How do we measure returns? The simplest way is to measure the principle at the start and then the market value at the end. e.g.
Beginning Value (BV): S$1m, 1 Jan 2008
Ending Value (EV): S$1.5m, 24 Sep 2010
Returns: (1.5 - 1)/1m = 50%
What if there was cash inflow or outflow in the interim?
BV: S$1m, 1 Jan 2008
Market Value (MV): S$1.5m 1 Jan 2010
Cash inflow: S$10m 1 Jan 2010
EV: S$11.6m
If you use the previous method, returns was actually 50% before cash inflow but fell to (S$11.6 - 11m)/11m = 5.45%
Due to the large cash inflow, the base has increased from S$1m to 10m. The performance of 50% from 1/1/08 to 1/1/10 has been dwarfed because of the cash inflow of 10m on 1/1/10.
The best way is to do a time-weighted return (TWR):
BV: S$1m, 1/1/08
MV: S$1.5m, 1/1/10
Return from 1/1/08 - 1/1/10: (1.5 - 1)/1 = 50%
Cash inflow: S$10m, 1/1/10
BV: S$11.5m, 1/1/10
EV: S$11.6m, 24/9/10
Return from 1/1/10 - 24/9/10: (11.6 - 11.5)/11.5 = 0.87%
Total Return = ((1+0.5)*(1+0.0087))-1 = 0.51305 or 51.3%
Annualised return = ((1.51)^(1/(964/365)))-1 = (1.51^(1/2.64))-1 = 16.89% per annum
Why 964? That is the number of days from 1/1/08 to 24/9/10. 2.64= number of years.
