# Find net cumulative return from my Investment Report for a 3 month period

I have an Investment Report for a 3 month period that shows me:

• Number of Shares
• Book Cost
• Market Price
• Market Value
• Estimated Income
• Estimated Yield
• Total Value %

How do I work out the cumulative return for that 3 month period?

• Is there something in particular you are planning on doing with that information? This will impact whether a simplistic or most accurate approach is most appropriate. – Grade 'Eh' Bacon Mar 31 '20 at 22:06

## 2 Answers

The simplest way to determine the return of an asset is to take the ending value and divide it by the starting value. Let's build that up in terms of how complex you may want to get:

1) If you start with \$100 in the bank, they pay you \$2 in interest, and you end the year with \$102. 102 / 100 = 102%, and after subtracting the 100% you started with, this is a 2% return.

2) If you start with 100 shares worth \$1 each, and at the end of the year they are worth \$1.05 each, your return is \$105 / \$100 - 1 = 5%.

3) If you have shares that pay dividends, and you have interest-earning assets, the formula is (ending value of all assets, including cash received as dividends and interest ) / (opening value of all assets when you started the account) - 1. So if scenario #1 & #2 were both correct, you ended the year with \$207 in value and started with \$200 in value, so the return would be 207/200 - 1 = 3.5%.

4) Further, that return above is 'simplistic', not 'annualized'. If you had a 3.5% return over 3 months, then we could simplistically multiply that by 4, to represent the expected return over a whole year, and 3.5% * 4 = 14%.

5) Finally, the method in #4 above doesn't consider "compounding"; so technically your return would be higher over the whole year, because the earnings in the 1st 3 months would continue to earn income, and the earnings in the next 3 months would also earn income, etc. The formula for this is (return over a length of time + 1) ^ (how many of those lengths of time you are considering) [ie 12 months in a year, 4 quarters in a year, 365 days in a year, etc.] -1.

So for a 3 month return where you need to account for 4 of those periods to get a yearly return, the formula would be: (3 month return + 1) ^ (4) - 1. So 1.035^4 - 1 = 14.75%. For most purposes if you just want a simple approximation of return, method in #4 above will be close.

This is not easy.

It is made harder by there being several measures of return. One is money-weighted rate of return and the other is time-weighted rate of return.

If you did not make any changes, the return is `100*(market_value_now / market_value_3mo_ago - 1)`. This formula requires that there are no dividends, or that you wish to exclude dividends from the calculated return.

However, for the `market_value_3mo_ago` you need your report from 3 months before the current report.

If you made changes to the portfolio or got dividends, please not that then time-weighted rate of return is different from money-weighted rate of return.