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# Internal rate of return

Internal rate of return (IRR) is the rate of return a portfolio earns per year, taking into account the change in value of the holdings of the portfolio, whether open or sold, and the length of time the positions have been held.

## Expanded Definition

IRR is best thought of as the yearly interest rate that matches the actual change in the investment over the time period, once changes in capital are taken into consideration. This means that shorter time periods will show a higher IRR than longer time periods, and larger positions will have more effect than smaller ones.

For example: You purchase two stocks on Jan. 1, 2009. You buy \$100 worth of Stock A, and \$200 worth of Stock B.

On Jan. 1, 2010, you sell both stocks. Stock A has doubled, and Stock B is down 25%.

 Ticker Buy Date Purchase Value Sell Date Sale Value Stock 1 Jan. 1, 2009 \$100 Jan. 1, 2010 \$200 Stock 2 Jan. 1, 2009 \$200 Jan. 1, 2010 \$150

Your initial outlay was \$300, and on Jan. 1, 2010, you had \$350. This is a one year return of 17%. Basically, when you have a one year period, both the IRR of your portfolio and your average returns are the same.

What if you purchased Stock A in 2008, and Stock B in 2009? Your IRR would be different because the time period has changed - a 100% increase over 2 years is less valuable than a 100% increase over 1 year. (This is because of the time value of money.)

Your portfolio table would look like this:

 Ticker Buy Date Purchase Value Sell Date Sale Value Stock 1 Jan. 1, 2008 \$100 Jan. 1, 2010 \$200 Stock 2 Jan. 1, 2009 \$200 Jan. 1, 2010 \$150

The average return would still be 17%, because you started with \$300 and ended up with \$350. Your IRR would be 12%, though, because your gains are now being counted over two years instead of one.