Rate of return on investment

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Investors frequently ask how they can calculate the return their portfolio is generating. This calculation is a calculation of actual returns realized (past tense: ex post), not the returns expected (future tense: ex ante using NPV or IRR methods). It will be a compounded yearly return because most all comparatives use that assumption.

Any investment 'PV', invested at 'r1' rate, will be worth PV*(1+r1)' at the end of the year. e.g. $1,000 at 10% will be worth $1,000(1+0.1) = $1,000*1.1 = $1,100. If the return realized in the second year is r2 (e.g. 15%), the investment will be worth (it's value after year one)*(1+r2) at the end of the second year. E.g. $1,100*1.15 = $1,265. For however many years, PV*(1+r1)(1+r2)(1+r3)...... = The future value (FV) of the investment.

To find your annual return over the full period, you must find the one 'r' that can be used to replace all the different individual returns, so that when the PV is compounded every year, it will end up being worth the actual FV. This uses the standard equation for PV of a dollar.

[edit] In practice

  1. Determine your return for each separate year using (FV/PV)-1. If you have added(withdrawn) savings during the year, you must decide whether or not these $transfers are part of the PV. If they were evenly spaced throughout the year, then calculate the return twice (with and without the $transfers) and take the average return.
  2. Apply the first year's rate of return to a nominal $100 (PV). This will give a nominal 100(1+r1).
  3. Apply the second year's return to the result above. This gives a nominal 100(1+r1)(1+r2).
  4. Continue this process for each year's return, to give the final (FV) value of a nominal $100.
  5. Use the PV of a dollar equation, or financial calculator, to calculate the average annual return using the PV and FV of the nominal $100, and the number of years. Solve for the rate of return.

An example of an Excel spreadsheet using this method is at [1]

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