dmar

it's really not as bad as it looks...

Basically, you raise the product to: x/y, where:
x = number of periods over which we want the time-weighted return over
y = sum of periods covered by the component returns

much easier to explain with actual numbers. So taking the original example:
x = 12 months (coz we want the annual time-weighted return)
y = 12 months (4 quarters)

so you raise it by 12/12 = 1.

if we wanted to calculate the ANNUALIZED time-weighted return, given returns from SIX quarters:
x = 12 (coz, annual)
y = 18 (6 quarters)

so, we'd raise the product by: 12/18 = 0.67