A stupid question probably… In the TWR calculation, where is the “time-weight” element?
eg. the modified dietz method…weighs the cash inflows and outflows based on the amount of time they have been in / out of the portfolio… thus the time factor…
I had the same question sometime back mumu, modified dietz and TWR is not caluclated the same way …agree with you mod dietz accounts for the time weight element
Mod Dietz is an estimate of the true TWRR. As such, it is a form of TWR (as opposed to MWR). I think it is more like a continuum, with MWR at one end and true TWR at the other. Moving from left to right you would have MWR->Original Dietz->Mod Dietz->I think there is some bankers return here?!->True TWRR. From left to right the affect of cash flow is further removed.
Consider the following example: Investment on May 1: 1M$ Value on May 11: 1.01M$ Then, on May 11, a cash inflow occurs of 1.01M$, resulting in 2.02M$ balance. On May 16, the position is worth 2.05M$ So, the holding period returns are: Period 1 (May1-11): (1.01-1)/1 = 0.01 = 1% Period 2 (May11-16):(2.05-2.02)/2.02 = 0.014851 = 1.49% The TWR can be obtained by simply chain-linking (I think that’s what it was called) these holding period returns: 1.01 * 1.014851 -1 = 0.025 = 2.5% So far, so unclear. However, these are holding period returns, and not annualized ones (or standardized to any other time unit). By calculating daily returns for both periods: Period 1 daily return (10 days) = 10th root of 1.01 - 1 = 0.000996 = 0.0996% Period 2 daily return (5 days) = 5th root of 1.014851 - 1 = 0.002953 = 0.2953% Now, the reason why this is called “time” weighted is that you can obtain the result (TWR) by linking the individual returns, or viewed another way, you can count the number of days that each return occurs (which is exactly inverse to the procedure above). For daily returns, the calculation would be: 1.000996^10 * 1.004951^5 = 1.01 * 1.014851 - 1 = 0.025 = 2.5% The fact that you usually use holding period returns obscures the fact that the return for each day (or whatever the unit, could be month, year, or minute) is “counted” once. Calculating with HPR is of course a shortcut, you would not solve the problem above by first computing the daily returns, as it involves calculating HPRs first, obtaining daily returns, and finally getting HPRs again, which would be totally pointless and an unnecessary detour. Furthermore, “money” weighted should actually be called “money-and-time” weighted, as it is the same as the TWR, but additionally weighting each daily (or HP) return by the amount of cash invested over the period. The TWR does NOT consider that the first period has more funds invested than the second, while the money weighted would double the second period’s return’s influence in the calculation.
Good example, OA.
Thanks old_akakaraka for your brilliant example ! MH
excellent… well said…