1. "Either you think probability is the most fascinating topic in the world or you don't. If you don't I feel sorry for you." - Robert Solow, Noble Laureate in Economics, 1987, Source: Ron Ross, The Unbeatable Market, p. 115
	2. "It is a truth very certain that when it is not in our power to determine what is true we ought to follow what is most probable." - Rene Descartes, Discourse on Method, Lady Luck, the theory of probability by Warren Weaver (Also see the Probability Calculator)
	3. "We can extrapolate from the study that for the long-term individual investor who maintains a consistent asset allocation and leans toward index funds, asset allocation determines about 100% of performance." - Roger Ibbotson, Ibbotson Associates, The True Impact of Asset Allocation on Returns (more Probability Quotes)

Portfolio Simulator

The portfolio simulator includes 35 years of Backtested Performance Information for the 20 portfolios of indexes and the S&P 500. Each time you click on a portfolio or chart mode, you will generate a random monte carlo simulation (the markets are random in nature) of the possible outcomes of annualized returns or growth of your starting investment within the risk and return parameters specified. Also see leptokurtic distributions.
1. Portfolio: Input data on your portfolio based on 20 years (preferably 35 years) of risk and return characteristics. You can then compare it to the twenty IFA portfolios, after both DFA and IFA fees for the entire period and the S&P 500.

2. IFA Index Portfolio: Click on the portfolio that was recommended in your Investment Policy Statement at the end of your Risk Capacity™ Survey.

3. Ending Wealth is expressed as the average or Expected Return based on the last 34 years of Backtested Performance Information (see footnote below), but is definitely not a guarantee of future returns. Also see Netirement and this retirement calculator. The following three articles are useful in understanding the difficulty in determining how long your money will last. 1) Financial Planning in Fantasyland, 2) The Retirement Calculator from Hell, and 3) Retirement Savings and Withdrawal Rates. A few good rules of thumb are to save 10% or more of your income, invest in a portfolio matched to your Risk Capacity™ at all times and don't spend more that 5% of your portfolio per year in your retirement.

4. Chart Mode: Change the Chart Mode to Ending Wealth, and you will see the randomly generated Monte Carlo Simulation of the balance after the time horizon specified in the table and the average or expected value of the range possible outcomes, based on the last 34 years*. Past performance does not guarantee future results.

5. Riskese™: To better understand the Portfolio Simulator, you may need to brush up on your Riskese™, the language of risk. If you don't speak Riskese™, you may want to reconsider hopping on the roller coaster of risk. There are two statistical concepts and terms that are important for investors to understand, standard deviation and standard error. The standard deviation is a statistic that tells you how tightly all the various annual returns are clustered around the average of the total period. When the annual returns are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the annual returns are spread apart and the bell curve is relatively flat, that tells you you have a relatively large standard deviation. The combination of the average and the standard deviation characterize create various bell curve shapes and those shapes represent the risk and return of the portfolio. When you have in excess of 20 years of data, the confidence level of the data starts to be somewhat valuable. Less than that and there is little meaningful information in the data. This is why past performance is not a good indicator of future performance. Most past performances of actively managed investments are less than 20 years old. Even with twenty years of data there is substantial unknown risks. If there were no risk, why should investors earn a return?

Figure 11-5: Standard Deviation	Computing the value of a standard deviation is a little complicated. Figure 11-5 shows you graphically what a standard deviation represents. One standard deviation away from the average in either direction on the horizontal axis (the red area on the graph) accounts for somewhere around 68 percent of the annual returns in the time period. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the annual returns. And three standard deviations (the red, green and blue areas) account for about 99 percent of the annual returns. Standard deviation expresses the spread of individual observations around the mean or average. A standard deviation is the square root of the variance. Variance is the measure of the spread of variability of quantitative measurements. The standard error of the mean indicates the degree of uncertainty in calculating an estimate from a sample, like a series of returns data. A standard error can be calculated from the standard deviation by dividing the standard deviation by a square root of n (with n representing the number of years measured). So with only 3 years of returns data on the S&P 500, the error in the average return is 2.6 times larger than having 20 years of data.
Figure 11-6: Standard Error

1. "Statisticians will tell you that you need 20 years worth of data -- that's right, two full decades -- to draw statistically meaningful conclusions [about mutual funds]. Anything less, they say, and you have little to hang your hat on. But here's the problem for fund investors: After 20 successful years of managing a mutual fund, most managers are ready to retire. In fact, only 22 U.S. stock funds have had the same manager on board for at least two decades--and I wouldn't call all the managers in that bunch skilled." - by Susan Dziubinski, University editor with Morningstar.com Note: Index Funds are the only source of reliable 20 year risk and return data.

2. "Those who are ignorant of investment history are bound to repeat it. Historical investment returns and risks of various asset classes should be studied. Investment results for an asset over a long enough period (greater than 20 years) are a good guide to the future returns and risks of that asset. Further, it should be possible to approximate the future long-term return and risk of a portfolio consisting of such assets." - If your broker [or investment advisor] is not familiar with the concept of standard deviation of returns, get a new one." - by William Bernstein, The Intelligent Asset Allocator - -"I go home and tell my wife sometimes, 'I wonder if [Bernstein] doesn't know more than me.' It's humbling." - John Rekenthaler, Research Chief, Morningstar Inc.

3. "Anyone who says active managers can win should wear a T-Shirt that says, "I Can't Add." - Larry Swedroe, What Wall Street Doesn't Want You to Know.


In the figure below, you can see a 10-year annualized return of efficient index portfolios compared to the average mutual fund (the green X), the S&P 500, and the only 86 managers in the Morningstar database with 20 years of managing the same fund. Morningstar® Principia® risk data does not go beyond 10 years, so the chart is shown using the 10 years from 1995 to 2005. About 10 actively managed funds are shown to be more efficient than the line of index portfolios. That means they are in the top left quadrant above the colorful line of buttons. Keep in mind that to have selected those funds 20 years ago would have been a near impossible task. Hindsight is 20/20. But index portfolios are always a better choice because they are consistent in their strategies.

Chart 2: Efficient Portfolios - 10 years

X = Average Mutual Fund, Gray Dot = SP500, Blue Diamond = the only managers with 20 year tenure. The colored buttons are the IFA portfolios. Chart by Gordon Shuler, Source: Morningstar Principia Pro and DFA