How to Measure Returns

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.