Which return is right?

I was recently asked to do some analysis on a firm's return calculation process; this request stemmed from the fact that they were getting different returns for the same period. I surprised them, I think, when I said that more than one return could be "right."

During a Fundamentals of Performance Measurement class I am teaching this week in Sydney (Australia), I mentioned this discussion. I also mentioned how once again, Bill Clinton's famous "it depends on what you mean by the word 'is,' is" came to mind. In this case, it's the word "right" that is interesting.

What is "right"? In performance measurement it's deriving a rate of return using an acceptable method. Historically, there have been more "acceptable" methods, but this number has dwindled in recent years, mainly because of the Global Investment Performance Standards (GIPS(R)), but also because of the industry's general interest in providing more accurate returns (in 1988 I attended an event sponsored by the ICAA (now the IAA), that addressed this very topic). Gone (so to speak) are the Original Dietz method (which treated flows as mid-period events), as well as Modified Dietz and Modified BAI (which day-weight cash flows), unless you revalue for "large cash flows."

And so, we have three or  more "acceptable" methods to choose from:

• Modified Dietz (revalue for large cash flows)
• Modified BAI (revalue for large cash flows)
• Exact (revalue for all cash flows.

Does this mean that the most number of returns we might have is three? No, because we have to contend with the weighting method chosen; here we could have:

• Start-of-day (for all cash flows)
• End-of-day (for all cash flows)
• Start-of-day (for inflows) and end-of-day (for outflows)
• Start-of-day (for outflows) and end-of-day (for inflows)
• Middle-of-day (something I'm not a fan of, but know that some folks like).

This suggests that we might have 15 different returns. But, when you consider that one vendor allows the weights to go from 0 (end of day) to 1 (start), with increments of 0.1 (i.e., 0.1, 0.2, ... 0.9), the number jumps even higher!

And this is only the time-weighted variety. What about the Internal Rate of Return (IRR) as a money-weighted return?  That is arguably "right," too! You could use the IRR (the exact money-weighted return) or Modified Dietz (as an approximation).

Perhaps the exact method is the most right return (nice choice of words!), but even here there might be at least four varieties, based on how we choose to handle the cash flows, and of course exact for TWRR and MWRR will be different returns showing different results (unless there are no cash flows).

You still have the opportunity to encounter "wrong" returns (e.g., returns based on settlement date accounting, that ignore large flows, that use erroneous data, based on faulty methods, that don't revalue at least monthly), but they are, in most case, clearly "wrong."

You obviously want to avoid reporting different returns to the same party (this only leads to confusion, concern, and credibility issues). In the case of our client, they were getting two different returns from their performance system, one which I determined to be wrong.

Most firms are familiar with the challenge of having to reconcile their return to the custodian's and/or client's consultant, all of which may be technically "right." This whole subject makes for interesting discussions, I think.