Returns can be shown for a day, a few days, a week, a month, a quarter, a year, etc. Risk statistics typically rely upon a series of returns. But how many and which ones?
The standard seems to be 36. This conforms well with the usual expectation that we have at least 30 observations for standard deviation to be meaningful. But 36 what? Can we use days, for example?
Well, on the surface that would seem to make some sense, yes? Why not start reporting risk after a strategy or portfolio or composite has been managed for a month or so? We can run numbers, right?
Well, yes, we can. But, we generally think daily returns as being “too noisy.” What do we mean by this? Essentially that the fluctuations are too extreme and don’t necessarily exhibit anything. We can see choppy days that smooth out a bit when we shift to months. If we were to find days acceptable, why not hours? We could measure hourly returns and track the prior 36; or, the prior 36 minute returns; or, to be REALLY extreme, the prior 36 seconds. This is all possible, but would serve no purpose other than to confuse.
I think we’d actually prefer to use quarters, but the 30 observation rule would mean we couldn’t begin reporting until we’ve been at it for 7 1/2 years; that seems a bit long. Thus, we’ve pretty much settled on months.
Could we run our risk measures using less than 30 observations? Yes, of course we could; we could, for example use just a few months. But to do so would mislead, I believe. To show someone a return for the prior quarter, for example, along with its associated standard deviation (based either on days or months) would suggest that the number has meaning, when, in reality, it doesn’t; the period just isn’t long enough (or, if days were used, as noted above, it’s too noisy). One must guard against reporting anything that could be misconstrued; we can’t mislead our clients or prospects.
What if the client insists on seeing risk measures immediately? Then, of course, do what the client wants; but also include a disclaimer regarding the shortcomings of using a short period to draw any sort of viable or valid conclusion.
GIPS(R) (Global Investment Performance Standards) now requires compliant firms to report an ex post, annualized, 36-month standard deviation. We again see the use of 36 months. Could you report for shorter periods? Again, of course you could. But, I think it’s better not to, unless you include a disclaimer; something like “we are showing you a 24-month cumulative return, and so decided to show its associated 24-month annualized standard deviation, but given that this is for a relatively short period, please don’t put a lot of emphasis on it, because the statistic doesn’t have a whole lot of value until we reach 30 months.