Time-weighted rate of return (Quants)

CFA Level I
#1

The quarterly returns on a portfolio are as follows:

Support

Quarter. Return

  1.         20%

  2.        -20%

  3.         10%

  4.         -10%

Q. The time-weighted rate of return of the portfolio is closest to:
A) -5%
B) -1.3%
C) 0%

I am getting B
{(1+0.20)(1-0.20)(1+0.10)(1-0.10)}^0.25 - 1
= -1.26%

The solution says answer is A
Bec they did

{(1+0.20)(1-0.20)(1+0.10)(1-0.10)} - 1
= -5%

But TWR is same as Geometric Mean so please help why raise to (1/4) is not taken

#2

No, it isn’t.

The question is asking for the total return, not the average quarterly return.

#3

It’s asking the time weighted return right?

#4

Yes. The TWR is an annualised (yearly number)
You have data for 4 quarters
When you multiple 4 quarters together in form "(1+r) … - 1 "etc you get an annual number.

If you had been given 4 YEARS of data your approach would be correct

#5

Thank you so much for clearing the concept :slight_smile: