## Monday, April 5, 2010

### What does "daily attribution" mean?

We're working with a client who needs to be able to respond to RFPs that ask "do you have daily attribution?" But what exactly does this mean? Does it mean "do you calculate attribution daily" or "can you report attribution from any day to any day"?

As I mentioned in March's newsletter, when it comes to transaction-based attribution there is no reason to calculate the effects daily: monthly works fine. But what if someone wants to report attribution ending (and/or beginning) for a day other than month-end? Not a problem: you just value the portfolio as of that date and calculate the effects between that point and the prior (or ending, if it's the starting point) month end, taking  into consideration the trading that occurs in the interim.

Why should a prospect care whether or not you actually calculate the effects daily? They should be concerned with the ability to report from any date to any date accurately, and this can be achieved without calculating daily effects.

And, as I mentioned previously, this doesn't apply to holdings-based, where more frequent processing is required to ensure a better degree of accuracy.

1. David,
I agree that what clients should be concerned about is "the ability to report from any date to any date accurately." The problem is that no version of modified Dietz can do that accurately for the full range of situations that clients regularly face. Since the more advanced methods that avoid such fatal problems require that the returns be calculated using daily data, I do not believe the approach you suggest achieves the result you desire.

2. Thanks for your comments, but I don't follow. We're talking capturing buys and sells (and perhaps corporate actions and income). Modified Dietz works fine. Daily isn't needed. Whatever you can do daily you can do monthly.

3. David,
If, for example, you mean the standard modified Dietz calculation, consider the case of an issue that is sold out in the middle of the period after it tripled in price:
RmD = (Vf – Vi + S – P)/[Vi + (P – S)/2]
= (0 – 1 + 3 – 0)/[1 + (0 – 3)/2] = -400%.
Thus, modified Dietz does not ‘work fine’ in 'capturing buys and sells' in this situation. Rather, as occurs in many cases, it completely fails, both because it gives a very negative return for a very good investment situation and because returns of less than -100% are meaningless.
A proper advanced daily return calculation that recognizes that daily trades settle after the close never has these problems. Daily is different than monthly because settlement can occur within the month.

4. David,
For one example of how modified Dietz can fails instead of working fine, consider calculating the return of a component of a portfolio over two days. On the first day its opening value is 10, part of it is sold for 30 and 20 remains. Good going.
On the second day the 10 doubles to 20. Good going again.
Now lets calculate the modified Dietz value for the returns of the first and second day and then time-link them.
( I take the modified Dietz return to be: R = (Vf + S – P –Vo)/[Vo + (P – S)/2].
I use this “divide trade-flow in the basis by two” version of modified Dietz since no information is given about the time of day of the trade and they are all probably settled after the close anyway. But analogous examples can be constructed for any version of modified Dietz or, in fact, for any trade-inclusive return model that simply follows the values of components rather than the flow of value through a period.)

R1 = (20 + 30 – 10)/(10 - 30/2) = -800%.
R2 = (20 – 10)/10 = 100%.
R12 = (1 + R1)*(1 + R2) – 1 = (1 – 800%)*(1 + 100%) -1 = -1500%.

So, for a great first day we get an absurdly negative value.
The second day alone is fine by itself, but when combined with the first day it makes things even worse.
The fact that modified Dietz can lead to absurdities in some case and the fact that it is a continuous model implies that it is almost always wrong. Further, it can be very wrong in situations where our intuitions are not good enough to spot the egregiousness of the errors. To me, this is a very dangerous foundation for an investment process that hopes to learn anything from its past experience.

Also, the reason that I believe that it is not the case that “whatever you can do daily you can do monthly” is that settlement does not scale that way.
Andre

5. David,
If, for example, you mean the standard modified Dietz calculation, consider the case of an issue that is sold out in the middle of the period after it tripled in price:
RmD = (Vf – Vi + S – P)/[Vi + (P – S)/2] = (0 – 1 + 3 – 0)/[1 + (0 – 3)/2] = -400%.
Thus, modified Dietz does not ‘work fine’ in 'capturing buys and sells' in this situation. Rather, as occurs in many cases, it completely fails, both because it gives a very negative return for a very good investment situation and because returns of less than -100% are meaningless.
A proper advanced daily return calculation that recognizes that daily trades settle after the close never has these problems. Daily is different than monthly because settlement can occur within the month but not within a day.