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How Vanguard Calculates Historical Growth

If you’re a long time investor with Vanguard, chances are you’ve taken a look at their “Hypothetical growth of $10,000” chart included with each of their mutual funds. If you’re like me, chances are you take a peek but never spend much time digging much deeper. I tend to focus on expense ratio, average annual performance versus a benchmark, risk potential, and some other metrics like SEC yield, portfolio composition and characteristics.

Reader Javier looks a little more closely and found something that seemed, at least initially, distressing. He took a peek at Vanguard’s Short Term Treasury Fund (VFISX [3]) and found the nice upward trending chart a little at odds with the one at Yahoo [4]. At first glance, it looks significantly different (stretch it out to start in 2000).

So he emailed Vanguard to ask what was up… and this is their reply:

As mentioned in our previous e-mail, Vanguard’s chart shows a hypothetical one time investment of $10,000 with the funds dividends and capital gains distributions reinvested. This graph depicts the calculation of total return for the time period specified.

If you would like to view the daily price history chart on our website you can go to the same chart as you did previously, however, there is a link that says “view price history chart”. Simply click on the link and the chart will resemble the Yahoo! chart.

The main problem with using a price history chart is that the size of spikes and dips seems amplified even if the range is really not that great. This fund is a great example – as of October 31, 2010, the chart shows a low of $10.18 and a high of $10.94. The range of 76 cents is a mere 7.45% change from the beginning value.

Our default Growth of $10,000 chart, however, shows the power of compounding (through reinvestment of dividends and capital gains) and long-term investing. Starting at a flat $10,000 investment, after ten years of continuous reinvestment in the fund, the total value is $15,756.77 – a cumulative return of almost 57% as of October 31, 2010.

Although Vanguard does not provide customized total returns, you may use one of the following formulas to calculate the total return of a fund.

If the fund has made no distributions >>

[(Ending price / Beginning price) – 1] x 100 = Total Return

Or, if the fund has made distributions, follow these four steps >>

1. (1st (earliest) distribution/1st reinvestment price) + 1 = 1st reinvestment factor
2. [(2nd distribution x 1st reinvestment factor) / 2nd reinvestment price ] + 1st reinvestment factor = 2nd reinvestment factor
3. Repeat step 2 until all reinvestment prices have been used.
4. [(Ending price x Last reinvestment factor / Beginning price) – 1] x 100 = Total Return

Please remember:
* The beginning price is the last closing net asset value (NAV) before the beginning of the period.
* The calculations must go to at least five decimal places to ensure accuracy.
* Total return calculations are net of expenses.
* Total return percentages illustrate past performance and are not representative of an investment made to the fund today.

A quick summary of the larger email is that reinvestment makes a very big difference. While it’s hard for us to look back at the historical dividends and distributions of the fund, the basic argument is that while the price can fluctuate, it’s fluctuation is small compared to the compounded gains and reinvestment of dividends.

It’s a plausible explanation that satisfies me (and Javier). Does it satisfy you?