Background
I am trying to figure out the computational difference between Time-Weighted Rate of Return (TWRR) and Money-Weighted Rate of Return (MWRR).
Let's say, I have a portfolio looking like this:
- 2012-Q4 - Begin Market Value (BMV) is $10,000, and End Market Value (EMV) $11,000. So, over the quarter, I made 10% on my stocks.
- 2013-Q1 - I decide I will invest another $4,000 in Cash Flow (C), so my BMV is now $15,000. If I make 5% this quarter, my EMV is now $15,750.
- 2013-Q2 - My portfolio didn't go so well last quarter, so I take $2,000 (C) out. My BMV is $11,750. I make 10% over this quarter so my EMV is now $12,925.
MWRR
If I calculate my MWRR ( (EMV - BMV) / BMV
):
- 2012Q4 =
($11,000 - $10,000) / $10,000
= 10% - 2013Q1 =
($15,750 - $15,000) / $15,000
= 5% 2013Q2 =
($12,925 - $11,750) / $11.750
= 10%MWRR =
(2012Q4 x 2013Q1 x 2013Q2) ^ (1/3)
= 7.93%
TWRR
Then the TWRR ( (EMV-BMV-C)/(BMV + .5 x C)
):
- 2012Q4 =
($11,000 - $10,000 - $0) / ($10,000 + 0.5 x $0)
= 10% - 2013Q1 =
($15,750 - $15,000 - $4,000) / ($15,000 + 0.5 x $4,000)
= -19.1% 2013Q2 =
($12,925 - $11,750 + $2,000) / ($11,750 + 0.5 x -$2,000)
= 29%TWRR =
(2012Q4 x 2013Q1 x 2013Q2) ^ (1/3)
= ??
Questions
So, my two questions:
- As there are negatives in my TWRR's, it doesn't make sense to use a Geometric Mean (nor is it possible with imaginary numbers). The rates are still dependent in time, so a geometric mean would SEEM the appropriate way to weight them. What other ways can I aggregate my TWRR's?
- The TWRR numbers seem way off. I certainly wouldn't have lost 20%, even weighted for cash-in/cash-out. What am I doing wrong?