# Is this the right formula to use implied volatility to gauge probability of a stock being within a certain range?

I read online somewhere, and I can't find it now, that to find the probability of a stock hitting a certain price within a certain time frame, we can use Implied Volatility:

``````X = StockPrice * IV * SQRT(DaysTillExpire / 365)
``````

`X` would then be 1 standard deviation (or a +/- 34% probability)

So first, is this accurate and second, how does this work?

• I'm voting to close this question as off-topic because it belongs on quant.stackexchange.com Commented Apr 21, 2017 at 14:15
• To give a hint, though, recognize that implied vol is an annualized standard deviation of returns, and look up formulas for z-scores. Commented Apr 21, 2017 at 14:16
• @DStanley it would likely be perceived as being to basic for the quant page so I htink it actually probably does belong here. Commented Apr 21, 2017 at 14:53
• @MD-Tech I disagree, but in any case it's already been migrated and marked as a duplicate. Commented Apr 21, 2017 at 15:23
• I'm voting to leave this question open. It is about investing in the stock market. Just because it might be on topic on a different site does not necessarily automatically make it off-topic here. See this meta question. Commented Apr 21, 2017 at 15:41

To get the probability of hitting a target price you need a little more math and an assumption about the expected return of your stock. First let's examine the parts of this expression.

• IV is the implied volatility of the option. That means it's the volatility of the underlying that is associated with the observed option price. As a practical matter, volatility is the standard deviation of returns, expressed in annualized terms. So if the monthly standard deviation is Y, then Y*SQRT(12) is the volatility.

• From the above you can see that IV*SQRT(DaysToExpire/356) de-annualizes the volatility to get back to a standard deviation. So you get an estimate of the expected standard deviation of the return between now and expiration.

• If you multiply this by the stock price, then you get what you have called X, which is the standard deviation of the dollars gained or lost between now and expiration. Denote the price change by A (so that the standard deviation of A is X).

Note that we seek the expression for the probability of hitting a target level, Q, so mathematically we want

1 - Pr( A < Q - StockPrice)

We do 1 minus the probability of being below this threshold because cumulative distribution functions always find the probability of being BELOW a threshold, not above.

If you are using excel and assuming a mean of zero for returns, the probability of hitting or exceeding Q at expiration, then, is

``````1 - NORM.DIST(Q, StockPrice, X, TRUE)
``````