# Calculating Returns

Mike is a member of The Motley Fool Blog Network -- entries represent the personal opinion of the blogger and are not formally edited.

It's getting to be the end of the year and this is always the perfect time to see how you fared relative to your favorite benchmark.  But how exactly do you do that?  It becomes especially vexing if you're constantly putting money into the market (like a typical person who was employed and contributing to an IRA or 401(k) or if you are withdrawing money regularly (like a typical retiree).  How do you factor that in?

I calculate my returns monthly. When you calculate returns you have the option to pick pretty much whatever frequency sample rate you want. You could do it daily, weekly, monthly, quarterly, annually, etc. I find that monthly gives me enough granularity without driving me nuts with the bookkeeping that daily updating would. I then use these monthly returns to calculate my annual total return.

Calculating my returns monthly gives me enough granularity to take into account any new money I'm adding into my portfolio and any money I might withdraw from my portfolio. It's important not to include new money added or money taken out in your portfolio returns or you won't be able to fairly compare your stock picking performance to the S&P 500 index or whatever other benchmark you are using. The method I describe here is the method used by mutual funds to calculate their returns, as they also do not want to be penalized or rewarded for client cash flows that are not in their control. This method is called the time-weighted rate of return, or TWRR for short.  Here's how it works:

Each month I record my portfolio's balance at the beginning of the month and then at the end of the month. To get the return for the month I perform this calculation:

( (end of month value - net new cash added) - beginning of month value)/beginning of month value = return for the month

For example, If my starting balance for the month was \$10,000, I added \$2,000 at the beginning of the month from my paycheck, and the end of the month balance was \$15,000, my portfolio return was not (\$15,000-\$10,000)/\$10,000 = 50%. Instead, it is (\$13,000-\$10,000)/\$12,000 = 25%.

Likewise, if my starting balance for the month was \$10,000, I withdrew \$2,000 at the beginning of the month from my account, and the end of the month balance was \$9,000, my portfolio return was not (\$9,000-\$10,000)/\$10,000 = -10%. Instead, it is (\$11,000-\$10,000)/\$8,000 = 12.5%.

I then multiply all of the months' returns together to get my annual total return. So if for month 1 I got a 20% return, month 2 I got a 5% return, and month 3 I got a -10% return, my three month return would look like this:

[1.2 * 1.05 * (1 - 0.1)] - 1 = 13.4% rate of return

Remember that when you are multiplying returns together you do not use negative numbers. Instead you subtract the negative return from 1 and use the result.

Granted, you can get a more and more accurate total return the more samples you take, especially if you are putting in money or are taking out money very frequently. If you are adding money twice a month maybe you'd want to calculate your returns weekly, or maybe the extra accuracy isn't worth the hassle. You could even calculate your returns daily. At this point it all depends on how accurate you want to get and how much work you want to do.