# Volatility and resampling

Some funds publish a new NAV value once a day. Theoretically a fund could smooth its returns by posting smaller gains and smaller losses. This practice is both dodgy and forbidden.

However, this may pop up in a computation of the annualized volatility. I could use daily data, weekly data and monthly data

def volatility(nav):
# given daily data, compute the annualized volatility
return 100*np.sqrt(260)*nav.pct_change().std()

def volatility_week(nav):
return 100*np.sqrt(52)*nav.resample("W").last().pct_change().std()

def volatility_month(nav):
return 100*np.sqrt(12)*nav.resample("M").last().pct_change().std()


Obviously it's unlikely that all those volatility estimates "agree". However, how much deviation shall we accept.

Here're some examples. I tested like 10 funds. 3 funds flag up:

Daily;Weekly;Monthly

4.57;6.12;6.73

5.44;7.61;9.61

3.91;4.54;6.07

What's a good test for this?

Obviously smoothing the NAV will underestimate the annualized volatility if measured using daily data.

Kind regards Thomas

Your examples, where daily vol < weekly vol < monthly vol would imply (in this case, with the magnitude of the difference, actually a quite strongly) positive autocorrelation for daily returns.

One way to test this would be to estimate the autoregression of the daily fund NAVs and compare the results to the autocorrelation of the daily returns of the corresponding market index. If a smoothing effect is to be found, there can of course be some natural explanations (ones not implying any misconduct on part of the fund manager) to it.

For example, if the funds holdings are not very liquid, the prices used to calculate NAV could be stale, with the price changes "belonging" to previous trading day getting attributed to the next day (if there are no completed trades in the last few trading hours). I imagine this could be the case especially when dealing with corporate bond funds (which, from your posted volatility levels could be the case in this particular instance).

Edit: I calculated the daily/weekly/monthly annualized vol for the iBoxx USD Liquid High Yield Index from 2010 onwards, and got the following results: 0.047, 0.062, 0.069. The autocorrelation for the daily returns of the index measured at 0.39, so actually, at least for high yield bonds, it seems natural for the annualized vol measured from a higher frequency to be lower than the one measured from lower frequency returns.