# Using mutual funds and ETFs for short-term savings (5 years)

In investing, we make personal choices about how much risk we are willing to take if we think we can get higher return in exchange. Using mutual funds and ETFs for short-term savings (5 years) compares historical performance of similar funds that are appropriate for short-term savings.[Note 1]

Volatility--fluctuations in value--are an important aspect of risk. In financial economics, volatility is often measured by a statistical value called the standard deviation, represented by the Greek letter sigma (σ). The standard deviation of mutual funds can be found on sites like Morningstar or PortfolioVisualizer. However, it is hard to relate this number to a practical question, like "how much risk would I be taking by putting money I need a year from now into a short-term bond fund instead of a money market fund?" This article tries to help with this kind of question.

## Overview

In this article, we calculate some other measures of risk by calculating what would have happened to an investment of \$10,000, held for short periods of time, in a mutual fund or exchange-traded fund (ETF). You might do this in hope of making more than you would have made in a money market mutual fund, and accepting the possibility of sometimes making less.[Note 2] The possibility of making less is depicted in two ways:

1) What percentage of the time would you have made less than in a money market fund? We chose VMMXX, the Vanguard Prime Money Market Fund, because it is one of the oldest money market fund and gave us a long period of comparison. We also show what percentage of the time you would have actually lost money--ended up with less than \$10,000 at the end of the time period--and what percentage of time you would have failed to keep up with inflation.

2) It's important to know not just when a fund or ETF underperformed a money market mutual fund, but by how much. In the case of short-term funds, the losses, when they did occur, were so small that some might call them negligible To quantify this, we present two numbers. One is the average loss that occurred in those periods in which losses did occur; and the other is the largest loss that ever occurred within the body of data that was used.

Notice that a high probability of underperforming may not be important at all. If two investments have the same return and volatility, but just fluctuate randomly with respect to each other, you would expect each of them to underperform the other about 50% of the time.

We have chosen to present data going back for as far as Morningstar has data. As a result, there are two caveats. First, the data range shown for each fund is different and results for different funds cannot be directly compared. For example, the Vanguard Short-Term Treasury Fund, VFISX, beat VMMXX by an average of \$117.10 while the Vanguard Short-Term Treasury Index fund, VGSH, only beat it by \$33.17. But this is almost entirely due to VGSH's inception in 2009 versus VFISX's inception in 1991. If we restrict our view of VFISX to the same years as VGSH, the benefit for VFISX was only \$44.05. Second, this underlines the problem with all historical data, which is that the present time--and thus the short-term future--may be quite different from the historical averages.

### Median and average (mean)

We show both the average and the median for some key values. A reader requested this. We have a scattered group of values: the return from an investment over many different periods of time. To represent the center of such a group with a single number, we often calculate and average or mean. In the case here, when we are looking, for example, at losses, and only seeing "the tail of the distribution," the average may give the wrong impression because it's influenced by extreme values. The median is another measure, and represents the value that is halfway based on counting. If the median loss of an investment is \$600, it means you had a 50% chance of losing more over \$600 and a 50% chance of losing less than \$600.

### Holding bond funds for the average "duration" of the fund

A "duration" is a calculation based on bond math that gives a number of years, related to the bond's term but shorter. One interpretation of the duration is that it is the "point of indifference." It is too well known that when interest rates rise, bond values fall. What is less well known is that if a bond is held for its duration, at the end of that period of time it will have the same value regardless of what interest rates do, provided the yield curve moves in parallel. This does not apply to a bond fund because the bonds in a fund are all different "ages" at any given time, and because the yield curve doesn't move in parallel. So there are no guarantees, but, nevertheless, the duration tells us a holding period over which the fund is unlikely to lose money.

This leads us to expect, for example, that "short-term" bond funds--like the Vanguard Short-Term Bond Index Fund, with a duration of 2.7 years--will sometimes lose money over periods of 6 or 12 months, but rarely lose money over periods of 5 years. This expectation is borne out by history.

A bond fund may not lose money, in the sense of dollars, yet lose value to inflation.

### Holding stocks "for five years"

Authorities advice against using stocks for money you will need in less than five years; Vanguard says ten. If you are considering using stocks for money you will need in five years, then you should familiarize yourself with the data for stocks held for five years. See Using mutual funds and ETFs for short-term savings (5 years).

Vanguard itself puts all of it stock funds in risk categories 4 and 5 and says "these funds may be appropriate for investors who have a long-term investment horizon (10 years or longer)."

A few other authorities say:

"Do not invest any money in stocks you will need in less than five years.”—William J. Bernstein, The Four Pillars of Investing.

“A rule of thumb in investing is that you should not invest money in stocks or stock funds that you will need in less than five years.”—Jack Brennan and Marta McCave, “Straight Talk on Investing.”

“Owning stocks for the short term (less than five years) is foolish.”—Kiplinger’s Personal Finance, Nov, 2004.

“Money you know you will need in the five to 10 years does not belong in stocks.”—Suze Orman, Suze Orman’s Action Plan.

Even Jim Cramer has said “If you need the money for something serious in the next four years, you cannot risk keeping it in stocks.”--Jim Cramer, Getting Back to Even.

## Money market

### BTFXX: BlackRock Liquidity

 Length of holding period 60 months Total number of overlapping 60-month periods 307 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1078.11 (average), +\$248.00 (median) Average CAGR (annualized rate of return) of those 307 60-month periods 2.07% Standard deviation (σ) of single-month returns, annualized 0.72%
 Number of periods in which BTFXX made less than VMMXXAverage/median shortfall versus VMMXX over those 307 periods 307/307 = 100.0%-\$453.48 (average), -\$158.68 (median) Number of periods in which BTFXX lost moneyAverage/median dollar loss over those 95 periods 95/307 = 30.9%\$0.00 (average), \$0.00 (median) Number of periods in which BTFXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 183 periods 183/307 = 59.6%-\$969.77 (average), -\$967.11 (median)
 Compared to VMMXX, 4/2004 - 3/2009 -\$1820.56 Dollar loss, 12/2010 - 11/2015 \$0.00 Real loss (inflation-corrected), 8/2003 - 7/2008 -\$1961.07
 Compared to VMMXX BTFXX vs VMMXX, 4/2004 - 3/2009
 Average/median additional return above VMMXX, over 307 overlapping 60-month periods -\$453.48 (average), -\$158.68 (median)

### SWPXX: Schwab Government Money Market Portfolio™

 Length of holding period 60 months Total number of overlapping 60-month periods 247 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1121.72 (average), +\$1107.28 (median) Average CAGR (annualized rate of return) of those 247 60-month periods 2.15% Standard deviation (σ) of single-month returns, annualized 0.62%
 Number of periods in which SWPXX made less than VMMXXAverage/median shortfall versus VMMXX over those 247 periods 247/247 = 100.0%-\$141.49 (average), -\$146.82 (median) Number of periods in which SWPXX lost money 0/247 = 0.0% Number of periods in which SWPXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 151 periods 151/247 = 61.1%-\$551.19 (average), -\$578.76 (median)
 Compared to VMMXX, 7/1994 - 6/1999 -\$273.46 Dollar loss, 9/2010 - 8/2015 +\$4.92 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1119.22
 Compared to VMMXX SWPXX vs VMMXX, 7/1994 - 6/1999
 Average/median additional return above VMMXX, over 247 overlapping 60-month periods -\$141.49 (average), -\$146.82 (median)

### SWRXX: Schwab Investor Money

 Length of holding period 60 months Total number of overlapping 60-month periods 249 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1136.98 (average), +\$1106.67 (median) Average CAGR (annualized rate of return) of those 249 60-month periods 2.18% Standard deviation (σ) of single-month returns, annualized 0.62%
 Number of periods in which SWRXX made less than VMMXXAverage/median shortfall versus VMMXX over those 249 periods 249/249 = 100.0%-\$139.81 (average), -\$165.03 (median) Number of periods in which SWRXX lost money 0/249 = 0.0% Number of periods in which SWRXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 152 periods 152/249 = 61.0%-\$541.17 (average), -\$553.48 (median)
 Compared to VMMXX, 7/1995 - 6/2000 -\$242.28 Dollar loss, 5/2011 - 4/2016 +\$5.00 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1119.13
 Compared to VMMXX SWRXX vs VMMXX, 7/1995 - 6/2000
 Average/median additional return above VMMXX, over 249 overlapping 60-month periods -\$139.81 (average), -\$165.03 (median)

### SWVXX: Schwab Value Advantage Money

 Length of holding period 60 months Total number of overlapping 60-month periods 272 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1353.84 (average), +\$1337.23 (median) Average CAGR (annualized rate of return) of those 272 60-month periods 2.57% Standard deviation (σ) of single-month returns, annualized 0.63%
 Number of periods in which SWVXX made less than VMMXXAverage/median shortfall versus VMMXX over those 272 periods 272/272 = 100.0%-\$42.46 (average), -\$44.65 (median) Number of periods in which SWVXX lost money 0/272 = 0.0% Number of periods in which SWVXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 144 periods 144/272 = 52.9%-\$518.52 (average), -\$555.28 (median)
 Compared to VMMXX, 12/2004 - 11/2009 -\$90.28 Dollar loss, 8/2009 - 7/2014 +\$3.95 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1118.67
 Compared to VMMXX SWVXX vs VMMXX, 12/2004 - 11/2009
 Average/median additional return above VMMXX, over 272 overlapping 60-month periods -\$42.46 (average), -\$44.65 (median)

### TSCXX: T. Rowe Price Cash Reserves

 Length of holding period 60 months Total number of overlapping 60-month periods 254 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1252.12 (average), +\$1221.67 (median) Average CAGR (annualized rate of return) of those 254 60-month periods 2.39% Standard deviation (σ) of single-month returns, annualized 0.64%
 Number of periods in which TSCXX made less than VMMXXAverage/median shortfall versus VMMXX over those 254 periods 254/254 = 100.0%-\$56.58 (average), -\$53.19 (median) Number of periods in which TSCXX lost money 0/254 = 0.0% Number of periods in which TSCXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 146 periods 146/254 = 57.5%-\$521.44 (average), -\$571.96 (median)
 Compared to VMMXX, 1/2015 - 12/2019 -\$132.87 Dollar loss, 10/2009 - 9/2014 +\$4.89 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1114.31
 Compared to VMMXX TSCXX vs VMMXX, 1/2015 - 12/2019
 Average/median additional return above VMMXX, over 254 overlapping 60-month periods -\$56.58 (average), -\$53.19 (median)

### VUSXX: Vanguard Treasury Money Market

 Length of holding period 60 months Total number of overlapping 60-month periods 264 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1290.53 (average), +\$1297.62 (median) Average CAGR (annualized rate of return) of those 264 60-month periods 2.46% Standard deviation (σ) of single-month returns, annualized 0.61% Link to Vanguard's web page for VUSXX VUSXX Vanguard's risk potential classificationRisk level 1(conservative) Vanguard funds are classified as conservative if their share prices are expected to remain stable or to fluctuate only slightly. Such funds may be appropriate for the short-term reserves portion of a long-term investment portfolio or for investors with short-term investment horizons (3 years or less).
 Number of periods in which VUSXX made less than VMMXXAverage/median shortfall versus VMMXX over those 246 periods 246/264 = 93.2%-\$77.87 (average), -\$71.88 (median) Number of periods in which VUSXX lost money 0/264 = 0.0% Number of periods in which VUSXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 146 periods 146/264 = 55.3%-\$513.52 (average), -\$572.07 (median)
 Compared to VMMXX, 2/2005 - 1/2010 -\$176.79 Dollar loss, 11/2010 - 10/2015 +\$6.21 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1113.51
 Compared to VMMXX VUSXX vs VMMXX, 2/2005 - 1/2010
 Average/median additional return above VMMXX, over 264 overlapping 60-month periods -\$71.84 (average), -\$67.91 (median)

### VMMXX: Vanguard Prime Money Market

 Length of holding period 60 months Total number of overlapping 60-month periods 474 Average/median number of dollars earned in 60 months on a \$10,000 investment \$2960.76 (average), +\$2604.05 (median) Average CAGR (annualized rate of return) of those 474 60-month periods 5.32% Standard deviation (σ) of single-month returns, annualized 1.11% Link to Vanguard's web page for VMMXX VMMXX Vanguard's risk potential classificationRisk level 1(conservative) Vanguard funds are classified as conservative if their share prices are expected to remain stable or to fluctuate only slightly. Such funds may be appropriate for the short-term reserves portion of a long-term investment portfolio or for investors with short-term investment horizons (3 years or less).
 Number of periods in which VMMXX lost money 0/474 = 0.0% Number of periods in which VMMXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 154 periods 154/474 = 32.5%-\$494.57 (average), -\$525.12 (median)
 Dollar loss, 11/2010 - 10/2015 +\$14.62 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1096.06

### VMFXX: Vanguard Federal Money Market

 Length of holding period 60 months Total number of overlapping 60-month periods 401 Average/median number of dollars earned in 60 months on a \$10,000 investment \$2154.10 (average), +\$2259.55 (median) Average CAGR (annualized rate of return) of those 401 60-month periods 3.98% Standard deviation (σ) of single-month returns, annualized 0.93% Link to Vanguard's web page for VMFXX VMFXX Vanguard's risk potential classificationRisk level 1(conservative) Vanguard funds are classified as conservative if their share prices are expected to remain stable or to fluctuate only slightly. Such funds may be appropriate for the short-term reserves portion of a long-term investment portfolio or for investors with short-term investment horizons (3 years or less).
 Number of periods in which VMFXX made less than VMMXXAverage/median shortfall versus VMMXX over those 401 periods 401/401 = 100.0%-\$66.68 (average), -\$42.54 (median) Number of periods in which VMFXX lost money 0/401 = 0.0% Number of periods in which VMFXX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 143 periods 143/401 = 35.7%-\$505.02 (average), -\$555.78 (median)
 Compared to VMMXX, 9/1981 - 8/1986 -\$386.74 Dollar loss, 9/2010 - 8/2015 +\$6.50 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1109.81
 Compared to VMMXX VMFXX vs VMMXX, 9/1981 - 8/1986
 Average/median additional return above VMMXX, over 401 overlapping 60-month periods -\$66.68 (average), -\$42.54 (median)

## Very short-term

### BIL: SPDR® Bloomberg Barclays 1-3 Month T-Bill

 Length of holding period 60 months Total number of overlapping 60-month periods 91 Average/median number of dollars earned in 60 months on a \$10,000 investment \$85.97 (average), +\$13.26 (median) Average CAGR (annualized rate of return) of those 91 60-month periods 0.17% Standard deviation (σ) of single-month returns, annualized 0.33%
 Number of periods in which BIL made less than VMMXXAverage/median shortfall versus VMMXX over those 91 periods 91/91 = 100.0%-\$97.66 (average), -\$99.47 (median) Number of periods in which BIL lost moneyAverage/median dollar loss over those 43 periods 43/91 = 47.3%-\$23.51 (average), -\$25.47 (median) Number of periods in which BIL failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 91 periods 91/91 = 100.0%-\$737.85 (average), -\$690.81 (median)
 Compared to VMMXX, 7/2007 - 6/2012 -\$211.25 Dollar loss, 2/2011 - 1/2016 -\$37.63 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1141.65
 Compared to VMMXX BIL vs VMMXX, 7/2007 - 6/2012
 Average/median additional return above VMMXX, over 91 overlapping 60-month periods -\$97.66 (average), -\$99.47 (median)

### FULIX: Federated Ultrashort Bond

 Length of holding period 60 months Total number of overlapping 60-month periods 211 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1419.59 (average), +\$1398.37 (median) Average CAGR (annualized rate of return) of those 211 60-month periods 2.69% Standard deviation (σ) of single-month returns, annualized 1.23%
 Number of periods in which FULIX made less than VMMXXAverage/median shortfall versus VMMXX over those 24 periods 24/211 = 11.4%-\$420.50 (average), -\$384.87 (median) Number of periods in which FULIX lost money 0/211 = 0.0% Number of periods in which FULIX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 82 periods 82/211 = 38.9%-\$166.40 (average), -\$102.85 (median)
 Compared to VMMXX, 1/2004 - 12/2008 -\$894.49 Dollar loss, 5/2013 - 4/2018 +\$527.63 Real loss (inflation-corrected), 11/2003 - 10/2008 -\$746.85
 Compared to VMMXX FULIX vs VMMXX, 1/2004 - 12/2008
 Average/median additional return above VMMXX, over 211 overlapping 60-month periods +\$449.36 (average), +\$464.14 (median)

### SHV: iShares Short Treasury Bond

 Length of holding period 60 months Total number of overlapping 60-month periods 95 Average/median number of dollars earned in 60 months on a \$10,000 investment \$180.35 (average), +\$92.75 (median) Average CAGR (annualized rate of return) of those 95 60-month periods 0.36% Standard deviation (σ) of single-month returns, annualized 0.46%
 Number of periods in which SHV made less than VMMXXAverage/median shortfall versus VMMXX over those 72 periods 72/95 = 75.8%-\$36.23 (average), -\$32.52 (median) Number of periods in which SHV lost money 0/95 = 0.0% Number of periods in which SHV failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 95 periods 95/95 = 100.0%-\$656.60 (average), -\$612.94 (median)
 Compared to VMMXX, 5/2014 - 4/2019 -\$74.45 Dollar loss, 1/2011 - 12/2015 +\$10.76 Real loss (inflation-corrected), 6/2009 - 5/2014 -\$1085.59
 Compared to VMMXX SHV vs VMMXX, 5/2014 - 4/2019
 Average/median additional return above VMMXX, over 95 overlapping 60-month periods -\$25.78 (average), -\$18.43 (median)

### SHY: iShares 1-3 Year Treasury Bond

 Length of holding period 60 months Total number of overlapping 60-month periods 149 Average/median number of dollars earned in 60 months on a \$10,000 investment \$1087.90 (average), +\$668.06 (median) Average CAGR (annualized rate of return) of those 149 60-month periods 2.09% Standard deviation (σ) of single-month returns, annualized 1.29%
 Number of periods in which SHY made less than VMMXXAverage/median shortfall versus VMMXX over those 19 periods 19/149 = 12.8%-\$37.85 (average), -\$23.28 (median) Number of periods in which SHY lost money 0/149 = 0.0% Number of periods in which SHY failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 85 periods 85/149 = 57.0%-\$402.96 (average), -\$417.21 (median)
 Compared to VMMXX, 11/2013 - 10/2018 -\$97.49 Dollar loss, 5/2013 - 4/2018 +\$163.25 Real loss (inflation-corrected), 4/2009 - 3/2014 -\$621.59
 Compared to VMMXX SHY vs VMMXX, 11/2013 - 10/2018
 Average/median additional return above VMMXX, over 149 overlapping 60-month periods +\$399.64 (average), +\$337.04 (median)

### VMLTX: Vanguard Limited-Term Tax-Exempt

 Length of holding period 60 months Total number of overlapping 60-month periods 328 Average/median number of dollars earned in 60 months on a \$10,000 investment \$2095.84 (average), +\$2049.61 (median) Average CAGR (annualized rate of return) of those 328 60-month periods 3.88% Standard deviation (σ) of single-month returns, annualized 1.84% Link to Vanguard's web page for VMLTX VMLTX Vanguard's risk potential classificationRisk level 1(conservative) Vanguard funds are classified as conservative if their share prices are expected to remain stable or to fluctuate only slightly. Such funds may be appropriate for the short-term reserves portion of a long-term investment portfolio or for investors with short-term investment horizons (3 years or less).
 Number of periods in which VMLTX made less than VMMXXAverage/median shortfall versus VMMXX over those 79 periods 79/328 = 24.1%-\$318.80 (average), -\$307.09 (median) Number of periods in which VMLTX lost money 0/328 = 0.0% Number of periods in which VMLTX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 58 periods 58/328 = 17.7%-\$169.29 (average), -\$138.18 (median)
 Compared to VMMXX, 6/1995 - 5/2000 -\$787.94 Dollar loss, 5/2013 - 4/2018 +\$451.01 Real loss (inflation-corrected), 7/2003 - 6/2008 -\$624.23
 Compared to VMMXX VMLTX vs VMMXX, 6/1995 - 5/2000
 Average/median additional return above VMMXX, over 328 overlapping 60-month periods +\$426.54 (average), +\$469.27 (median)

## Short-term

### VFISX: Vanguard Short-Term Treasury

 Length of holding period 60 months Total number of overlapping 60-month periods 278 Average/median number of dollars earned in 60 months on a \$10,000 investment \$2113.60 (average), +\$2291.78 (median) Average CAGR (annualized rate of return) of those 278 60-month periods 3.91% Standard deviation (σ) of single-month returns, annualized 1.95% Link to Vanguard's web page for VFISX VFISX Vanguard's risk potential classificationRisk level 1(conservative) Vanguard funds are classified as conservative if their share prices are expected to remain stable or to fluctuate only slightly. Such funds may be appropriate for the short-term reserves portion of a long-term investment portfolio or for investors with short-term investment horizons (3 years or less).
 Number of periods in which VFISX made less than VMMXXAverage/median shortfall versus VMMXX over those 7 periods 7/278 = 2.5%-\$37.75 (average), -\$41.37 (median) Number of periods in which VFISX lost money 0/278 = 0.0% Number of periods in which VFISX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 76 periods 76/278 = 27.3%-\$348.41 (average), -\$368.01 (median)
 Compared to VMMXX, 11/2013 - 10/2018 -\$71.49 Dollar loss, 5/2013 - 4/2018 +\$170.54 Real loss (inflation-corrected), 5/2013 - 4/2018 -\$604.20
 Compared to VMMXX VFISX vs VMMXX, 11/2013 - 10/2018
 Average/median additional return above VMMXX, over 278 overlapping 60-month periods +\$695.51 (average), +\$592.63 (median)

### VFIIX: Vanguard GNMA

 Length of holding period 60 months Total number of overlapping 60-month periods 414 Average/median number of dollars earned in 60 months on a \$10,000 investment \$4436.15 (average), +\$4003.39 (median) Average CAGR (annualized rate of return) of those 414 60-month periods 7.62% Standard deviation (σ) of single-month returns, annualized 4.88% Link to Vanguard's web page for VFIIX VFIIX Vanguard's risk potential classificationRisk level 2(conservative to moderate) Vanguard funds classified as conservative to moderate are subject to low to moderate fluctuations in share prices. In general, such funds may be appropriate for investors with medium-term investment horizons (4 to 10 years).
 Number of periods in which VFIIX made less than VMMXX 0/414 = 0.0% Number of periods in which VFIIX lost money 0/414 = 0.0% Number of periods in which VFIIX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 1 periods 1/414 = 0.2%\$0.00 (average), \$0.00 (median)
 Compared to VMMXX, 5/2013 - 4/2018 +\$502.65 Dollar loss, 5/2013 - 4/2018 +\$714.56 Real loss (inflation-corrected), 5/2013 - 4/2018 -\$60.18
 Compared to VMMXX VFIIX vs VMMXX, 5/2013 - 4/2018

### VFITX: Vanguard Intermediate-Term Treasury

 Length of holding period 60 months Total number of overlapping 60-month periods 278 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3101.87 (average), +\$3398.19 (median) Average CAGR (annualized rate of return) of those 278 60-month periods 5.55% Standard deviation (σ) of single-month returns, annualized 4.72% Link to Vanguard's web page for VFITX VFITX Vanguard's risk potential classificationRisk level 2(conservative to moderate) Vanguard funds classified as conservative to moderate are subject to low to moderate fluctuations in share prices. In general, such funds may be appropriate for investors with medium-term investment horizons (4 to 10 years).
 Number of periods in which VFITX made less than VMMXX 0/278 = 0.0% Number of periods in which VFITX lost money 0/278 = 0.0% Number of periods in which VFITX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 18 periods 18/278 = 6.5%-\$207.17 (average), -\$189.33 (median)
 Compared to VMMXX, 5/2013 - 4/2018 +\$4.02 Dollar loss, 5/2013 - 4/2018 +\$215.93 Real loss (inflation-corrected), 5/2013 - 4/2018 -\$558.80
 Compared to VMMXX VFITX vs VMMXX, 5/2013 - 4/2018

### VBISX: Vanguard Short-Term Bond Index

 Length of holding period 60 months Total number of overlapping 60-month periods 249 Average/median number of dollars earned in 60 months on a \$10,000 investment \$2199.64 (average), +\$2128.98 (median) Average CAGR (annualized rate of return) of those 249 60-month periods 4.06% Standard deviation (σ) of single-month returns, annualized 2.03% Link to Vanguard's web page for VBISX VBISX Vanguard's risk potential classificationRisk level 1(conservative) Vanguard funds are classified as conservative if their share prices are expected to remain stable or to fluctuate only slightly. Such funds may be appropriate for the short-term reserves portion of a long-term investment portfolio or for investors with short-term investment horizons (3 years or less).
 Number of periods in which VBISX made less than VMMXXAverage/median shortfall versus VMMXX over those 2 periods 2/249 = 0.8%-\$32.26 (average), -\$32.26 (median) Number of periods in which VBISX lost money 0/249 = 0.0% Number of periods in which VBISX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 42 periods 42/249 = 16.9%-\$188.70 (average), -\$169.68 (median)
 Compared to VMMXX, 10/2003 - 9/2008 -\$47.94 Dollar loss, 5/2013 - 4/2018 +\$327.33 Real loss (inflation-corrected), 5/2013 - 4/2018 -\$447.41
 Compared to VMMXX VBISX vs VMMXX, 10/2003 - 9/2008
 Average/median additional return above VMMXX, over 249 overlapping 60-month periods +\$922.85 (average), +\$864.65 (median)

### VSGBX: Vanguard Short-Term Federal

 Length of holding period 60 months Total number of overlapping 60-month periods 324 Average/median number of dollars earned in 60 months on a \$10,000 investment \$2577.15 (average), +\$2731.89 (median) Average CAGR (annualized rate of return) of those 324 60-month periods 4.69% Standard deviation (σ) of single-month returns, annualized 2.02% Link to Vanguard's web page for VSGBX VSGBX Vanguard's risk potential classificationRisk level 1(conservative) Vanguard funds are classified as conservative if their share prices are expected to remain stable or to fluctuate only slightly. Such funds may be appropriate for the short-term reserves portion of a long-term investment portfolio or for investors with short-term investment horizons (3 years or less).
 Number of periods in which VSGBX made less than VMMXX 0/324 = 0.0% Number of periods in which VSGBX lost money 0/324 = 0.0% Number of periods in which VSGBX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 69 periods 69/324 = 21.3%-\$219.19 (average), -\$201.62 (median)
 Compared to VMMXX, 6/1995 - 5/2000 +\$30.83 Dollar loss, 5/2013 - 4/2018 +\$250.18 Real loss (inflation-corrected), 5/2013 - 4/2018 -\$524.56
 Compared to VMMXX VSGBX vs VMMXX, 6/1995 - 5/2000

## Intermediate-term

### VBMFX: Vanguard Total Bond Market Index

 Length of holding period 60 months Total number of overlapping 60-month periods 336 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3453.65 (average), +\$3548.61 (median) Average CAGR (annualized rate of return) of those 336 60-month periods 6.11% Standard deviation (σ) of single-month returns, annualized 3.81% Link to Vanguard's web page for VBMFX VBMFX Vanguard's risk potential classificationRisk level 2(conservative to moderate) Vanguard funds classified as conservative to moderate are subject to low to moderate fluctuations in share prices. In general, such funds may be appropriate for investors with medium-term investment horizons (4 to 10 years).
 Number of periods in which VBMFX made less than VMMXX 0/336 = 0.0% Number of periods in which VBMFX lost money 0/336 = 0.0% Number of periods in which VBMFX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 1 periods 1/336 = 0.3%\$0.00 (average), \$0.00 (median)
 Compared to VMMXX, 11/2003 - 10/2008 +\$39.41 Dollar loss, 5/2013 - 4/2018 +\$652.07 Real loss (inflation-corrected), 5/2013 - 4/2018 -\$122.66
 Compared to VMMXX VBMFX vs VMMXX, 11/2003 - 10/2008

### VWIUX: Vanguard Intermediate-Term Tax-Exempt

 Length of holding period 60 months Total number of overlapping 60-month periods 447 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3582.15 (average), +\$3052.93 (median) Average CAGR (annualized rate of return) of those 447 60-month periods 6.31% Standard deviation (σ) of single-month returns, annualized 5.48% Link to Vanguard's web page for VWIUX VWIUX Vanguard's risk potential classificationRisk level 2(conservative to moderate) Vanguard funds classified as conservative to moderate are subject to low to moderate fluctuations in share prices. In general, such funds may be appropriate for investors with medium-term investment horizons (4 to 10 years).
 Number of periods in which VWIUX made less than VMMXXAverage/median shortfall versus VMMXX over those 64 periods 64/447 = 14.3%-\$3541.41 (average), -\$3415.36 (median) Number of periods in which VWIUX lost moneyAverage/median dollar loss over those 1 periods 1/447 = 0.2%\$0.00 (average), \$0.00 (median) Number of periods in which VWIUX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 34 periods 34/447 = 7.6%-\$3088.48 (average), -\$3528.18 (median)
 Compared to VMMXX, 12/1977 - 11/1982 -\$7849.79 Dollar loss, 12/1977 - 11/1982 -\$137.30 Real loss (inflation-corrected), 12/1977 - 11/1982 -\$5969.28
 Compared to VMMXX VWIUX vs VMMXX, 12/1977 - 11/1982
 Average/median additional return above VMMXX, over 447 overlapping 60-month periods +\$801.80 (average), +\$1252.20 (median)

## Long-term

### VNYTX: Vanguard New York Long-Term Tax-Exempt

 Length of holding period 60 months Total number of overlapping 60-month periods 344 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3347.41 (average), +\$3172.62 (median) Average CAGR (annualized rate of return) of those 344 60-month periods 5.94% Standard deviation (σ) of single-month returns, annualized 5.29% Link to Vanguard's web page for VNYTX VNYTX Vanguard's risk potential classificationRisk level 3(moderate) Vanguard funds classified as moderate are subject to a moderate degree of fluctuation in share prices. In general, such funds may be appropriate for investors who have a relatively long-term investment horizon (more than 5 years).
 Number of periods in which VNYTX made less than VMMXXAverage/median shortfall versus VMMXX over those 22 periods 22/344 = 6.4%-\$347.57 (average), -\$357.43 (median) Number of periods in which VNYTX lost money 0/344 = 0.0% Number of periods in which VNYTX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 9 periods 9/344 = 2.6%-\$296.84 (average), -\$281.81 (median)
 Compared to VMMXX, 12/2003 - 11/2008 -\$770.14 Dollar loss, 12/2003 - 11/2008 +\$1017.17 Real loss (inflation-corrected), 10/2003 - 9/2008 -\$636.77
 Compared to VMMXX VNYTX vs VMMXX, 12/2003 - 11/2008
 Average/median additional return above VMMXX, over 344 overlapping 60-month periods +\$1551.91 (average), +\$1652.10 (median)

## Balanced

### VBINX: Vanguard Balanced Index

 Length of holding period 60 months Total number of overlapping 60-month periods 265 Average/median number of dollars earned in 60 months on a \$10,000 investment \$4839.19 (average), +\$4408.20 (median) Average CAGR (annualized rate of return) of those 265 60-month periods 8.21% Standard deviation (σ) of single-month returns, annualized 8.79% Link to Vanguard's web page for VBINX VBINX Vanguard's risk potential classificationRisk level 3(moderate) Vanguard funds classified as moderate are subject to a moderate degree of fluctuation in share prices. In general, such funds may be appropriate for investors who have a relatively long-term investment horizon (more than 5 years).
 Number of periods in which VBINX made less than VMMXXAverage/median shortfall versus VMMXX over those 50 periods 50/265 = 18.9%-\$658.78 (average), -\$366.78 (median) Number of periods in which VBINX lost moneyAverage/median dollar loss over those 3 periods 3/265 = 1.1%-\$524.48 (average), -\$383.93 (median) Number of periods in which VBINX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 23 periods 23/265 = 8.7%-\$621.82 (average), -\$532.47 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$2789.91 Dollar loss, 3/2004 - 2/2009 -\$970.18 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$2366.15
 Compared to VMMXX VBINX vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 265 overlapping 60-month periods +\$3472.18 (average), +\$3553.53 (median)

### VASIX: Vanguard LifeStrategy Income

 Length of holding period 60 months Total number of overlapping 60-month periods 243 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3101.13 (average), +\$2737.43 (median) Average CAGR (annualized rate of return) of those 243 60-month periods 5.55% Standard deviation (σ) of single-month returns, annualized 4.33% Link to Vanguard's web page for VASIX VASIX Vanguard's risk potential classificationRisk level 2(conservative to moderate) Vanguard funds classified as conservative to moderate are subject to low to moderate fluctuations in share prices. In general, such funds may be appropriate for investors with medium-term investment horizons (4 to 10 years).
 Number of periods in which VASIX made less than VMMXXAverage/median shortfall versus VMMXX over those 9 periods 9/243 = 3.7%-\$658.03 (average), -\$527.14 (median) Number of periods in which VASIX lost money 0/243 = 0.0% Number of periods in which VASIX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 7 periods 7/243 = 2.9%-\$416.26 (average), -\$412.48 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$1399.01 Dollar loss, 3/2004 - 2/2009 +\$420.72 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$975.25
 Compared to VMMXX VASIX vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 243 overlapping 60-month periods +\$1866.12 (average), +\$1839.51 (median)

### VSCGX: Vanguard LifeStrategy Conservative Growth

 Length of holding period 60 months Total number of overlapping 60-month periods 243 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3455.06 (average), +\$2897.98 (median) Average CAGR (annualized rate of return) of those 243 60-month periods 6.12% Standard deviation (σ) of single-month returns, annualized 6.68% Link to Vanguard's web page for VSCGX VSCGX Vanguard's risk potential classificationRisk level 3(moderate) Vanguard funds classified as moderate are subject to a moderate degree of fluctuation in share prices. In general, such funds may be appropriate for investors who have a relatively long-term investment horizon (more than 5 years).
 Number of periods in which VSCGX made less than VMMXXAverage/median shortfall versus VMMXX over those 26 periods 26/243 = 10.7%-\$614.02 (average), -\$539.32 (median) Number of periods in which VSCGX lost moneyAverage/median dollar loss over those 2 periods 2/243 = 0.8%-\$248.09 (average), -\$248.09 (median) Number of periods in which VSCGX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 10 periods 10/243 = 4.1%-\$761.92 (average), -\$625.94 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$2308.30 Dollar loss, 3/2004 - 2/2009 -\$488.57 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$1884.54
 Compared to VMMXX VSCGX vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 243 overlapping 60-month periods +\$2220.05 (average), +\$2170.73 (median)

### VSMGX: Vanguard LifeStrategy Moderate Growth

 Length of holding period 60 months Total number of overlapping 60-month periods 243 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3898.08 (average), +\$3361.96 (median) Average CAGR (annualized rate of return) of those 243 60-month periods 6.80% Standard deviation (σ) of single-month returns, annualized 9.40% Link to Vanguard's web page for VSMGX VSMGX Vanguard's risk potential classificationRisk level 3(moderate) Vanguard funds classified as moderate are subject to a moderate degree of fluctuation in share prices. In general, such funds may be appropriate for investors who have a relatively long-term investment horizon (more than 5 years).
 Number of periods in which VSMGX made less than VMMXXAverage/median shortfall versus VMMXX over those 50 periods 50/243 = 20.6%-\$765.60 (average), -\$421.90 (median) Number of periods in which VSMGX lost moneyAverage/median dollar loss over those 3 periods 3/243 = 1.2%-\$714.72 (average), -\$580.11 (median) Number of periods in which VSMGX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 33 periods 33/243 = 13.6%-\$565.56 (average), -\$373.98 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$3011.84 Dollar loss, 3/2004 - 2/2009 -\$1192.12 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$2588.09
 Compared to VMMXX VSMGX vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 243 overlapping 60-month periods +\$2663.08 (average), +\$2616.12 (median)

### VASGX: Vanguard LifeStrategy Growth

 Length of holding period 60 months Total number of overlapping 60-month periods 243 Average/median number of dollars earned in 60 months on a \$10,000 investment \$4216.55 (average), +\$3837.30 (median) Average CAGR (annualized rate of return) of those 243 60-month periods 7.29% Standard deviation (σ) of single-month returns, annualized 12.27% Link to Vanguard's web page for VASGX VASGX Vanguard's risk potential classificationRisk level 4(moderate to aggressive) Vanguard funds classified as moderate to aggressive are broadly diversified but are subject to wide fluctuations in share prices because they hold virtually all of their assets in common stocks. These funds may be appropriate for investors who have a long-term investment horizon (10 years or longer).
 Number of periods in which VASGX made less than VMMXXAverage/median shortfall versus VMMXX over those 81 periods 81/243 = 33.3%-\$1124.46 (average), -\$880.50 (median) Number of periods in which VASGX lost moneyAverage/median dollar loss over those 17 periods 17/243 = 7.0%-\$517.02 (average), -\$306.74 (median) Number of periods in which VASGX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 73 periods 73/243 = 30.0%-\$921.98 (average), -\$827.74 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$3870.15 Dollar loss, 3/2004 - 2/2009 -\$2050.42 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$3446.39
 Compared to VMMXX VASGX vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 243 overlapping 60-month periods +\$2981.55 (average), +\$2946.99 (median)

### VWELX: Vanguard Wellington

 Length of holding period 60 months Total number of overlapping 60-month periods 474 Average/median number of dollars earned in 60 months on a \$10,000 investment \$7353.43 (average), +\$6741.95 (median) Average CAGR (annualized rate of return) of those 474 60-month periods 11.65% Standard deviation (σ) of single-month returns, annualized 10.11% Link to Vanguard's web page for VWELX VWELX Vanguard's risk potential classificationRisk level 3(moderate) Vanguard funds classified as moderate are subject to a moderate degree of fluctuation in share prices. In general, such funds may be appropriate for investors who have a relatively long-term investment horizon (more than 5 years).
 Number of periods in which VWELX made less than VMMXXAverage/median shortfall versus VMMXX over those 28 periods 28/474 = 5.9%-\$1314.67 (average), -\$1220.14 (median) Number of periods in which VWELX lost moneyAverage/median dollar loss over those 1 periods 1/474 = 0.2%\$0.00 (average), \$0.00 (median) Number of periods in which VWELX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 23 periods 23/474 = 4.9%-\$989.39 (average), -\$900.46 (median)
 Compared to VMMXX, 7/1977 - 6/1982 -\$3155.26 Dollar loss, 3/2004 - 2/2009 -\$110.72 Real loss (inflation-corrected), 10/1976 - 9/1981 -\$2522.53
 Compared to VMMXX VWELX vs VMMXX, 7/1977 - 6/1982
 Average/median additional return above VMMXX, over 474 overlapping 60-month periods +\$4392.66 (average), +\$4134.69 (median)

### VWINX: Vanguard Wellesley Income

 Length of holding period 60 months Total number of overlapping 60-month periods 474 Average/median number of dollars earned in 60 months on a \$10,000 investment \$6487.01 (average), +\$6003.33 (median) Average CAGR (annualized rate of return) of those 474 60-month periods 10.52% Standard deviation (σ) of single-month returns, annualized 6.94% Link to Vanguard's web page for VWINX VWINX Vanguard's risk potential classificationRisk level 3(moderate) Vanguard funds classified as moderate are subject to a moderate degree of fluctuation in share prices. In general, such funds may be appropriate for investors who have a relatively long-term investment horizon (more than 5 years).
 Number of periods in which VWINX made less than VMMXXAverage/median shortfall versus VMMXX over those 38 periods 38/474 = 8.0%-\$1384.20 (average), -\$1105.93 (median) Number of periods in which VWINX lost money 0/474 = 0.0% Number of periods in which VWINX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 24 periods 24/474 = 5.1%-\$1462.55 (average), -\$1460.40 (median)
 Compared to VMMXX, 8/1977 - 7/1982 -\$3925.58 Dollar loss, 3/2004 - 2/2009 +\$496.10 Real loss (inflation-corrected), 10/1976 - 9/1981 -\$2674.06
 Compared to VMMXX VWINX vs VMMXX, 8/1977 - 7/1982
 Average/median additional return above VMMXX, over 474 overlapping 60-month periods +\$3526.25 (average), +\$3461.27 (median)

## Stock

### VFINX: Vanguard 500 Index Investor

 Length of holding period 60 months Total number of overlapping 60-month periods 460 Average/median number of dollars earned in 60 months on a \$10,000 investment \$8110.06 (average), +\$8769.87 (median) Average CAGR (annualized rate of return) of those 460 60-month periods 12.61% Standard deviation (σ) of single-month returns, annualized 14.67% Link to Vanguard's web page for VFINX VFINX Vanguard's risk potential classificationRisk level 4(moderate to aggressive) Vanguard funds classified as moderate to aggressive are broadly diversified but are subject to wide fluctuations in share prices because they hold virtually all of their assets in common stocks. These funds may be appropriate for investors who have a long-term investment horizon (10 years or longer).
 Number of periods in which VFINX made less than VMMXXAverage/median shortfall versus VMMXX over those 98 periods 98/460 = 21.3%-\$1950.32 (average), -\$1990.57 (median) Number of periods in which VFINX lost moneyAverage/median dollar loss over those 49 periods 49/460 = 10.7%-\$892.25 (average), -\$796.92 (median) Number of periods in which VFINX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 102 periods 102/460 = 22.2%-\$1503.42 (average), -\$1448.25 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$4760.22 Dollar loss, 3/2004 - 2/2009 -\$2940.49 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$4336.46
 Compared to VMMXX VFINX vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 460 overlapping 60-month periods +\$5214.23 (average), +\$4869.13 (median)

### VGT: Vanguard Information Technology Index Fund

 Length of holding period 60 months Total number of overlapping 60-month periods 131 Average/median number of dollars earned in 60 months on a \$10,000 investment \$8254.93 (average), +\$9490.13 (median) Average CAGR (annualized rate of return) of those 131 60-month periods 12.79% Standard deviation (σ) of single-month returns, annualized 17.64% Link to Vanguard's web page for VGT VGT Vanguard's risk potential classificationRisk level 5(aggressive) Vanguard funds classified as aggressive are subject to extremely wide fluctuations in share prices. These funds may be appropriate for investors who have a long-term investment horizon (10 years or longer). The unusually high volatility associated with these funds may stem from a number of strategies.
 Number of periods in which VGT made less than VMMXXAverage/median shortfall versus VMMXX over those 12 periods 12/131 = 9.2%-\$1521.32 (average), -\$666.36 (median) Number of periods in which VGT lost moneyAverage/median dollar loss over those 5 periods 5/131 = 3.8%-\$1426.21 (average), -\$753.09 (median) Number of periods in which VGT failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 8 periods 8/131 = 6.1%-\$1812.93 (average), -\$1929.76 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$4942.99 Dollar loss, 3/2004 - 2/2009 -\$3123.26 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$4519.23
 Compared to VMMXX VGT vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 131 overlapping 60-month periods +\$7701.26 (average), +\$9410.77 (median)

### VTI: Vanguard Total Stock Market Index Fund

 Length of holding period 60 months Total number of overlapping 60-month periods 272 Average/median number of dollars earned in 60 months on a \$10,000 investment \$6576.57 (average), +\$6223.33 (median) Average CAGR (annualized rate of return) of those 272 60-month periods 10.64% Standard deviation (σ) of single-month returns, annualized 14.50% Link to Vanguard's web page for VTI VTI Vanguard's risk potential classificationRisk level 4(moderate to aggressive) Vanguard funds classified as moderate to aggressive are broadly diversified but are subject to wide fluctuations in share prices because they hold virtually all of their assets in common stocks. These funds may be appropriate for investors who have a long-term investment horizon (10 years or longer).
 Number of periods in which VTI made less than VMMXXAverage/median shortfall versus VMMXX over those 77 periods 77/272 = 28.3%-\$1736.71 (average), -\$1673.11 (median) Number of periods in which VTI lost moneyAverage/median dollar loss over those 40 periods 40/272 = 14.7%-\$696.45 (average), -\$555.81 (median) Number of periods in which VTI failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 79 periods 79/272 = 29.0%-\$1344.13 (average), -\$1293.83 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$4539.19 Dollar loss, 3/2004 - 2/2009 -\$2719.47 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$4115.44
 Compared to VMMXX VTI vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 272 overlapping 60-month periods +\$5180.28 (average), +\$5146.28 (median)

### VTIAX: Vanguard Total International Stock Index

 Length of holding period 60 months Total number of overlapping 60-month periods 224 Average/median number of dollars earned in 60 months on a \$10,000 investment \$3130.72 (average), +\$1778.26 (median) Average CAGR (annualized rate of return) of those 224 60-month periods 5.60% Standard deviation (σ) of single-month returns, annualized 16.81% Link to Vanguard's web page for VTIAX VTIAX Vanguard's risk potential classificationRisk level 5(aggressive) Vanguard funds classified as aggressive are subject to extremely wide fluctuations in share prices. These funds may be appropriate for investors who have a long-term investment horizon (10 years or longer). The unusually high volatility associated with these funds may stem from a number of strategies.
 Number of periods in which VTIAX made less than VMMXXAverage/median shortfall versus VMMXX over those 85 periods 85/224 = 37.9%-\$2116.79 (average), -\$1916.87 (median) Number of periods in which VTIAX lost moneyAverage/median dollar loss over those 55 periods 55/224 = 24.6%-\$1089.60 (average), -\$1019.98 (median) Number of periods in which VTIAX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 88 periods 88/224 = 39.3%-\$1653.81 (average), -\$1412.22 (median)
 Compared to VMMXX, 4/1998 - 3/2003 -\$5362.13 Dollar loss, 4/1998 - 3/2003 -\$3037.87 Real loss (inflation-corrected), 4/1998 - 3/2003 -\$4394.22
 Compared to VMMXX VTIAX vs VMMXX, 4/1998 - 3/2003
 Average/median additional return above VMMXX, over 224 overlapping 60-month periods +\$2047.05 (average), +\$767.67 (median)

### VTSAX: Vanguard Total Stock Market Index

 Length of holding period 60 months Total number of overlapping 60-month periods 272 Average/median number of dollars earned in 60 months on a \$10,000 investment \$6575.64 (average), +\$6215.42 (median) Average CAGR (annualized rate of return) of those 272 60-month periods 10.64% Standard deviation (σ) of single-month returns, annualized 14.44% Link to Vanguard's web page for VTSAX VTSAX Vanguard's risk potential classificationRisk level 4(moderate to aggressive) Vanguard funds classified as moderate to aggressive are broadly diversified but are subject to wide fluctuations in share prices because they hold virtually all of their assets in common stocks. These funds may be appropriate for investors who have a long-term investment horizon (10 years or longer).
 Number of periods in which VTSAX made less than VMMXXAverage/median shortfall versus VMMXX over those 77 periods 77/272 = 28.3%-\$1736.86 (average), -\$1673.04 (median) Number of periods in which VTSAX lost moneyAverage/median dollar loss over those 40 periods 40/272 = 14.7%-\$695.44 (average), -\$553.42 (median) Number of periods in which VTSAX failed to keep up with inflationAverage/median real loss (inflation-corrected) over those 79 periods 79/272 = 29.0%-\$1344.15 (average), -\$1298.61 (median)
 Compared to VMMXX, 3/2004 - 2/2009 -\$4542.25 Dollar loss, 3/2004 - 2/2009 -\$2722.52 Real loss (inflation-corrected), 3/2004 - 2/2009 -\$4118.49
 Compared to VMMXX VTSAX vs VMMXX, 3/2004 - 2/2009
 Average/median additional return above VMMXX, over 272 overlapping 60-month periods +\$5179.34 (average), +\$5140.95 (median)

## Notes

1. John Bogle, in his 1994 classic, Bogle on Mutual Funds, suggested using a low-cost short-term treasury bond fund, with its government backed credit rating, as a prudent substitute for a money market fund for investment reserves distinct from savings and transaction account balances. (p.132 in the text)
2. For funds and ETFs, calculations are based on data made publicly available free of charge from Morningstar. Data for the CPI is CPI-U, "CPI for All Urban Consumers," not seasonally adjusted, obtained from the Bureau of Labor Statistics.