The Compounded Time-Weighted Return is the total return when the monthly return is compounded monthly. If you take your beginning balance, add the 3.4% return for the first month, then add the 0.2% return for the second month, etc., your ending balance is 12.8% more than you started with. Since this is a 12-month period, this return or yield is the same concept as APR or APR. If you had more or less than a 12-month period, it is no longer an annual yield, so you could call it the total yield for the period.

The Annualized Time-Weighted Return is the average of the monthly returns expressed as an annual percentage without compounding. The average is computed geometrically over the entire period to weight the monthly returns accurately. That monthly average is then simply multiplied by 12 months to give an nominal, annualized rate.

If you plug the Annualized Time-Weighted Return into a financial calculator and compound it monthly, you will get the Compounded Time-Weighted Return. If you have a 12-month report like yours, that’s all there is too it.

If you a reporting for more than twelve months, it might be useful to also know the Annualized Compounded Time-Weighted Return (the compounded return expressed on an annual basis). If your investments had the same performance for a second year, the 2-year Compounded Time-Weighted Return would be on the report as 27.2%. The Annualized Compounded Time-Weighted Return (not currently on our reports) would be the same 12.8% that is on your 1-year report. Likewise the Annualized Time-Weighted Return would be unchanged at 12.1%. Should we add the Annualized Compounded Time-Weighted Return to ROI reports? This may not be important to you until you start doing multi-year reports.

If you a reporting for less than twelve months, annualized returns are not reported at all, since that would require an assumption that the return for the short period would continue for the rest of the year. This is not allowed by most accounting standards.

This is all pretty heady stuff. I’d be happy to discuss it further or hear any suggestions how to make the reports clearer. I have some sample data that has just one investment so it’s easier to see what’s going on.

If you want to verify the numbers:

Compounded Time-Weighted Return = ((1+Jan return) * (1+Feb return)…*(1+Dec return)) – 1 = 12.754%
or more simply
Compounded Time-Weighted Return = ((Ending balance) - (Starting balance)) / (Starting balance)

For your 12-month period:
Annualized Time-Weighted Return = ((((1+Jan return) * (1+Feb return)…*(1+Dec return)) ^(1/12)) – 1) * 12 = 12.065%