# Calculating returns

I wrote this in response to the following question from Chris. It’s a great question and although the answer will take some concentration, it’s worth following.

My question is if you really had such high returns or if they may have been inflated by new money that was added. I’d also like to know how to properly calculate returns because I like to monitor my performance versus the major equity indices. Thanks.

Great question, Chris,

I retired in July 1996, so I’ve actually been taking out money to live on ever since, instead of adding money.

Here’s how to calculate it. Say you start the year with \$14,000. You want to equate that with 100% and calculate gains and losses from there. So you ask yourself “What number (factor) would I multiply \$14,000 by to get 100?”

By simple arithmetic we have 14000 x F = 100

And thus F = 100/14000 = .0071428

Sure enough 14,000 x .0071428 = 100

Now say three weeks later you have \$14,740 and you want to see how you are doing, you multiply that number by .0071428 and you get 105.3 (so you are up 5.3%). If you don’t add or subtract money, that factor will work for the whole year.

Now say you add \$2300 of fresh money, but you don’t want that to screw up your estimate of how well you are doing.

You add the \$2300 to the \$14,740 and get \$17,040 which is your new balance that you are investing with. That’s your new starting point. It doesn’t affect how you’ve done up to here. You haven’t suddenly done better because you added money. You can’t still multiply by .0071428 because you’d get 121.7 and it would look as if you were up 21.7%, when you are really only up 5.3%.

So you need to change your factor to make it smaller so it will still reflect the 5.3% gain you’ve made so far. You figure: “What would I multiply my new balance (\$17,040) by to get 105.3, to reflect my 5.3% gain so far this year?”

F x 17,040 = 105.3

F = 105.3/17,040 = .0061795

And that’s your new factor. If you multiply it by 17,040, sure enough you get 105.3. Now you continue to see how you will do for the rest of the year.

If a little later you are at \$18,000, you multiply 18,000 by .0061795 and you get 111.2, so you know that your investing is now up 11.2% for the year.

Same, if you take money out. You don’t want it to look as if you lost money. You calculate a new factor so you start from the same percentage where you were.

On January 1st of the next year, you write down how you did for the year and start over at 100 for the next year.

Hope this helps

Saul

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