Assume stock is 50 dollars. From what I understand, an annualized vol of 20% means there is a ~68% chance the stock will be between 40 and 60 a year from now; a ~95% chance it will be between 30 and 70; and so on.

What if volatility is 100% or higher? Would that mean ~68% of the time it will be between 0 and 100 a year from now? A ~95% chance between 0 and 150? Am I interpreting this correctly? Can someone explain how this makes sense since stocks cannot go below zero?

  • 2
    $\begingroup$ For stock, vol is commonly defined as the standard deviation of a lognormal random variable. $\endgroup$ Oct 17 at 4:16
  • 3
    $\begingroup$ As Kermitfrog said, vol of 20% means the log of stock price will change up or down by 0.2. As far as the price itself, it will be multiplied or divided by $e^{0.2}=1.2214$. Vol of 120% means multiply or divide price by $e^{1.2}=3.3201$. So starting at 100 price could go to 332 or 30.12 in a year. Unusual but not impossible. HTH. $\endgroup$
    – noob2
    Oct 17 at 6:00
  • $\begingroup$ This doesn't line up with what Natenberg says in his book. Please see page 10 of the following lecture notes: assets.website-files.com/5b2969683fdf7e534e99ded7/… $\endgroup$ Oct 17 at 14:41

Shelly Natenberg has a typo. He means lognormal


Not the answer you're looking for? Browse other questions tagged or ask your own question.