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The Nuts and Bolts of Monte Carlo

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The future of financial planning is in Monte Carlo. No, not the city. The technique. Already, many leading advisory firms have integrated Monte Carlo into their planning process. The vast majority of advisors, however, are just beginning to explore probabilistic forecasting, and there are some serious misconceptions about how it works.

I’ve spent four months running Monte Carlo simulations, speaking with vendors who offer tools for making Monte Carlo calculations, and chatting with planners who are using it. I’m not professing to be an expert in Monte Carlo simulation. But I have asked planners and vendors to run simulations to test different scenarios that I came up with, and I have spent hours on conference calls with advisors taking tours of leading Monte Carlo applications. Here’s what I’ve learned.

Discussions at conferences and media coverage of Monte Carlo simulation often focus on minutiae about statistical techniques. But two rocket scientists who develop these applications tell me that when advisors get into heavy discussions about these statistical issues they sound a bit foolish, or, as one put it, like Professor Irwin Corey, the 1970s comic famed for his gibberish.

Most advisors know that Monte Carlo is a way to model the randomness of investment returns. What many don’t understand is that even though Monte Carlo simulation lets you model the randomness of the stock market and other assets, you still have to make assumptions about the future of the investment markets that you want to model.

Not long ago, an advisor grilled me about an article I had written explaining the logic of Monte Carlo simulation. The article explained the case of a 65-year-old couple in excellent health and with a $1 million nest egg from which they wanted to draw $60,000 a year.

I explained why the couple stood a very likely chance of eating Friskies Buffet in their old age, assuming they would live as long as the actuarial tables used by life insurance companies suggest. The simulation was based on an assumption that equities would return 8% annually, intermediate term bonds would stay at their current yield, and inflation would remain at 3%. Based on these assumptions, if the couple invested 60% in stocks, 30% in bonds, and 10% in 30-day Treasuries, the forecast showed they stood a 68% chance of running out of money in 26 years–and there’s a 50-50 chance one of them will live that long.

The financial advisor questioning me about the simulation told me that something must be wrong with my story. It should not be assuming an 8% return on stocks and making these other assumptions about expected returns, he told me. The whole purpose of Monte Carlo, he said, is to simulate the randomness in returns the couple would likely face. This is a widely held misconception about Monte Carlo. “Your expected return assumptions in Monte Carlo simulations matter as much as they do if you were using a deterministic model,” says Christopher Jones, executive vice president at Financial Engines, a Palo Alto, California-based advice company founded by Nobel laureate William Sharpe.

When you use Monte Carlo analysis, you still have to make assumptions about the future. Most of the professional Monte Carlo software tools come with assumptions built in, and they simulate the randomness of an asset class based on history, a view of the future, and risk.

Assumptions Will Differ

For example, Financial Engines Professional Advisor Service, one of the leading firms selling a Monte Carlo advice platform to advisors, assumes a 7.5% real return on large-cap stocks and an unconditional 3.5% inflation rate. But Morningstar Advisor Workstation assumes a 7% real return on large caps. The scientists who create these programs examine the historic risk–variance and standard deviation–for each asset class and make an assumption about the future based on their world view. When you run a simulation, the randomness it simulates is around its forecasted return for an asset class, and its risk and its other assumptions about the capital markets.

“What’s important about Monte Carlo simulation is that it focuses attention on scenarios that are something other than the expected return,” explains Jones. “The point that Monte Carlo makes, as opposed to other techniques, is that the probability of achieving the expected return can be in some cases a small number. Monte Carlo shows the range of possibilities and that, in fact, you are unlikely to achieve the exactly expected return.”

Based on your starting assumptions, the simulation randomly spits out returns that a client will get over his or her lifetime. In the case of my 65-year-old couple with $1 million, for instance, in year one of their retirement portfolio, the simulation may assume that they will get a 12% return, but the following year could result in an 8% loss. Based on capital markets assumptions programmed by the makers of the Monte Carlo software tool you’re using, a simulator randomly assumes returns for every year the couple is expected to live, thus creating a simulation for their lifetime with randomly generated inputs. But it doesn’t stop there.

Many Lifetimes

A Monte Carlo simulator will make a client live more than one lifetime. The 65-year-old couple’s lifetimes could be simulated thousands of times. Based on capital market assumptions about the assets in the portfolio, the couple’s portfolio could thus be tested to see how the randomness of the markets would impact them if they lived 500, 2,000 or even, 10,000 times. What you and your client come away with is a chance of achieving a given financial goal. You can tell clients that, say, in 30% of the simulations, they have enough to retire, pay for college, or achieve other goals.

This kind of statistical analysis is better than traditional planning forecasts. It more realistically reflects the way the markets behave, illustrating the probability and magnitude of possible outcomes. The deterministic models still used by planners and investment managers do not reflect the probability of achieving a goal.

Until Monte Carlo came along with the advent of faster computers and better software tools, many advisors relied upon history as a guide to assemble a projection of returns and behavior of the markets and create a forecast. In its simplest form, the equation is easy to understand: Large-cap stocks since 1926 have averaged about a 10.5% return annually. So our 65-year-old couple can plan to get that kind of return over their lifetime. But returns don’t come in 10.5% increments every year. Just ask a 65-year-old who rolled over her nest egg from a qualified plan into a self-directed IRA in the stock market in 2000. Because she may have lost 45% or 50% of her capital in the early years of her retirement, she may never recover, of course, and her spending plans may no longer make sense. My point is to explain the pitfalls of Monte Carlo to advisors before adoption of the technology becomes widespread.

I first reviewed a Monte Carlo planning tool three years ago, when Financeware (FW) became the first Web-based application targeting independent advisors. (Financeware products are offered through Investment Advisor’s Web site). FW’s introduction of a Monte Carlo simulator was followed by other professional forecasting tools from startups, while other Monte Carlo simulators, such as Financial Engines (FE) and m-Power, targeted retail consumers directly and through 401(k) plans. In recent months, a spate of new professional products for advisors has been launched, and I’ve spent the last few months trying to understand how these tools would work for advisors.

With the help of a panel of six advisors, some of whom were already using Monte Carlo analysis to serve their clients, I reviewed Financial Engines Professional Advisor Service in the December 2001 issue of Investment Advisor. I followed up with a review by many of the same advisors of Morningstar Advisor Workstation in February 2002. In March, I spent time testing the Monte Carlo simulator created by I’m about to tell you about two more Monte Carlo simulators that have emerged in recent months, Efficient Portfolios and Ibbotson Portfolio Strategist software.

Adoption of these tools by independent advisors has been slow, although the granddaddy of them all, Financeware, does claim a good bit of success. In addition to sales directly to institutions, nearly 3,000 advisors have independently purchased FW from wirehouses, regional B/Ds, and independents, according to David Loeper, FW’s chairman and CEO. Last June, Thomson Financial invested in Financeware and licensed parts of the program in an advisor technology platform being offered to brokerages and independent B/Ds. But Financeware, which has received $16 million of venture capital in two rounds of financing, has not lived up to my initial enthusiasm. Despite all the creativity and buzz and money at the company, Financeware is not widely used by independent advisors I know. This is not to slam FW; it’s more about advisor resistance to new technology.

An ASP With No Sting

I believe that the main reason Financeware has not had greater penetration is that it is a Web-based application service provider. With an ASP, you run your application over the Internet. The application itself is stored on a Web server. Sometimes client data is, too. That’s different from installing an application locally on your computer. ASPs have a very important benefit. When a new version of the software comes out, you don’t have to install it on all the machines in your office. The ASP installs the upgrade once on its server and you get the benefits immediately without the hassles of installing updates on your PCs’ hard drives. Despite this benefit, most advisors remain uncomfortable with ASP technology for advice tools. RIAs seem to have the greatest aversion.

Most entrepreneurs running their own RIA are control freaks. That’s why they chose to start advisory firms. They don’t like the idea of an application running remotely and being dependent on their Internet connection to conduct business. They are squeamish about giving data to third-party software providers. They are concerned about privacy issues for their clients. So the ASP model is likely to gain greater acceptance with registered reps. If you are a registered rep affiliated with a B/D, compliance is a hassle and the ASP can simplify the supervision tasks.

While Financeware became the best-known Monte Carlo application sold to RIAs and reps that was delivered over the Web, others have followed suit. Two of the big players in Monte Carlo–Morningstar and Financial Engines–are in fact actively trying to sell their applications to B/Ds. Each has seen some success. Components of Morningstar’s Advisor Workstation are being deployed by Merrill Lynch and Nationwide, although no brokerages or custodians have yet signed on for its Monte Carlo tool. Thomson, which uses Financeware’s Monte Carlo technology, recently signed a deal with Janney Montgomery Scott. Financial Engines has inked an agreement with TD Waterhouse. Despite these successes, it’s not clear that the ASP model will win the battle for independent advisor desktops.

Java Jive

A different breed of Monte Carlo calculator has been offered for a couple of years by Unlike the big companies it competes against, NETirement is tiny, but it is innovative and offers a solution that could appeal to many independent advisors. It’s technically an ASP but relies on a Java applet that runs on your computer and only pulls the statistical data it needs from a Web server. This has several benefits. Because it is an applet that runs locally and not over the Internet like an ASP, you can run up to 10,000 simulations in seconds. Also, the applet does not transmit your client data over the Internet. Instead it uses cookies. The cookie, a small unique file that is commonly used on the Internet, contains all your client’s data and then the Java applet converts the cookie into a Microsoft database (MDB) file on planners’ own PCs

The reason why this architecture is not used by the big firms making Monte Carlo tools is that it is not as scalable as an ASP. Most of the MC tool developers have long-term strategic business plans that project adoption by tens of thousands of advisors and hundreds of thousands or millions of clients. NETirement’s current architecture would not support that scale of numbers but can work just fine for an advisory firm with hundreds of clients.

Gerald Wagner, the person behind NETirement, is an unusual guy. Wagner received a master’s degree and Ph.D. in business economics at Harvard’s Graduate School of Business. He was mentored by John Lintner, one of the founding fathers of modern portfolio theory, who died in 1983. After a five-year stint in academia, Wagner in 1976 began a career in the financial world at San Diego Trust & Savings, where as Chief Investment Officer he managed $2 billion in stocks and bonds. Since 1990, he has worked on reverse mortgage software and design at Ibis Capital LLC.

But Wagner’s fascination has been It has just three employees. But they have yielded impressive results. Wagner joined with Educational Technology, a training firm, and came in behind Financial Engines in bidding for the Florida Retirement System 401(k) plan education contract. But his tools are being used by the American Association of Retired Persons and TIAA-CREF.

Another approach is offered by Efficient Portfolios. Like the other Monte Carlo providers, EP, a relatively new ASP, offers more than just forecasting as part of its toolset. It features a risk tolerance questionnaire–standard in all of these tools mentioned previously–”that lets you find your client’s risk tolerance range, the ‘asset class’ mixture, and individual assets required to construct an individually tailored portfolio that meets the risk and return objectives of that client.”

Backtest and Optimize

Tapping a Lipper Analytical Services database, a mutual fund finder lets you find funds with higher returns, lower risk, or higher returns and lower risk than a portfolio or a single stock or mutual fund. A stock finder uses another rich database to calculate risk and return of a stock and to find stocks in the same industry with higher return, lower risk, or higher return and lower risk. You can backtest a portfolio over the past five years, see the range of likely returns of a portfolio, and use an optimizer to see the optimal portfolio mix on the efficient frontier, according to EP.

This is a lot of tools for $89 a month, and EP is attracting attention. At a recent conference, one detail-oriented planner dragged me over to the EP exhibit booth and declared that the firm would provide the answers to her needs for her clients. But I don’t think it will. Three financial planners, along with Moshe Milevsky, a professor of finance at York University in Toronto, who has written extensively on probabilistic analysis, were given a one-hour Web tour, along with me, of EP by the company’s president, Susan Ahlstrom. While its user interface is easy to work with and can be educational, EP’s MC forecasting tool makes a strong case for performing due diligence on these tools. You really need to understand how these tools operate before using them because you may decide that the way a particular forecasting system works runs contrary to the way you want to practice.

“Their goal is noble,” says Milevsky. “To bring modern portfolio theory to the masses is a good thing. To educate the consumer about the importance of diversification is good.” But EP allows you to perform MC analysis on individual stocks and mutual funds, and this may be regarded as a misapplication of MPT by some advisors. “It’s not for nothing that Bill Sharpe and Financial Engines and Morningstar do not rely solely on historical returns to do these simulations on individual securities,” he adds. “We are less confident with stochastic models for individual securities and funds compared with asset classes.”

In addition, EP lets you perform MC simulations using performance and risk assumptions that are based on how the stock or fund performed over the past 10 years, and EP allows you to run MC simulations based on as few as three years of data. “If you tell me that the S&P 500 will grow by an average of 8% a year for the next 20 years, I can accept this,” says Milevsky. “But if you tell me that Merrill Lynch will grow at 8% a year for the next 20 years, I’ll feel queasy. I don’t know if Merrill will exist in five years, let alone that if it does exist, its performance over the past five years will give us any indication of what its next five years will be like.”

Jeffrey Schaff, who is president of Ardor Financial in Northfield, Illinois, observes that an index is unlikely to fall to zero, unless you believe the S&P 500 can be rendered worthless. A stock can go to zero value. Along the same lines, Milevsky says that if you use three or five years of history on Enron or Global Crossing or other individual securities with bizarre behavior to predict their future behavior, your projection will yield ridiculous outcomes. “MPT was not meant to do this,” he says.

Milevsky says EP does not deal with the issue of stochastic dominance. This is when one security with much lower risk and much higher returns than other securities in a portfolio when run through an optimizer will dominate the efficient frontier and tell you to put all your assets in that security. Typically, optimizers come with restraints so you won’t wind up with a portfolio that is 40% in emerging markets or dominated by other wild asset classes.

“We’re not RIAs,” says Ahlstrom of EP, “and Financial Engines and Morningstar are. We build software and we do that well, and we won’t impose our philosophy on financial professionals.”

Watch That Bell Curve

Wagner says EP bases its Monte Carlo calculation on a simple normal distribution. If you plot returns of a security, a simple normal distribution would resemble a bell curve. But NETirement, Financeware, Financial Engines, and Morningstar Workstation use log normal distributions of returns. When plotted, a log normal distribution of returns doesn’t have the same bell curve shape. Instead it rises slightly and then slopes down more gently because it reflects the outliers–unusual returns from a security that occur less frequently but can wreak havoc on a portfolio.

The consequences of using a simple normal distribution, Wagner explains, is that if you have a year where your portfolio rises by 100% followed by a year when it declines 50%, EP’s Web-based application will tell you that your portfolio is up 25%, while using logarithms would give the correct answer: you have a flat return of 0% for that period.

“Who is standing behind the product? And who endorsed their algorithm?” asks Milevsky. “When you go to Financial Engines, the people behind the product did not misinterpret MPT. They developed MPT. These concepts need a Good Housekeeping seal of approval. They are not widgets. They are nuclear reactors. I would like to know that a competent nuclear engineer built my reactor. I know that with Morningstar and Ibbotson and Financial Engines, and with mPower, which had 20 Ph.D.s working on staff on its algorithms.”

Morningstar Workstation and Financial Engines impose their view of the world on you and don’t let you change their capital markets assumptions. As you can see from the complications discussed here about EP, this may not be a bad thing. But the leading Monte Carlo tools have totally different ways of implementing their output and coming to their capital market assumptions that you should be familiar with.

One common thread in Morningstar, Financial Engines, and NETirement simulators is that history is no indication of future results. Explains Paul Kaplan of Morningstar: “It is generally understood by many investment professionals and academics that simply extrapolating the past, as in the Ibbotson data book, would be a poor perception of the future.” Indeed, Morningstar and FE assume that the stock market’s return in the future will be lower than the historical return.

The assumptions about future equity returns made by Wagner at NETirement are about as optimistic as Morningstar or FE. The default assumption in NETirement of a nominal 11% return on large-cap stocks, along with the assumption of an 11% nominal return by FE and a pre-inflation return of 7% by Morningstar, is unrealistic, according to some of the best planners in the country.

Tom Connelly, a financial planner at Keats, Connelly & Associates in Phoenix, says that he feels an “obligation to clients to be realistic.” He builds Monte Carlo projections using software from Daniel H. Wagner Associates that lets him make his own inputs. He feels comfortable assuming a 6% nominal return on large caps and an 8% nominal expected return on global stocks that include emerging market and small cap and value stock premiums. “But Tom,” I say, “the consensus among financial economists surveyed in an academic journal recently is for an 11% return on large caps.” Answers Connelly: “If 20 of the world’s leading financial economists jumped off a bridge, would you?”

Connelly says the built-in, unchangeable assumptions of Morningstar and Financial Engines would not work for him. While the default assumptions in NETirement are also too high, he says, NETirement does give a planner the ability to change them. “The other element of making assumptions on your own and changing the inputs is that standard deviation is likely not to be constant through a long period,” says Connelly, “so planners need to understand whether their software tool models those changes in variance over time or keeps variance stationary.”

What’s Your Style?

The other crucial aspect of the calculators is how they implement their advice. FE relies on style analysis, the invention of Bill Sharpe. Basically, you input your current portfolio of stocks, mutual funds, and fixed-income instruments, and FE runs an analysis that tells you what combination of asset classes best explains the behavior of your portfolio. It’s using returns on the securities and attributing their characteristics to a set of asset classes. FE software then will propose changes to the portfolio that its models say are more efficient, giving you different weightings of your current holdings and suggesting new holdings where its model deems it appropriate. This is a very clean approach theoretically; you can come up with recommendations of specific securities to fulfill an optimized asset mix based on clients’ risk tolerance and goals. But it requires relying on style analysis. And style analysis is like religion. You either believe or you don’t.

Morningstar Workstation does not rely on style analytics. Indeed, a recent paper by Morningstar slammed style analytics. Basically, after assessing a client’s risk tolerance and goals, Workstation’s Monte Carlo analysis uses asset classes–the equivalent of no-cost index funds. This results in an optimal mix of asset classes that you should own to achieve your goals. Then the advisor must pick securities to fulfill that asset class recommendation. What’s less than perfect about this is that you are making an asset class recommendation based on passively managed, expense-free index funds. But you may be using actively managed funds that have expenses, and other securities whose behavior may differ in the future from asset classes used in the MC analysis.

For those interested in one other alternative, consider Ibbotson’s Associates’ Portfolio Strategist. Roger Ibbotson, a professor at Yale whose data on historical returns of asset classes is an industry standard, heads a Chicago-based firm that made this excellent piece of software. Ibbotson’s reputation for brains comes through. It uses style analytics like FE does and includes unchangeable expected return assumptions, and it runs locally on your computer and is not an ASP. A more complete review will be included in a future article. Planner Schaff uses a version of Portfolio Strategist that costs about $2,600 a year and buys Morningstar Principia Pro for about $1,000 annually, and says he is pleased with the combo.

Morningstar charges $5,000 annually for the Workstation advice platform, but individual components are available for less. FE is expected to be priced at about $100 a year per client, but the advisor product is still in development, and pricing varies. Financeware offers packages ranging from $900 to $3,000 a year, while comes in at $400 to $800. While Workstation offers the package that’s closest to performing financial planning, most planners will still need to use financial planning software in tandem with these goal planners.