Monte Carlo

Simulation runs the probability of achieving a desired return and gauges the risk of returns that

are worse. A range of outcomes is determined and advice is given to investors based on the

average of those outcomes.

Monte Carlo simulation has since become a tool to assist, or in some cases, replace a financial

advisor, especially in the 401(k) market. For example, an advisor who is servicing a dozen plans,

with an average of 100 participants per plan, or 1,200 participants, may recommend a Monte

Carlo-driven solution to best leverage his or her time.

Lawsuits, fear, and the ever-changing economic environment have plan sponsors demanding

that advisors provide education or service to each of their participants.

The growing access to technology and the use of the internet in our daily lives have made

investment advice readily available to participants. Many online software programs have been

developed as a solution for participants needing guidance.

Using the Monte Carlo simulation method, these programs attempt to calculate how much

money a participant needs to save in order to meet his retirement goals, the probability of

meeting that goal, and how he should invest that money in order to achieve these goals.

Problems with the Monte Carlo Method

"You can't do well in investments unless you think independently," said Warren Buffett. "And

the truth is, you're neither right nor wrong because people agree with you. You're right

because your facts and reasoning are right. In the end that's all that counts. And there wasn't

any question about the facts or reasoning being correct."

While online retirement education and advice tools have become popular among advisors, plan

sponsors, and vendors, how effective are they? Monte Carlo is a backward-looking approach to

investing; it simulates the past instead of focusing on the now and looking forward.

Monte Carlo, overwhelmingly so, does not recommend professionally managed portfolios; it

uses only asset classes available in a plan’s core lineup, excluding many non-correlated asset

classes being used by top money managers. This process leads to a flaw in design that is then

multiplied by the Monte Carlo simulation, leading participants to make investment decisions

that may not be appropriate for them, given their desired outcome.

Popular software programs utilized by advisors, plan sponsors, and record-keeping platforms

today include Financial Engines, Mastery Point, Guided Choice, and many others. Each of these

programs uses Monte Carlo as the engine analyzing the past in order to predict the future.

Although "history repeats itself" is a familiar saying, this axiom does not hold true for the

vagaries of the financial market.

One cannot move forward safely if using only the rearview mirror as a guide. Unfortunately,

this is the approach that most consultants/record-keeping platforms are providing to plans and

their participants.

When a plan sponsor provides guidance that does not take into consideration the current

economic environment, he or she is, in essence, gambling with participants’ retirement

accounts. If participants knew how to play the market, then they would be working on Wall

Street. Instead, they trust their plan sponsor to provide them with the correct tools to help

them invest.

Frank Sortino is most famous for the development of the Sortino Ratio, a method used to

calculate downside risk. In a 2005 article criticizing Monte Carlo simulation, he states:

This application of [Monte Carlo simulation] confuses a procedure for generating a probability distribution with a methodology for estimating risk. It equates risk with the probability of a bad outcome. Probability is only one component of risk. There is a magnitude component as well. An investment strategy may only have a 10% chance of failure, but like Long Term Capital Management, failure could result in financial disaster.

Standard deviation is a probability weighted function of returns about the mean. Downside risk is a probability weighted function of returns below the required return (RR) an investor needs to accomplish his or her goal.

[Monte Carlo simulation] assumes the individual’s RR is irrelevant. Therefore, all investors agree on the degree of risk for all assets. In terms of a Fishburn utility function, investor’s who make their decisions based on probabilities of a bad outcome are risk takers and the exponent in equation 1 is equal to 0. Behavioral finance shows investors tend to ignore a very small chance of a very bad outcome. Thus, they become risk takers for events like the dot com bubble. Thus, it would seem that the way Monte Carlo simulation is used supports a flaw in the decision making ability of investors that leads them to buy into bubbles at the top.

At least value at risk assumes the exponent in equation 1, is equal to 1. In which case, investors are risk neutral and their utility function is linear below the RR. Risk neutral investors believe losing all their money is only twice as painful as losing half of it. Firms that use Monte Carlo simulation focus on the average return and standard deviation when evaluating managers or determining the asset allocation.

In his article Is Financial Monte Carlo Dead? Allan Roth of CBS Money Watch writes that it is not

the concept of Monte Carlo that is bad, or even the formula, but what is being inputted into the

system which produces the inaccurate results. In talking about the questionnaires using Monte

Carlo simulation, he points out "that roughly 99 percent of those are using assumptions that

only exist in a fantasy world…[I]t’s not the Monte Carlo simulation that’s flawed, but rather the

garbage that is input into the simulation. Put another way, 'garbage in, garbage out'.”

In The Wall Street Journal, Eleanor Laise wrote, “There is little chance your Monte Carlo

simulation, named for the gambling mecca, would have highlighted a scenario like the market

slide just seen. Though these tools typically run a portfolio through hundreds or thousands of

potential market scenarios, they often assign minuscule odds to extreme market events. Yet

these extreme events seem to be happening more often.”

She continues in her 2009 article to reiterate what Roth posited in his article, that she is not

criticizing Monte Carlo simulation, but the data inputted into the simulation. It is an

appropriate tool for some industries, but not for an industry with so much unpredictable

volatility.

Laise continues, analyzing the bell-shaped curve typically used in Monte Carlo simulations (see

graphic below). Based on this assumption, the probability of the market having a monthly

decline that is greater than 13% is extremely slim. Since 1926, however, this has happened

more than 10 times. In fact, the market has experienced a more than 35% bear market decline

twice in the last 10 years. Are these the kinds of odds you want to have stacked against you

when preparing for retirement?

Financial Engines, the source of the above graphic, is one of the most widely utilized tools for

participant advice; however, the guidance given to participants barely addresses past outliers in

the market. The main focus of returns in this equation is the probability that a participant's

account will only increase or decrease slightly over time. Analyzing the above graph, we see

that the greatest percentage indicates that this particular participant will retire with a balance

ranging from $133,000 - $236,000. Financial Engines is confident in this result; over 70%

confident in this result, in fact.

Still using the above graph as an example, let's say that participant John Smith logs onto

Financial Engines. Based on the past 20 years, it is recommended that he more than double his

account’s exposure in bonds; obviously, that makes sense based on the Monte Carlo simulation.

However, John Smith watches the news quite frequently, and his daughter works in the

financial industry, so he hesitates to invest more into bonds. But Financial Engines tells John

Smith that if he does this, he’ll retire with sunny skies! There is more than an 85% chance that

he will retire with a balance exceeding his annual goal of $133,000. He trusts that his plan

sponsor would not provide him or his fellow employees with a tool less than prudent. So, John

Smith increases the bond exposure in his account. What is going to happen in the next few

years when interest rates rise and the bond bubble bursts?

Normalcy bias addresses how prepared one may be for a disaster. When faced with this bias,

people underestimate the probability for a large disaster occurring and therefore inadequately

prepare themselves to face the disaster. People who fit this bias believe that because a certain

disaster has never occurred in the past, then it won’t occur in the future. Monte Carlo

simulation contributes to this bias and possible false sense of security. In the case of John

Smith, he would believe that because there has been an abnormally long bull market in bonds,

it will continue.

Julie Cradshaw addresses Monte Carlo Simulations in her article Why Some Advisors Just Say No

to Monte Carlo Simulations. She writes that “this technique [Monte Carlo simulation] has some

unfortunate failings as a financial planning tool. For starters, it doesn't recognize that portfolio

performance depends at least as much on the sequence of future investment returns as it does

on the average of those returns. Moreover, the thousands of iterations Monte Carlo simulators

produce can lull clients into believing they've considered all the possible financial outcomes

they could experience, when in fact the numbers generated may have little relevance to their

particular financial situation. Further, Monte Carlo doesn't measure bear markets well. Finally,

this kind of simulation is not capable of connecting projected investment returns with realistic

cash flows.”

Similar to the guidance/advice often given to participants, gap analysis is done based on Monte

Carlo Simulation. In gap analysis, a participant’s current age versus his expected retirement age,

and current income versus desired income at retirement are evaluated, and then, based on

past performance of asset classes, a probability of obtaining the desired retirement income and

his expected retirement age is produced. As previously discussed, looking backward and giving

little odds to extreme market events may mislead investors to be overly optimistic as to when

they can actually retire. If a participant is expecting to retire in 3 years based on his Monte

Carlo simulation gap analysis, and then he experiences an unexpected downturn in the market,

he might have to work another 10 years or more to make up for the loss in expected income.

As it stands, the Monte Carlo simulation is currently the most widely used method for assisting

participants in saving for their retirement; however, it is not the safest. Monte Carlo simulation

was a tool developed to win solitaire; instead, plans use it to gamble with their participants'

retirement accounts. Plan sponsors should be providing their participants with options that

analyze current economic trends and conditions and how they may affect the future. Simply

put: Anyone can predict the past.

Monte Carlo simulation was best depicted in a paper written by Alan D. Sokal, a professor of

mathematics and physics at both University College London and New York University. His paper

titled Monte Carlo Methods in Statistical Mechanics was based on a lecture given in Lausanne,

Switzerland, by Professor Michael Droz at the Cours de Troisieme Cycle de la Physique en Suisse

Romande in 1989.

Sokal states, “Before embarking on hours of lectures on Monte Carlo methods, let me offer

a warning: Monte Carlo is an extremely bad method; it should be used only when all alternative

methods are worse.”

Other Trouble Facing Monte Carlo Simulation Solutions

Although the arguments against Monte Carlo simulation may be enough evidence to lead

participants away from guidance provided by their company, research shows that there may be

even more compelling cases against products already available.

Behavioral Finance & Cognitive Biases

Registered Rep. points out another important flaw of the Monte Carlo simulation that should be

considered: It assumes that the participant will be putting away the same amount of money

each paycheck and that the money will grow, untouched. To be realistic, especially in this

economy, the number of participants who are taking loans and/or hardship withdrawals from

their accounts is rising significantly. The simulation also doesn’t take plan participants'

emotions under consideration. As the market drops and economic news worsens, participants

let their emotions get the better of them instead of riding out the bear markets as they are

instructed. Monte Carlo simulation assumes that people stay invested, even through bear

markets.

Cognitive biases are the primary aspects behind behavioral finance. Cognitive bias can best be

described as the poor judgments people make as a result of a certain situation, regardless of

information to the contrary. Why do we make the decisions that we do regarding our

investments? For instance, if you had money invested in a diversified portfolio and the stock

market took a downturn, when would you sell your riskier investments and put the money in

safer assets? Participants have been educated not to sell any of their investments as we

continue to follow a consistent long-term investment strategy. However, due to their fear,

they might sell at the first sign of loss.

Usage Rate

The programs that are currently being utilized average a usage rate of less than 10%. Stepping

away from the argument that the tools provided are flawed, plan sponsors should be asking

themselves, how good is the guidance if plan participants will not use it?

The low utilization rate stems from a multitude of ideas:

• Questionnaires are too time-consuming

• Participants do not have the required documents readily available, i.e. last year's tax

returns and/or earnings statements

• Questionnaires are seen as intrusive and intimidating

• The record keeper's site is not user-friendly

• Retirement planning is seen as intangible, confusing, or distant

Whatever the reason, whether it is viable or just a matter of participant perception, the current

questionnaires are not being utilized as they should.

Delivery through Print

The U. S. Department of Labor recognized that the advice should be an unbiased, computer-

generated solution for a reason.

In most questionnaires, numerical values are assigned to each answer. On some solutions

these values are listed for the participant to see. Subconsciously, some participants already

believe themselves to be aggressive, moderate, or conservative investors. When they see the

numerical values assigned to each answer, they subconsciously associate the lower value with

the conservative answer. The participant will begin to focus on the numbers (i.e., 1 is

conservative) based on how he views himself rather than the correct answer, thereby placing

him in what may not be the proper allocation.

In addition, when a paper questionnaire is used, participants may add up their scores

incorrectly, placing them in an unintended portfolio.

Words and Meanings

Dynamic. Tactical. Aggressive. Moderate. Balanced. Quantitative. Alternative. Non-

Correlated. Asset Class. Dollar Cost Averaging. Alpha. Beta.

While these are typically associated with investing and retirement plans, how many people can

relay an accurate definition of what these investment terms mean and how they are affected

by them?

The average participant does not understand investment jargon.

Most people would rather do nothing than do something that they do not understand.

Compounding this problem in investments, many guidance solutions seem to be written by the

academics from Wharton in their ivory towers above Wall Street with little to no understanding

of a layperson's vocabulary or lack thereof. There is a huge disconnect between the people

writing most questionnaires and the participants utilizing them.

Biased Results

Plan sponsors and advisors take on the role of fiduciary for a plan. They set up investment

policy statements and systems of checks and balances to make sure that they are providing the

best services to participants. They evaluate record keeper's websites, administrators, funds,

and fees. But how well do they evaluate the advice offered to their participants?

Questionnaires designed by fund companies will only direct a participant to the funds of that

particular company. If a plan sponsor and advisor were really doing their due diligence on a

questionnaire, they would want to offer something to their participants that was investment

agnostic.

To be fair, a prudent advice/guidance solution is as much art as science. One must be astute in

communication, delivery, investing, psychology, and marketing. I’m sure you have recognized

from the previous list that most of those characteristics have nothing to do with money

management and everything to do with people.

What Does a Good Advice Solution Look Like?

Who is to say what makes advice appropriate for plan participants? Research shows that most

solutions are not truly viable options.

The U.S. Department of Labor began endorsing unbiased computer-generated advice to

participants in August of 2008. According to the DOL, this had to be a repeatable prudent

process:

In § 2550.408g-1 Investment advice – participants and beneficiaries of EBSA, it is proposed that:

(i) A computer model shall be designed and operated to –- (A) Apply generally accepted investment theories that take into account the historic risks and returns of different asset classes over defined periods of time, although nothing herein shall preclude a computer model from applying generally accepted investment theories that take into account additional considerations; (B) Take into account investment management and other fees and expenses attendant to the recommended investments; (C) Request from a participant or beneficiary and, to the extent furnished, utilize information relating to age, time horizons (e.g., life expectancy, retirement age), risk tolerance, current investments in designated investment options, other assets or sources of income, and investment preferences; provided, however, that nothing herein shall preclude a computer model from requesting and taking into account additional information that a plan or a participant or beneficiary may provide; (D) Utilize appropriate objective criteria to provide asset allocation portfolios comprised of investment options available under the plan; (E) Avoid investment recommendations that:

(1) Inappropriately favor investment options offered by the fiduciary adviser or aperson with a material affiliation or material contractual relationship with the fiduciary adviser over other investment options, if any, available under the plan; (2) Inappropriately favor investment options that may generate greater income for the fiduciary adviser or a person with a material affiliation or material contractual relationship with the fiduciary adviser; or (3) Inappropriately distinguish among investment options within a single asset class on the basis of a factor that cannot confidently be expected to persist in the future; and

(F)(1) Except as provided in paragraph (b)(F)(2) of this section take into account all designated investment options, within the meaning of paragraph (c)(1) of this

section, available under the plan without giving inappropriate weight to any investment option. (2) A computer model shall not be treated as failing to meet the requirements of this paragraph merely because it does not make recommendations relating to the acquisition, holding or sale of an investment option that:

(i) Constitutes an investment primarily in qualifying employer securities; (ii) Constitutes an investment fund, product or service that allocates the invested assets of a participant or beneficiary to achieve varying degrees of long-term appreciation and capital preservation through equity and fixed income exposures, based on a defined time horizon (such as retirement age or life expectancy) or level of risk of the participant or beneficiary, provided that, contemporaneous with the provision of investment advice generated by the computer model, the participant or beneficiary is also furnished a general description of such funds, products or services and how they operate; or (iii) Constitutes an annuity option with respect to which a participant or beneficiary may allocate assets toward the purchase of a stream of retirement income payments guaranteed by an insurance company, provided that, contemporaneous with the provision of investment advice generated by the computer model, the participant or beneficiary is also furnished a general description of such options and how they operate.

Beyond the scope of the DOL's parameters, the most effective advice experience will limit or

help control the participants' fight or flight instinct. The same psychological instinctual

behavior that helps one survive a dangerous situation becomes active during the pain of a

market downturn. Subconsciously, an investor cannot differentiate between a dangerous

situation and market pain. Self-preservation and pain avoidance cause participants to sell at

the worst possible time. The graphic below illustrates how the average investor's market panic

and lack of professional advice cause underperformance in investments.

Average equity investor

underperforms the

benchmark by 5.31%

per year or 106.2% for

20 years.

An advice solution’s

mission is to close that

gap and get the

average investor to

market returns.

Monte Carlo simulation solutions do not help participants at a time when they are seeking

assistance. The more volatile the market, the more unreliable Monte Carlo becomes, and the

need for forward-looking, professionally managed portfolios grows.

In addition, appropriate asset allocation is more important than fund selection. Monte Carlo

simulation focuses on a participant’s core lineup, when the participant should really be focusing

on a portfolio that helps him to be properly allocated across a diverse set of asset classes,

including non-correlated asset classes predominantly excluded from a core lineup, but included

by professionally managed portfolios. Fred Reish, nationally recognized ERISA attorney,

concurs that, "[f]iduciaries should consider actively managing their risk, rather than relying on a

legal "shield" that may not be available. The key to managing the risk is to have as many

participants as possible invest in professionally designed portfolios that are appropriate for the

participant." Adviceware helps the participant determine which of those portfolios is right for

him.

Adviceware: Changing Retirement One Portfolio at a Time

We began development of our cutting-edge online software program, Adviceware, in 2002 with

the same ideas in mind the Department of Labor endorsed 6 years later. The software will

evaluate a participant’s responses and recommend an asset-allocated model portfolio for

implementation.

Adviceware was developed based on studies of behavioral finance including work from Dr.

Daniel Kahneman, who in 2002 became the only non-economist to win the Nobel Prize in

Behavioral Economics for his studies in behavioral finance.

According to The U.S. Department of Labor, “on average, participants and beneficiaries who are

advised make investment errors at one-half the rate of those who are not.”

Our usage rate on the software is approximately 60-70%; the average usage rate for 401(k)

participant advice software programs is about 10%.

A study from Plan Adviser Dash states:

• Participants who received financial advice held an average of 8.67 funds versus 4.98

funds for those who did not receive advice

• Those who received financial advice achieved a 3-year annualized rate of return ending

6/30/10 that was an average 2.67 percentage points better than those who did not

receive advice

• The average account balance for participants who utilized financial advice was $107,558

vs. $44,178 for those who did not

This study focuses on face-to-face/one-on-one meetings with participants. These types of

meetings do not have the fiduciary protection for plan sponsors that our software provides.

The software will generate consistent advice for participants. Advice proposed during a one-

on-one meeting varies and is difficult to document and scale to the masses.

Adviceware has been certified by Dalbar, the nation's leading financial services market

reasearch firm, as a certified participant advice solution. According to the U.S. Department of

Labor, 401(k) advice solutions need to be a repeatable prudent process and certified by an

independent third party. Dalbar has been approved by the U.S. Department of Labor to certify

401(k) advice solutions.

One of the main differentiators between Adviceware and most of the current solutions out

there is that, underneath the bells and whistles, those software systems are utilizing a Monte

Carlo back test when giving their recommendations for asset allocation to participants. We

utilize a forward-looking approach with professionally managed portfolios.

Adviceware has not only the solid imprimatur of Dalbar, but also the foundation of research

done by a Nobel laureate and other creative thinkers in many areas of finance. Our software

does not rely on the past; with an eye toward the individual investor's behavioral response, it

recommends professionals who analyze current trends and the volatility of the market.

Adviceware's high usage rate by participants indicates that its platform is user-friendly, and the

resulting documentation is invaluable for both the plan sponsor and advisor, providing a record

of compliance and participant choices from start to finish.

Isn't it time that Adviceware was working for you and your retirement? For more information,

contact: kristin.novotny@rehmann.com or info@adviceware.net

Adviceware. We speak retirement.

www. .net

Adviceware Monte Carlo

Forward looking

Professionally asset allocated

Considers all asset classes

Always rebalanced

Takes under 10 minutes

High utilization

Helps reduce fiduciary liability

Documents process, start to finish

Considers investor behavior

Can be private labeled

Can generate additional revenue over level comp

Combines the benefits of trustee and participant

directed design

Bibliography

Cradshaw, Julie (2003). Why Some Advisors Just Say No to Monte Carlo Simulations, Registered

Rep (http://registeredrep.com/advisorland/career/finance_why_advisors_say/)

Dalbar, Inc (2011). Quantitative Analysis of Investor Behavior

Eckhardt, Roger (1987). Stan Ulam, John von Neumann, and the Monte Carlo method, Los

Alamos Science, Special Issue (15), 131-137

Laise, Eleanore (2009). Odds-On Imperfection: Monte Carlo Simulation, The Wall Street Journal

(http://online.wsj.com/article/SB124121875397178921.html)

Plan Adviser Staff (2011). Participants Benefit from Advice, Plan Adviser Dash

(http://www.planadviser.com/Participants_Benefit_from_Advice,_Survey_Shows.aspx)

Reish, Fred. White Paper on Fiduciary Responsibility for 401(k) Investments

Roth, Allan (2010). Is Financial Monte Carlo Simulation Dead? CBS Money Watch

(http://moneywatch.bnet.com/investing/blog/irrational-investor/is-financial-monte-carlo-

simulation-dead/1126/)

Sokal, Alan (1996). Monte Carlo Methods in Statistical Mechanics: Foundations and New

Algorithms. New York City.

Sortino, Frank (2005). Monte Carlo Simulation: a beginning… not an end result, Some Thoughts

on Monte Carlo (http://www.sortino.com/htm/Thoughts%20on%20Monte%20Carlo.htm)

U.S. Department of Labor (2008). Press Release. U.S. Labor Department proposes rules on

investment advice exemption for 401(k) plans and IRAs. Washington.

U.S. Department of Labor (2009). Investment Advice – Participants and Beneficiaries.

Washington.