## Wednesday, May 16, 2012

### Modified Dietz or BAI, which to choose?

I got an email this week from someone who wanted to know the difference between Modified Dietz and Modified BAI. Briefly:
1. They are both approximations to the true, time-weighted rate of return
2. They are both based on the concept of linking money-weighted returns to derive a time-weighted return
3. They should yield equivalent results.
Modified BAI is actually, in my view, a misnomer, or perhaps more precisely, the use of an inappropriate qualifier; I will explain below.

The Bank Administration Institute (BAI) developed the first performance measurement standards in 1968. In that document they offered three methods to calculate time-weighted returns:
1. The exact method, which requires revaluing the portfolio for all cash flows. The BAI recognized that it was unlikely that this could be accomplished very easily at that time, and so offered the other methods as alternatives.
2. The linked IRR (internal rate of return) involves calculating returns for subperiods (ideally, no longer than a month) and geometrically linking these returns to obtain approximations to the TWRR.
3. The third involves an alternative approach to geometric linking: "The time-weighted rate of return is ... the average of the rates for [the] subperiods with each rate being given a weight proportionate to the length of time in its subperiod." Suffice it to say, this approach has died away, though we retain the term, "time-weighting" (in spite of the fact that we do not weight time).
What we think of today as the "Modified BAI" is actually BAI's Linked IRR. We are not modifying anything; it is just one of the three methods. And so, we link subperiod internal rates of return to obtain an approximation to the true TWRR.

An unlinked Modified Dietz (MD) is an approximation to the IRR. And so, by linking subperiod MD returns (as we do with linking the IRR), we obtain an approximation to the true TWRR.

Which is better? I don't think it matters. Linking Modified Dietz returns is easier than linking internal rates of return, since the IRR is an iterative formula while Modified Dietz is solved directly. The results should be identical, or at least very close. Is one "more correct"? Not in my view.