**Christian Charest: **For Morningstar, I'm Christian Charest. A standard element in any financial projection, and one of the most controversial, is the rate of return that we expect to get on our investments over a specified period. We know the returns are going to vary, but because we don't know what they are going to be, a standard method is to use the average return markets have produced in the past and assume that return is going to be achieved year-after-year in the future. And that carries some significant risks according to my guest, Morningstar's Director of Research, Dr. Paul Kaplan.

Paul, thanks for joining us today.

**Paul Kaplan: **Thanks for having me.

**Charest: **So, to start with, can you give us a brief overview of the risks involved in using a single rate of return as I just described?

**Kaplan: **Yeah. First of all, the rate of return that your investments are going to produce in the future is unknown and unknowable ahead of time. At best, when you are using an average, that's simply a center point of a whole range of possibilities. And the riskier your portfolio, the wider this range. If the actual rate of return ends up being too low, a plan based on the assumed rate of return will fail. Secondly, even if your projection for the overall rate of return turns out to be right, the sequence of returns can undo your plans.

When you are accumulating wealth for retirement, poor returns toward the end of the accumulation period could dash your plans even if early returns were good. Conversely, having poor returns at the beginning of retirement can curtail your plans even if later returns turn out to be good. Using a single number in place of an uncertain quantity is a serious mistake that Stanford Professor Sam Savage calls The Flaw of Averages. In a book by that title he goes at length to explain the problem and how to avoid it. In that book, he illustrates the problem with this cartoon showing a statistician crossing a river on the basis of its average depth but taking no account of how variable its depth is.

**Charest: **So, if it's wrong to use a single number, what can investors do?

**Kaplan: **They should not make financial plans using averages or quantities that are uncertain. Rather, they should use models that take uncertainty into account.

**Charest: **And what's the best way to implement that approach in practice?

**Kaplan: **In most cases, Monte Carlo simulation is the technique of choice. In Monte Carlo simulation, we use a computer to generate lots and lots of random numbers to bombard our models with lots of different possibilities.

**Charest: **And how does that work?

**Kaplan: **Within the model itself, year-in and year-out, the computer picks a random set of returns based on some model of how those returns might have been generated. We then model, given that set of random returns, what would have happened to the portfolio given the money going in and going out. We repeat this process 1,000 times, 2,000 times, maybe 5,000 times. And then we use basic statistical techniques to answer questions like, what is the probability of reaching $1 million by the time I retire, what is the probability of ending up with half a million or less, what is the probability of running out of money before I pass away.

Not only can we vary the investment strategy, we can vary some of our other assumptions. For example, if the person hasn't retired yet, we can model what would happen if he saves a little bit more. We know that's going to increase the probability of having a successful retirement. We can also model what would happen if instead of retiring at age 65, the investor works for another two years. It's a really interesting exercise because what people are often surprised by is how much of a better retirement they are going to have just by working a few more years.

**Charest: **So, obviously, this is a more, much more complicated process than what is allowed for by most financial calculators. What can investors do if they want to implement Monte Carlo simulation to get a more complete picture?

**Kaplan: **To avoid the flaw of averages investors need to avoid the overly simplistic models that typically are used in online calculators. Investors should ask advisors to use planning software that is based on Monte Carlo simulation. Morningstar Advisor Workstation is one such piece of planning software that uses Monte Carlo simulation to help advisors develop plans for their clients.

**Charest: **Paul, thank you very much for sharing all this with us today.

**Kaplan: **Thank you.

**Charest: **For Morningstar, I'm Christian Charest. Thank you for watching.