Money weight return vs Time weight return

CFA Level III Portfolio Management
#1

In the answer of one question in EOC of Reading 32, it states that MWR is sensitive to size and timing of external cashflow, while TWR is not …

But by definition the formular of TWD involves the timing and size of cashflow, while MWR is just the IRR which takes only the starting and ending value. Isn’t it then the opposite (MWR insensitive to size and timing of cf)? What is missing here please?

Quoted from CFA curriculum:

“The MWR represents the average growth rate of all dollars invested in an account, while the TWR represents the growth of a single unit of money invested in the account. Consequently, the MWR is sensitive to the size and timing of external cash flows contributed to and withdrawn from the account, while the TWR is not affected by the cash flows. Under “normal” conditions, these two return measures will produce similar results. However, when external cash flows occur that are large relative to the account’s value (rule of thumb: greater than 10%) and the account’s performance fluctuates significantly, then the MWR and the TWR can differ substantially.”

#2

TWR - Formula requires you to remove the CF, hence calculate the return per period without this CF, so not affected by CF or timing as you are removing this effect on returns

MWR - basicaly works out the return for the period with these CF included, starting and ending figure, hence no need to remove CF

#3

No, it doesn’t.

The formula for TWR is:

1 + TWR = [(1 + _r_1)(1 + _r_2) ∙ ∙ ∙ (1 + rn)]^(1/n)

No, it doesn’t.

MWR is the IRR taking into account all of the cash flows.

#4

Oh yes… Thanks so much.

My understanding was completely wrong lol

#5

My pleasure.