In asset allocation, you usually send reports to your clients where you will report the volatility of its portfolio. Assuming you only have monthly returns, you will compute volatility over a considered period of $n$ months with the classic sample volatility estimate:
$$\sigma_s=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}, \quad \bar{x}=\frac{1}{n}\sum_{i=1}^N x_i$$
The result you will get for $\sigma_s$ depends very much on the number of months $n$ you decide to take into account. Hence, I think that this measure can become pretty abstract to unsophisticated investors and they might find it pretty different from the "feeling" the have of the volatility of their portfolio, what I call the "experienced" volatility.
My question is, has there been any research aiming to find out which $n$ is the best to make sure that the measure is closest to the experienced volatility?
I believe this is very much linked to behavioral finance and it might very well depend on the risk-aversion or the sophistication of the investor.
I tried to answer my question by proposing the following:
I assume that investors will be biased by the most recent events in the market; if they have been with you 10 years, they will remember 2008-2012 and would have forgot the quiet and lucrative early years. Hence, I took $n=36$, 3 years, as I thought is was taking a recent enough sample, yet had enough data ($n>30$, intuitively... it might be arguable) to measure a properly the estimate $\sigma_s$.
Does this make sense?