Thursday, February 11, 2010

To how many decimal places?

I'm looking at a client report (fortunately not one that they would give to a client) that shows, for example, the return 41.29959483 percent. Such precision! To eight decimal places! I'm impressed. Well, actually I'm not.

Actually, this is a waste of ink, yes? One can't confuse precision with accuracy. What possible value would anyone have in a number to this level of detail? As if it's actually right? The report is produced from a software system: why would a vendor have this information default to such a value? Seems odd to me.

I was on a flight recently and the pilot announced that the flight would last 2 hours, 52 minutes, and 40 seconds. Actually, he said it would last "approximately" that long. Approximately? To paraphrase Dorothy from Jerry Maguire, you had me at 2 hours, 52 minutes; and, you could have rounded to 50 minutes (I won't be running my stopwatch to validate your accuracy). You could have probably just said "approximately three hours." But no doubt there are some folks that like to hear flight times to such precision and perhaps even believe they're accurate.

Even returns with three decimal places seem a bit ridiculous, except where excess returns (and returns in general) are so small that we need this additional precision or show zeroes.

Don't confuse precision with accuracy: they're two different things. We should strive for accuracy but recognize that even that isn't always as achievable as we'd like. There's a lot of noise out there that makes 8-decimal place returns a joke. 


  1. Bravo, Dave!

    Such a display is evidence of a number of things not least of which is colossal laziness both with respect to the report designer and the IT folks responsible for formatting the number.

    Those who truly understand the fragility of the underpinnings of today's diverse set of calculations (Modified BAI, Dietz, Daily valuation with, perhaps, varying assignments of flow timing) shudder at the attempt to put lipstick, actually a day's worth of spa work, on this pig.

    Until GIPS/CFA and even FINRA/SEC gets its act in gear and mandates a consistent calculation methodology with full disclosure, many us are reduced to howling at the moon.

  2. Excellent points and a great way to describe what's being attempted, whether intentional or otherwise.

  3. Sorry, I don't think this is because of laziness. Decimal places are saved probably trying to meet the need of the requesters. Yes, we certainly need accuracy in our numbers. However, I would argue that consistency should be focus first and then accuracy.

    If you're never involve in generating a fixed income return, you'd probably would not have experience the laborious tasks of combing the data, finding the problem, and then fixing the return. For example, what if someone claims a money market return is incorrect? Would you look at 2 or 3 decimal places (maybe event 4) for a quick refernce?

    However, I do agree some level group or entity needs to make a statement on this matter. Instead of 8, I think 4 demcimal place is all you need.

  4. Thanks for your note, though I doubt if anyone would ever ask for 8 decimal places; yes, in the world if fixed income 3 or 4 may make sense, but eight? Doubtful.

  5. I heard people requesting for 8 digits and was related to creating a super duper financial models. The justification: they want to be as accurate as possible.

    In addition, the above is another example where you SHOULD NOT be using daily time weighted to calculate a monthly portfolio return. Looking at the daily small numbers could drive a person insane. Using time weighted or modified dietz is probably a better chose then daily time weighted. Unless there is a major shift / inverse movement on the shorter end of the curve, external cash flows (if exists within the period) would probably have small impact to a short duration product when using other return methods.


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