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A name has 32%32\% annualised volatility. What is a one-standard-deviation daily move, in per cent?

Answer with a number in %. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

Show the answer and worked solution

Answer

2%2\%

Volatility scales with the square root of time, so σdaily=σann/252\sigma_{\text{daily}} = \sigma_{\text{ann}}/\sqrt{252}. Since 252≈15.87\sqrt{252} \approx 15.87, dividing by 1616 is accurate to under one per cent and is the version to use out loud: 32/16=2%32/16 = 2\% a day. The "rule of 16" runs both ways, so a name realising 1%1\% a day is realising about 16%16\% annualised, and being able to flip between the two units instantly is what lets you compare implied against realised in your head.

Worked solution

  1. Formula
    σdaily=σann252\sigma_{\text{daily}} = \frac{\sigma_{\text{ann}}}{\sqrt{252}}
  2. Substitute
    =32%16= \frac{32\%}{16}
  3. Solve
    =2%= 2\%
  4. Answer
    2% a day2\% \text{ a day}

Takeaway: Annual volatility divided by 16 is roughly the daily move.

Answer it in practice – your answer is marked and recorded.

Reported in interviews at

Optiver, SIG (Susquehanna), IMC Trading

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