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For example, I was viewing this mid-cap index fund: http://www.bloomberg.com/quote/VMGRX:US It says the annual return is 16.41%.

How is that calculated? The index has not risen enough in price over the past year to match with that figure. Am I miscalculating something?

Is it averaged over the past 5 years?

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That's the Total Return for the last 12 months.

There was a dividend of $0.63 on December 22, 2014, causing the price to drop about $0.63. If you reinvest that dividend at that time, that $0.63 will continue to grow till now.

Use proper tools to look at Total Return:

https://ycharts.com/mutual_funds/M:VMGRX

You would not see the gap down in December when using this tool, and the 1y Total Return on the chart clearly says ~16%

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