# How to assess stock price movement from implied volatility?

Assume that: - The underlying is at 100 - The implied volatility of ATM call/put is 30%.

Then, is it correct that expected 1-standard-deviation move over the next month is calculated as:

$$100 * 30\% \cdot \sqrt\frac{30}{252} = 10.35 ~ \text{points}$$

I am confused as to whether I should be taking the square root or not.

• It's the last time I let you post question with bad formatting. I already asked you nicely to pay attention in your last question. Next one like this will result in a ban. – SRKX Mar 5 '15 at 7:11
• @Victor123 The calculation is correct. For me, the problem with this calculation is that the volatility is a point on the volatility surface and the result not only depends on the moneyness (which you specified) but also on the term of the option. For a stock, you would typically give ONE volatility number OR concentrate on the investment horizon (here, you should probably take an appropriate value for "time to maturity" on the volatility surface). Maybe its better to calculate the stock's volatility directly if possible. – vanguard2k Mar 5 '15 at 11:04

## 2 Answers

I think you're doing some self study and it looks like you're on a good path. You have this right. It's the square root of time. I would just note as far as your example goes that there are not 30 days in the month of a 252 (trading day approximation) day year. It's closer to 20.

And vanguard2k points out in a comment that you need to consider implied vol from multiple expiries as much as scaling with the square root of time. In other words, the IV (that's implied vol) for the one month expiry and the 3 month expiry need not by related by the square root of 3. Those expiries' prices are independent market phenomena. The square root of time is more like how you can interpolate for points that don't have market prices or get some more information to substitute for reliance on prices that may be stale.

Yes, the answer is correct. Volatility scales with the square root of time, so always take square root. A simple trick to remember this, is to calculate the scaling factor as if volatility were linear (30/252) and then take the square root.

• I'm not sure I understand the "trick". One important thing though: the answer is only correct if the expected return of the stock is $\mu=0$, other wise he needs to add $\mu$ to +/- his result. – SRKX Mar 5 '15 at 7:25
• One would need $\mu$ but an option does not tell you anyting about the drift as it is assume to be the risk free rate (or you look at the implied forward) ... – Richard Mar 5 '15 at 8:04
• @Richard yeah I mean he has to estimate $\mu$ historically or get it somewhere obviously... – SRKX Mar 5 '15 at 8:41