Question

The money-weighted return is \(PV_{inflows}=PV_{outflows}\) which is \(0=\frac{a}{1+r}+\frac{b}{(1+r)^2}+...+\frac{z}{(1+r)^n}\) Where all numerators are either the outflows or inflows of that particular year.

Now the money-weighted return is basically the geometric mean of the holding period returns for each year which is \(((1+HPY_1)(1+HPY_2)...(1+HPY_n))^{\frac{1}{n}}-1\)

Now I have come across the following statement and I cant wrap my head around it.

Answer 1

"If funds are added to a portfolio just before a period of poor performance the money weighted return will be lower than the money weighted return. If funds are added just prior to a period of high returns the money weighted return will be higher than time weighted return"

Now the time-weighted return isnt affected by the cash flows. This is basically being affected by the time weighted return. Basically my question is how does the timing of the cash flows effect the money-weighted return

Answer 2

Seems prudent to create a three (3) cash-flow diagramme and see what happens. This provide a means always to find a solution (quadratic at worst).

Let's see some exploration.

Answer 3

An investor purchases a stock for $50 at time t=0 and another share at t=1 for $65. At the end of year 1 and 2 the stock paid a $2 dividend. Also at the end of year 2 the investor sold both stocks for $70
Lets find the time weighted-return and the money weighted return I guess