I have a question on Time-Weighted Rate of Return (TWRR) and then a question on the links between MWRR and TWRR,
An investor invested £100 in a fund on Jan 1st 1998 and another £100 on Jan 1st 1999. The following gives the price of a unit in the fund on Jan 1st:
Year Unit Price 1998 100 1998 125 2000 130
Calculate TWRR and MWRR for the period 1998-2000 (1st Jan).
I am aware of the definition, but when I looked at the solution to this question, it was rather bizarre.
For MWRR they got:
100 + 100(1+i)^-1 = 234(1+i)^-2 so i=10.93%
For TWRR they got:
125/100 x 234/225 = (1+i)^2 so i=14.02%
The ‘234’ comes from a ratio I think. They had these calculations:
Year Unit Price Invest 1998 100 100 1 100 1998 125 100 1+ 100/125 = 1.8 225 2000 130 1.8 234
Can you please explain this to me?
Also, the last part was a general proof. It asked ‘when is MWRR > TWRR’. Therefore, I am guessing we need to find a general interest rate (It) to show this is true. The questions hint is: Assume you invest 1 unit at time 0 and 1 unit at time 1. What’s the accumulation at time 2? This is guess but is the accumulation 1(1+I1)(1+I2) + 1(1+I2). But what’s this got to do with MWRR/TWRR? And how does it help? I am not sure how to do this and hope someone can help me! :)