Square-Root-of-Time Scaling in Your Head

Interviewers love asking "if daily vol is 2%, what's the annual vol?" because it tests whether you actually understand variance versus standard deviation, not just whether you memorized a formula. The trick to doing it in your head fast is remembering that variances of independent daily returns add, but volatility (standard deviation) is the square root of variance — so volatility scales with the square root of the number of periods, not the number of periods itself.

The shortcut: to scale a daily standard deviation to $n$ days, multiply by $\sqrt{n}$. For a year of roughly 252 trading days, $\sqrt{252} \approx 15.87$, which most desks just round to 16 for mental math. So annualizing is "multiply daily vol by 16." Going the other way, dividing an annual vol by 16 gives you the rough daily number.

Worked example: daily vol is 2%. Annual vol $\approx 2\% \times 16 = 32\%$. Check going backward: an index with 20% annual vol has daily vol $\approx 20\% / 16 = 1.25\%$. For a month (about 21 trading days), $\sqrt{21} \approx 4.6$, so a 1.5% daily vol becomes roughly $1.5\% \times 4.6 \approx 6.9\%$ monthly vol — useful for sanity-checking a monthly risk number against a daily one someone just quoted you.