## Thursday, December 1, 2011

### How to implement transaction-based attribution

I got an email from someone today asking how to calculate transaction-based attribution. I addressed this during our recent Attribution Week, but will touch on it briefly here, and in greater detail in this month's newsletter.

Recall that attribution relies on returns and weights.

The Weights

With a holdings-based appraoch we use the weight at the start of the period. For example, if the portfolio's initial value is 100,000, and Technology has 10,000 as its starting value, then its weight is 10% (10,000 / 100,000).

To have a transaction-based approach, we need to adjust the weight for any buys/sells/income that occur during the month. For example, if we bought another 2,000 at the middle of the month, then we weight the transaction the same way we do with Modified Dietz [(CD-D+1)/CD] and multiply this by the value (and so, 0.5 x 2,000 = 1,000). We add this to the starting value and get a revised weight [(10,000 + 1,000)/100,000 = 11%]
We use this weight in our formula.

The Returns

With holdings-based, we can simply account for the starting values to derive our returns. With transaction-based, I suggest you use Modified Dietz, so that you capture the activity that occurs. And so for our example above, if we ended with Technology being valued at 14,000, we'd have R = (VE-VB-CF)/(VB+w*CF)=(14,000-10,000-2,000)/(10,000+0.5*2,000).
[I'll let you do the math]

That's it! Again, I'll spend a bit more time on this in the newsletter.

1. Well said. Using a money weighted return is the only way to get the required consistency between the transaction adjusted weighting and the return. You might mention that it's the contribution to return that is the essential information, whereas the weighting and the return are simply ingredients. Of course, this approach will provide correct attribution analysis and will reconcile the changes in capital with the returns. Overall, this is a straightforward, yet robust way to approach the analysis of performance. We should expect this, since it is the most appropriate way to represent the investment decision process.

That said, the question now goes to those tireless advocates of the time weighted return as the best and most accurate way to represent any and all aspects of investment performance. The question they must answer is this: "How do you reconcile time weighted returns (which require NO transactions) with the reality that transactions DO occur within the performance measurement period?" Since attribution analysis requires a representative weighting for the period, and since transactions did occur, then a beginning weighting is not appropriate; neither will it reconcile the component return contributions to the total return.

Of course, the knee jerk response we often hear is that the money weighted return does not match the time weighted return. Of course it doesn't; these returns are measuring two different things and we expect their values to differ. TWR measures the manager effect (something the manager cares about) while MWR measures the portfolio return (something the client cares about.) But here's the key: at least the MWR is internally consistent; the TWR is not (at least, if you are going to have the intellectual honesty to acknowledge when cash flows do occur.) The industry's answer to this has been to increase the frequency of performance attribution, a rather silly notion made worse by the fact that the actual transactions are never really included in the analysis. They are simply assumed to have occurred between measurement periods while never being accounted for. Rather like magic...

The clarity of your presentation should be self-evident. I suspect that as analysts think this through they will come to agree.

2. Steve, thanks for your comment. Funny about the TWRR issue: given that internal cash flows will almost always be "large" (i.e., greater than 10% of the sector's market value), revaluation would be in order, which results in true TWRR, which completely eliminates them. I've heard that "no one does this," but why not? If you TRULY believe that TWRR rules; that it should be used EVERYWHERE, then why not abide by the fundamental TWRR rule that we revalue to get the highest degree of accuracy? A bit of contradiction, I believe.

Here, Modified Dietz makes the most sense, since it approximates MWRR, and will reconcile.

We agree on this topic!

3. Dave and Steve,
I think that one has to keep in mind the distinction between external flows into the fund and flows between components of the fund, both of which can significantly occur every day. This distinction is required to obtain the correct weights and returns of the components of the fund that are needed for attribution. I do not see how the Dietz method described can do this successfully over a single multi-day period.
There are many examples that show how problematic any Dietz-like approach is for this challenging problem. It was a difficult research project that took me years to address. I believe that the proper approach is far from as simple as you suggest. And I find that this challenge ends up being a very significant problem for many performance groups.
I also do not believe that contribution to return is sufficient for attribution.
And to directly address Steve’s question, I believe that calculating the daily weights and returns for components of a fund can be thought of as a MWR approach within the day. It is just that no version of the Dietz approach is adequate to the task. Once correct daily trade-inclusive weights and returns are obtained, they can be employed in attribution and then the resulting daily attributes need to be linked in an economically meaningful way (i.e. not by smoothing) and the returns can be linked (i.e. time-weighted).
If you want to money-weight the fund return you will not be able to meaningfully connect that result to component-level weights and returns in the presence of intermediate external flows.
As to Dave’s last point: Settlement happens as the close of each day, so internal time-stamps are irrelevant. Thus, daily weight and return calculations are exactly correct. All my clients use daily weights and returns.
I repeat, Modified Dietz over a single multiple-day period, where there are both external and internal flows every day, will not work, and all Dietz approaches within a day will cause problems below the fund level.
Andre

4. Andre, thanks for sharing your thoughts. Time-weighted attribution is wrong, pure and simple. It runs totally in conflict with the recognition that time-weighting's purpose is solely to eliminate the impact of cash flows, and since the manager controls internal flows (which is at the heart of attribution analysis), its use is by definition improper. I realize that I am stating this as if the world agrees with me, and I know that it doesn't. More work is needed on the money-weighted front, to demonstrate how it can be done in a superior way to time-weighting.