Friday, July 9, 2010

Why time-weighting if we don't weight time?

There seems to be some confusion as to what "time-weighting" actually means. The term was coined in the 1968 Bank Administration Institute (BAI) standards. The BAI proposed three ways to calculate returns:
• the "exact method," whereby we revalue the portfolio for any cash flow
• the "linked IRR," where we geometrically link subperiod (e.g., monthly) returns which were derived using the internal rate of return (IRR); this is similar to the Modified Dietz formula
• the time-weighted method, where instead of geometrically linking, we link returns based on the length of time between flows.
The third method can produce returns which are in error, thus it's been abandoned. However, the term "time-weighting" remains in our lexicon. But do we "weight" time? Nope! In fact, time has no bearing whatsoever on our returns. If we link a one day return, with a one week, one month, one quarter, one year, and one decade return, we will obtain a cumulative return across the full period, but in no way do we give extra "weight" to any of these periods.

In no way do we weight time in time-weighting. Granted, we weight cash flows based on their time in the Modified Dietz and Linked IRR, but this wasn't the source of the expression. Time-weighting simply means that we are eliminating or reducing the impact of cash flows. That's it! No time weighting.

1. On page 41 of your article, “Is the Modified Dietz Formula Money-Weighted or Time-Weighted”, you wrote “I do not know what the original derivation of the term time weighting is. It is quite confusing, I must admit.”

Would you say that you've now found that the original derivation of the term comes from the BAI 1968 standards? That would be quite interesting.

2. Michael, thanks for your post. This (the BAI Standards) is the first source I have found for it, so I am concluding that THIS is the original source. Dietz didn't use the term in his thesis or early papers so I am concluding that it's the source; if I find something earlier, I will retract this comment.

3. Stephen Campisi, Intuitive Performance SolutionsJuly 16, 2010 at 8:47 AM

Who would think that the origin of the term "time weighted return" would become one of the mysteries of the ages? I believe that the use of the term is mathematical in its origin. The TWR is a geometric average, so that it indicates the average rate of compound growth of a single amount invested at the beginning of a long period of individual shorter time periods. These individual time periods differ in both their returns and also in the amount of time for each. So, if we think of a series of different individual periodic returns (perhaps monthly) with each return compounded (or weighted) for its appropriate amount of time.

For example, if an asset grew at a compound rate of 15% per year for for 8 years and lost 12% per year for 2 years, then we would compound each return, weighting it by the amount of time over which each grew at its respective rate. Then we would take the average for the entire period, producing the time weighted return.

In this case the calculation would be:

[(1.15)^8 * (.88)^2]^1/10 -1 = 9.1%.

Since the individual time periods are unequal in length, each is weighted by compounding each appropriately. The average produced is the time weighted returns.

More simply, we are creating a geometric average for a single sum, so only the amount of time for each return matters. By contrast, a so-called "money weighted" return is the average return for a changing amount of capital invested, and so the returns are influenced (or "weighted") by the amounts of capital at work.

4. Interesting perspective.

5. The CIPM curriculum provides a description of the origin without providing a reference. I give the comments on my blog: http://cipmexamtipsandtricks.blogspot.com/2010/07/why-do-we-call-it-time-weighted.html

6. Thanks, John! The first reference I found was the BAI standards; if there's something prior to this I haven't seen it.

7. Very interesting background, thanks for posting!

8. You're welcome!