Let’s say you want to compute the annualized monthly volatility of your portfolio. There are two ways to go about doing  it :

  1. Compute the monthly volatility of each month for your portfolio, average it and multiply by sqrt(12)
  2. Create a moving window to capture monthly volatility, average it, and then multiply by sqrt(12). In this case, there will many more data points that give you an estimate of monthly volatility as compared to the first case.

In the second method, one can see that overlapping intervals are used to compute volatility. This means that volatility estimate is not independent across time slots and this dependency obviously smoothens the volatility. Intuitively one knows that the volatility computed from case 2 < volatility computed from case 1.  By how much does the volatility reduce by taking overlapping returns ? The answer is not that obvious. This paper by Ulrich Muller says that the volatility of overlapping returns is approximately 2/3rd of the volatility of non overlapping returns in the case of Gaussian iid.

So, if your portfolio annualized volatility is 24%, you can fudge it Smile by using overlapping time windows and show that your portfolio volatility is only ~ 2/3 * 24%  = 16%. Massive reduction in your portfolio volatility + improvement in your Sharpe ratio by merely choosing a moving time window!.