In the forum, it is often suggested that the Vanguard Total Stock Market Index Fund, VTSMX, is a better choice than VFINX, the Vanguard 500 Index Fund, because it includes small-caps (and more mid-caps) than VFINX. This image above is one way to look at the comparison.

When comparing funds, portfolios, or strategies, there are three questions that could be asked. 1) Which had higher performance? 2) Do we expect that outperformance to continue, and, if so, why? The third, which doesn't get asked enough, is 3) How big is that difference,

**compared to the uncertainty and of future fluctuations in portfolio value?**

Monte Carlo simulations are often used to show the likely variability of our future retirement savings, in order to measure it against our future needs. I decided to use it for comparisons between two funds, or two portfolio strategies. In order to see how the past difference in performance measures up against the likely future uncertainty of the alternatives.

This kind of diagram still leaves us with the question of how much conviction we have that the differences we've seen in the past will persist in the future. In the chart above, the difference between 500 index and Total Stock is small compared to the spread of outcomes from either one. However, someone might say that even a small statistical edge is worth having. So this won't settle any debates. It doesn't tells us which way the needle will move. But it does suggest how much changing a portfolio moves the needle, relative to the natural spread of outcomes.

Here's what the chart is showing.

- The green and red dots are the final outcomes of 500 Monte Carlo simulations of the possible performance of the two funds.
- The performance is not based on the growth of a single investment in the fund. It is, instead, based on the outcome of making periodic fund purchases of $100/month over the time period shown. It thus is closer to the way most of us actually invest.
- The green and red crosses mark the outcome based on the actual historical performance of the funds.
- The red and green range lines show the 10% and 90% percentiles of those results. In this case, 80% of the simulations showed final values for VFINX between $72,000 and $182,000; 10% were below $72,000, 10% were above $182,000. The middle mark, $113K, is the median.
- The basis for all of the data that went into the simulation is the set pf "monthly values" tabulated by PortfolioVisualizer, "Backtest Portfolio" tool.
- The range of time shown is that for all available data in PortfolioVisualizer.
- The vertical scale represents the final value in dollars.
- The horizontal scale is the annualized standard deviation of the monthly returns of the plotted assets. It is a measure of how much fluctuation you would see in portfolio value.

**underestimates**the range of variation. For comparison, here are the 10% and 90%-percentile outcomes for the S&P 500 and its predecessors, obtained by three methods.

1) My simulation: $72,000 - $182,000. Top = 2.5X bottom.

2) PortfolioVisualizer (extrapolated to 26 years): $59,501 - $311,076. Top = 5.3X bottom.

3) Actual historic, 26-year-periods starting 1870: $77,191 - 286,582. Top = 3.71X bottom.

**Other notes.**

1) I simply use the time period for which data is available for the investment being explored. This means that results for, say, a 26-year time period are not directly comparable in dollars to those for a 5-year time period. I did this for two reasons. The first is compounding affects everything equally, both the historical values and the simulation, while the semilog plot means that the effect of compounding is the same as the effect of a vertical zoom. A longer time period magnifies both the difference and the spread. Therefore, it doesn't interfere with the point of the exercise, which is to judge difference relative to spread. Second, I just couldn't come up with a way to "normalize" everything to the same time period that was easy to explain or to justify.

2) For the "baseline" comparison, I try to use Bogleheadish index funds and portfolios. I choose the baseline funds depending on how much data I have for the comparison fund; for example, Total Stock if it goes back as far as the comparison fund, but 500 Index if I need to go back farther.

3) For the most part, I try to compare funds or strategies in the context of a portfolio with both stocks and bonds, not in isolation.